* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download final report - Cordis
Quantum chromodynamics wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Supersymmetry wikipedia , lookup
Jack Sarfatti wikipedia , lookup
History of subatomic physics wikipedia , lookup
History of optics wikipedia , lookup
Field (physics) wikipedia , lookup
Electromagnetism wikipedia , lookup
Photon polarization wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Time in physics wikipedia , lookup
Probability amplitude wikipedia , lookup
Renormalization wikipedia , lookup
Path integral formulation wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Fundamental interaction wikipedia , lookup
Hydrogen atom wikipedia , lookup
Quantum field theory wikipedia , lookup
Quantum tunnelling wikipedia , lookup
Quantum mechanics wikipedia , lookup
Bell's theorem wikipedia , lookup
Relational approach to quantum physics wikipedia , lookup
Quantum gravity wikipedia , lookup
Quantum entanglement wikipedia , lookup
Condensed matter physics wikipedia , lookup
Quantum potential wikipedia , lookup
EPR paradox wikipedia , lookup
Quantum vacuum thruster wikipedia , lookup
History of quantum field theory wikipedia , lookup
Quantum state wikipedia , lookup
Canonical quantization wikipedia , lookup
Quantum chaos wikipedia , lookup
PROJECT FINAL REPORT Grant Agreement number: 233859 Project acronym: QUEVADIS Project title: Quantum Engineering via Dissipation Funding Scheme: Period covered: from 1/6/2009 to 30/9/2012 Name of the scientific representative of the project's co-ordinator1, Title and Organisation: Prof. Frank Verstraete Faculty of Physics University of Vienna Tel: +43 1 4277 51219, Mobile: +43 664 60277 51219 E-mail: [email protected] Project website address: 1 www.quevadis.at Usually the contact person of the coordinator as specified in Art. 8.1. of the Grant Agreement. 4.1 Final publishable summary report This section must be of suitable quality to enable direct publication by the Commission and should preferably not exceed 40 pages. This report should address a wide audience, including the general public. The publishable summary has to include 5 distinct parts described below: An executive summary (not exceeding 1 page). A summary description of project context and objectives (not exceeding 4 pages). A description of the main S&T results/foregrounds (not exceeding 25 pages), The potential impact (including the socio-economic impact and the wider societal implications of the project so far) and the main dissemination activities and exploitation of results (not exceeding 10 pages). The address of the project public website, if applicable as well as relevant contact details. Furthermore, project logo, diagrams or photographs illustrating and promoting the work of the project (including videos, etc…), as well as the list of all beneficiaries with the corresponding contact names can be submitted without any restriction. 4.1.1 Executive summary. The project QUEVADIS envisioned the study of dissipative processes as means of performing quantum information theoretic tasks. This point of view was certainly a paradigm shift, as dissipation had traditionally been perceived as the main enemy of quantum information. Since the start of this project, this line of idea has proven to open up many novel research opportunities, both experimental and theoretical. A lot of groups around the world have started working on dissipation-based ideas for quantum information processing. The QUEVADIS (Quantum Engineering via Dissipation) project consisted of 5 work packages; all 16 milestones and deliverables have been delivered. Furthermore, we are very happy that the project lead to many novel interesting research project that were not anticipated in the proposal, as should be for any theoretical project. As a consequence, a large number of research papers has been published in leading physics journals. In particular, QUEVADIS lead to the publication of 1 paper in Nature, 2 in Nature Physics, and 18 in Physical Review Letters. Highlights of the project include 1. The original paper identifying the possibility of using dissipation for quantum information theoretic tasks (Nat. Phys. 5, 633, 2009) 2. The uncovering of a relationship between quantum field theories and the description of quantum Markov chains (Phys. Rev. Lett 103, 080501, 2009) 3. A collaboration with experimentalists allowing for a quantum memory stabilized by engineered dissipation (Phys. Rev. Lett 107, 080503, 2011) 4. Setting up the mathematical framework for describing convergence rates of quantum Markov chains (J. Math. Phys. 51, 122201, 2010) 5. The construction of a quantum algorithm for simulating thermal states of generic quantum many-body Hamiltonians, as a quantum generalization of the ubiquitous Metropolis algorithm (Nature 471, 87, 2011) 6. The discovery of dissipative quantum phase transitions in central spin systems (Phys. Rev. A 86, 012116, 2012) 7. The construction of a dissipation based quantum algorithm for contracting tensor networks (Phys. Rev. Lett. 108, 110502, 2012) 4.1.2 Description of project context and objectives The project fits within the very active worldwide effort of trying to harness the power of quantum mechanics for information theoretic tasks. A central premise of this project has been the fact that dissipation can be a useful resource for information theoretic tasks. Within this project, we have on the one hand been able to show that novel quantum algorithms can be constructed that exploit dissipation, and on the other hand that engineering dissipation can lead to long-lived quantum memories. The project was divided into 5 workpackages; each was concerned with different aspects of dissipation: 1. Work package 1 aimed at constructing a mathematical theory of fixed points and convergence rates of quantum Markov chains. The milestones and deliverables were a. b. c. d. Criteria for emergence of symmetries, coherence and other fixed point properties Criteria which separate quantum from classical evolutions Quantum counterparts of results for convergence of Markov chains Criteria for the reachability of dissipative evolutions under coherent control. All were delivered. It turns out that the study of quantum Markov chains form a very rich mathematical subject, with connections to many different branches in mathematics and statistics. 2. Work package 2 had as topic the study of dissipative quantum engineering protocols. The milestones and deliverables were a. Estimate the speed of convergence for creating MPS, PEPS and/or quasi-free states b. Construct quantum Metropolis type algorithm for simulating thermal quantum states c. Quantify the computational complexity of finding ground states (in particular of quantum spin glasses) by means of the gap of the corresponding Liouvillian Also here, all were delivered. A real breakthrough has been the construction of a quantum algorithm for simulating generic quantum many-body systems, i.e. a quantum version of the Metropolis algorithm. 3. The topic of research for work package 3 was dissipative quantum computing. This opened up the possibility of doing quantum computing or building quantum memories with a scheme that violates most of the DiVincenzo criteria for quantum computation. The milestones and deliverables were a. Construction of a universal dissipative gate set b. Study of the robustness of code subspaces when stabilized by noisy quantum dissipative processes c. New quantum algorithms All deliverables were delivered, and we obtained a much better understanding of dissipatively engineered quantum memories, and constructed novel quantum algorithms for contracting tensor networks. 4. The central question addressed in workpackage 4 is to identify novel effects or phenomena that arise due to dissipation. For this, we have identified novel non-equilibrium phase transitions, and developed a whole range of matrix product / tensor network methods for simulating strongly correlated quantum systems. The milestones and deliverables were a. Characterize the phase diagram of non-equilibrium quantum models b. Develop numerical renormalization group methods for simulating quantum dissipative processes c. Develop a real-space renormalization group formalism for non-equilibrium quantum dissipative processes All deliverables were delivered. 5. Workpackage 5 was of crucial importance as it provided the link between the theoretical work and experiments. A highlight was certainly the demonstration of dissipatively driven entanglement of two macroscopic ensembles. The milestones and deliverables were a. Develop procedures for simulating quantum dissipative processes in ion traps b. Develop procedures for simulating quantum dissipative processes in neutral atoms c. Develop procedures for simulating quantum dissipative processes in atomic ensembles All deliverables were delivered. 4.1.3 Description of the main S&T results/foregrounds All the main results of the project have been published in high-quality physics journals. In this section, we will give a description of a representative selection of the published papers, arranged according to the different topics. Some papers are included several times as they were crucial for more than 1 WP; for those, the abstract is included only once. 1. WP1: Mathematical theory of fixed points and convergence rates a. Criteria for emergence of symmetries, coherence and other fixed point properties 1. Characterizing symmetries in Projected Entangled Pair States Authors: D. Pérez-García, M. Sanz, C.E. González-Guillén, M.M. Wolf, J.I. Cirac Journal: New J. Phys. 12, 025010 (2010) [arXiv:0908.1674]. We show that two different tensors defining the same translational invariant injective projected entangled pair state (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any local or spatial symmetry in the state. As an application of these results we prove that a SU(2) invariant PEPS with half-integer spin cannot be injective, which can be seen as a Lieb–Shultz–Mattis theorem in this context. We also give the natural generalization for U(1) symmetry in the spirit of Oshikawa–Yamanaka–Affleck, and show that a PEPS with Wilson loops cannot be injective. 2. PEPS as ground states: degeneracy and topology Authors: N. Schuch, J.I. Cirac, D. Pérez-García Journal: Annals of Physics 325, 2153 (2010) [arXiv:1001.3807]. We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground states of local Hamiltonians with finitely degenerate ground states and to characterize the ground state subspace. Subsequently, we apply our framework to show how the topological properties of these ground states can be explained solely from the symmetry: We prove that ground states are locally indistinguishable and can be transformed into each other by acting on a restricted region, we explain the origin of the topological entropy, and we discuss how to renormalize these states based on their symmetries. Finally, we show how the anyonic character of excitations can be understood as a consequence of the underlying symmetries. 3. The inverse eigenvalue problem for quantum channels Authors: Michael M. Wolf, David Perez-Garcia Journal: J. Math. Phys. (in press, 2011) [arXiv:1005.4545]. Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the non-zero part of the spectrum can essentially be given in terms of its classical counterpart - the non-zero spectrum of a stochastic matrix. A detailed comparison between the classical and quantum case is given. We discuss applications of our findings in the analysis of time-series and correlation functions and provide a general characterization of the peripheral spectrum, i.e., the set of eigenvalues of modulus one. We show that while the peripheral eigen-system has the same structure for all Schwarz maps, the constraints imposed on the rest of the spectrum change immediately if one departs from complete positivity. 4. Entanglement can completely defeat quantum noise Authors: Jianxin Chen, Toby S. Cubitt, Aram W. Harrow, Graeme Smith Phys. Rev. Lett. 107, 250504 (2011) Abstract: We describe two quantum channels that individually cannot send any information, even classical, without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero capacity channels. But our result is stronger still, as it even allows zeroerror quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver. b. Criteria which separate quantum from classical evolutions 1. M. M. Wolf, D. Pérez-García, Assessing Quantum Dimensionality from Observable Dynamics, Phys. Rev. Lett. 102, 190504 (2009). Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a model-independent way. We discuss the dependence on the number of conserved quantities, the relation to ergodicity and prove a converse showing that a Hilbert space of dimension D+2 is sufficient to describe every bounded sequence of measurements originating from any Ddimensional linear equations of motion. This is in sharp contrast to classical stochastic processes which are subject to more severe restrictions: a simple spectral analysis shows that the gap between the required dimensionality of a quantum and a classical description of an observed evolution can be arbitrary large. 2. Inverting the central limit theorem Miguel Navascues, David Perez-Garcia, Ignacio Villanueva arXiv:1110.2394v2 The central limit theorem states that the sum of N independently distributed n-tuples of real variables (subject to appropriate normalization) tends to a multivariate gaussian distribution for large N. Here we propose to invert this argument: given a set of n correlated gaussian variables, we try to infer information about the spectrum of the discrete microscopic probability distributions whose convolution generated such a macroscopic behaviour. The techniques developed along the article are applied to prove that the classical description of certain macroscopic optical experiments is infinitely more complex than the quantum one. 3. Operator Space Theory: A Natural Framework for Bell Inequalities Journal: Phys. Rev. Lett. 104, 170405 (2010) Authors: M. Junge, C. Palazuelos, D. Perez-Garcia, I. Villanueva, M.M. Wolf Abstract: In this Letter we show that the field of operator space theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular, regarding the scaling of their violation within quantum mechanics. We illustrate the power of this connection by showing that bipartite quantum states with local, Hilbert space dimension n can violate a Bell inequality by a factor of order √n/(log2n) when observables with n possible outcomes are used. Applications to resistance to noise, Hilbert space dimension estimates, and communication complexity are given. c. Quantum counterparts of results for convergence of Markov chains 1. The semigroup structure of Gaussian channels Journal: Quantum Inf. Comp. 10: 0619-0635 (2010) Author: T. Heinosaari, A.S. Holevo, M.M. Wolf Abstract: We investigate the semigroup structure of bosonic Gaussian quantum channels. Particular focus lies on the sets of channels which are divisible, idempotent or Markovian (in the sense of either belonging to one-parameter semigroups or being infinitesimal divisible). We show that the non-compactness of the set of Gaussian channels allows for remarkable differences when comparing the semigroup structure with that of finite dimensional quantum channels. For instance, every irreversible Gaussian channel is shown to be divisible in spite of the existence of Gaussian channels which are not infinitesimal divisible. A simpler and known consequence of non-compactness is the lack of generators for certain reversible channels. Along the way we provide new representations for classes of Gaussian channels: as matrix semigroup, complex valued positive matrices or in terms of a simple form describing almost all one-parameter semigroups. 2. The $\chi^2$ - divergence and Mixing times of quantum Markov processes Authors: K. Temme, M. J. Kastoryano, M. B. Ruskai, M. M. Wolf, F. Verstraete Journal: J. Math. Phys. 51, 122201 (2010) [arXiv:1005.2358]. We introduce quantum versions of the $\chi^2$-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approach similar to the one presented in the literature for classical Markov chains is taken to bound the trace-distance from the steady state of a quantum processes. A strict spectral bound to the convergence rate can be given for time-discrete as well as for time-continuous quantum Markov processes. Furthermore, the contractive behaviour of the $\chi^2$-divergence under the action of a completely positive map is investigated and contrasted to the contraction of the trace norm. In this context we analyse different versions of quantum detailed balance and, finally, give a geometric conductance bound to the convergence rate for unital quantum Markov processes. 3. Hilbert's projective metric in quantum information theory Authors: David Reeb, Michael J. Kastoryano, Michael M. Wolf Journal: J. Math. Phys. (in press) [arXiv:1102.5170]. We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical distinguishability of quantum states and on the decrease of entanglement under LOCC protocols or other cone-preserving operations. The results are formulated in terms of general cones and base norms and lead to contractivity bounds for quantum channels, for instance improving Ruskai's trace-norm contraction inequality. A new duality between distinguishability measures and base norms is provided. For two given pairs of quantum states we show that the contraction of Hilbert's projective metric is necessary and sufficient for the existence of a probabilistic quantum operation that maps one pair onto the other. Inequalities between Hilbert's projective metric and the Chernoff bound, the fidelity and various norms are proven. 4. Quantum logarithmic Sobolev inequalities and rapid mixing Michael J. Kastoryano, Kristan Temme arXiv:1207.3261 Abstract: A family of logarithmic Sobolev inequalities on finite dimensional quantum state spaces is introduced. These inequalities are shown to lead to very tight bounds on the convergence time of quantum dynamical semigroups to their fixed point. Convergence bounds on finite dimensional state spaces are particularly relevant for the field of quantum information theory. The framework of non-commutative Lpspaces is reviewed and the relationship between quantum logarithmic Sobolev inequalities and the hypercontractivity of quantum semigroups is discussed. This relationship is central for the derivation of lower bounds for the Log-Sobolev constants. Essential results for the family of inequalities are proved, and a bound of the generalized Log-Sobolev constant in terms of the spectral gap of the generator of the semigroup is shown. As a main example, illustrating the power of our framework, improved bounds on the mixing time of quantum expanders are obtained. 5. A Cutoff Phenomenon for Quantum Markov Chains Michael J. Kastoryano, David Reeb, Michael M. Wolf J. Phys. A: Math. Theor. 45 (2012) 075307 We derive upper and lower bounds on the convergence behavior of certain classes of one-parameter quantum dynamical semigroups. The classes we consider consist of tensor product channels and of channels with commuting Liouvillians. We introduce the notion of Cutoff Phenomenon in the setting of quantum information theory, and show how it exemplifies the fact that the convergence of (quantum) stochastic processes is not solely governed by the spectral gap of the transition map. We apply the new methods to show that graph states can be prepared efficiently, albeit not in constant time, by dissipation, and give the exact scaling behaviour of the time to stationarity. 6. Perturbation Bounds for Quantum Markov Processes and their Fixed Points Authors: Oleg Szehr, Michael M. Wolf Journal: arXiv:1210.1171 We investigate the stability of quantum Markov processes with respect to perturbations of their transition maps. In the first part, we introduce a condition number that measures the sensitivity of fixed points of a quantum channel to perturbations. We establish upper and lower bounds on this condition number in terms of subdominant eigenvalues of the transition map. In the second part, we consider quantum Markov processes that converge to a unique stationary state and we analyze the stability of the evolution at finite times. In this way we obtain a linear relation between the mixing time of a quantum Markov process and the sensitivity of its fixed point with respect to perturbations of the transition map. d. Criteria for the reachability of dissipative evolutions under coherent control. 1. Extending quantum operations Authors: Teiko Heinosaari, Maria A. Jivulescu, David Reeb, Michael M. Wolf Journal: arXiv:1205.0641 Abstract: For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on quantum states are trace-preserving completely positive maps, but we also consider variants of these requirements. We generalize the definition of complete positivity to linear maps defined on arbitrary subspaces, then formulate this notion as a semidefinite program, and relate it by duality to approximative extensions of this map. This gives a characterization of the maps which can be approximated arbitrarily well as the restriction of a map that is completely positive on the whole algebra, also yielding Arveson's extension theorem. For quantum channel extensions and extensions by probabilistic operations we obtain semidefinite characterizations, and we also elucidate the special case of Abelian in- or outputs. Finally, revisiting a theorem by Alberti and Uhlmann, we provide simpler and more widely applicable conditions for certain extension problems on qubits, and by using a semidefinite programming formulation we exhibit counterexamples to seemingly reasonable but false generalizations of the Alberti-Uhlmann theorem. 2. Are problems in Quantum Information Theory (un)decidable? Authors: Michael M. Wolf, Toby S. Cubitt, David Perez-Garcia arXiv:1111.5425v1 This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of entanglement theory and quantum channels turn out to be decidable via quantifier elimination as long as they admit a compact formulation without quantification over integers. For many asymptotically defined properties which have to hold for all or for one integer N, however, effective procedures seem to be difficult if not impossible to find. We review some of the main tools for (dis)proving decidability and apply them to problems in quantum information theory. We find that questions like "can we overcome fidelity 1/2 w.r.t. a two-qubit singlet state?" easily become undecidable. A closer look at such questions might rule out some of the "single-letter" formulas sought in quantum information theory. 2. WP2: Dissipative quantum state engineering a. Estimate the speed of convergence for creating MPS, PEPS and/or quasi-free states 1. Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation Authors: Frank Verstraete, Michael M. Wolf, J. Ignacio Cirac Journal: Nature Physics 5, 633 - 636 (2009) We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We show that such a model allows for efficient universal quantum computation with the result of the computation encoded in the steady state. Due to the purely dissipative nature of the process, this way of doing quantum computation exhibits some inherent robustness and defies some of the DiVincenzo criteria for quantum computation. We show that there is a natural class of problems that can be solved with such a model - the preparation of ground states of frustration free quantum Hamiltonians. This allows for robust and efficient creation of exotic states that exhibit features like topological quantum order and the creation of PEPS and it proves the existence of novel dissipative phase transitions. In particular the latter can in principle be verified experimentally with present day technology such as with optical lattices. 2. Martin Schwarz, Kristan Temme, Frank Verstraete, Contracting tensor networks and preparing PEPS on a quantum computer, Phys. Rev. Lett. 108, 110502 (2012) We present a quantum algorithm to prepare injective PEPS on a quantum computer, a problem raised by Verstraete, Wolf, Perez-Garcia, and Cirac [PRL 96, 220601 (2006)]. To be efficient, our algorithm requires well-conditioned PEPS projectors and, essentially, an inverse-polynomial spectral gap of the PEPS' parent Hamiltonian. Based on this algorithm, we also present a heuristic method for approximating the contraction value of general tensor networks on a quantum computer. b. Construct quantum Metropolis type algorithm for simulating thermal quantum states 1. Quantum Metropolis Sampling Authors: K. Temme, T.J. Osborne, K.G. Vollbrecht, D. Poulin, F. Verstraete Journal: Nature 471:87 (2011) [arXiv:0911.3635]. The original motivation to build a quantum computer came from Feynman, who imagined a machine capable of simulating generic quantum mechanical systems—a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman’s challenge was met by Lloyd, who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today’s technology. c. Quantify the computational complexity of finding ground states (in particular of quantum spin glasses) by means of the gap of the corresponding Liouvillian 1. Computational complexity of interacting electrons and fundamental limitations of density functional theory Authors: Norbert Schuch and Frank Verstraete Journal: Nature Physics 5, 732 - 735 (2009) Abstract: One of the central problems in quantum mechanics is to determine the ground-state properties of a system of electrons interacting through the Coulomb potential. Since its introduction1, 2, density functional theory has become the most widely used and successful method for simulating systems of interacting electrons. Here, we show that the field of computational complexity imposes fundamental limitations on density functional theory. In particular, if the associated ‘universal functional’ could be found efficiently, this would imply that any problem in the computational complexity class Quantum Merlin Arthur could be solved efficiently. Quantum Merlin Arthur is the quantum version of the class NP and thus any problem in NP could be solved in polynomial time. This is considered highly unlikely. Our result follows from the fact that finding the ground-state energy of the Hubbard model in an external magnetic field is a hard problem even for a quantum computer, but, given the universal functional, it can be computed efficiently using density functional theory. This work illustrates how the field of quantum computing could be useful even if quantum computers were never built. 2. A constructive commutative quantum Lovasz Local Lemma, and beyond Authors: Toby S. Cubitt, Martin Schwarz arXiv:1112.1413 (QIP2012) Abstract: The recently proven Quantum Lovasz Local Lemma generalises the wellknown Lovasz Local Lemma. It states that, if a collection of subspace constraints are "weakly dependent", there necessarily exists a state satisfying all constraints. It implies e.g. that certain instances of the kQSAT quantum satisfiability problem are necessarily satisfiable, or that many-body systems with "not too many" interactions are always frustration-free. However, the QLLL only asserts existence; it says nothing about how to find the state. Inspired by Moser's breakthrough classical results, we present a constructive version of the QLLL in the setting of commuting constraints, proving that a simple quantum algorithm converges efficiently to the required state. In fact, we provide two different proofs, one using a novel quantum coupling argument, the other a more explicit combinatorial analysis. Both proofs are independent of the QLLL. So these results also provide independent, constructive proofs of the commutative QLLL itself, but strengthen it significantly by giving an efficient algorithm for finding the state whose existence is asserted by the QLLL. We give an application of the constructive commutative QLLL to convergence of CP maps. We also extend these results to the non-commutative setting. However, our proof of the general constructive QLLL relies on a conjecture which we are only able to prove in special cases. 3. WP3: Dissipative quantum computing a. Construction of a universal dissipative gate set 1. Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation Authors: Frank Verstraete, Michael M. Wolf, J. Ignacio Cirac Journal: Nature Physics 5, 633 - 636 (2009) 2. Precisely timing dissipative quantum information processing M. J. Kastoryano, M. M. Wolf, J. Eisert Journal: arXiv:1205.0985 Abstract: Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by weak (Markovian) systemenvironment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource, and consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that large classes of initial states are rapidly driven to desirable steady states. One apparent drawback of this scheme is that it does not seem to allow for precisely timed sequential operations, conditional measurements or error correction. In this work, we provide a solution to these challenges, by introducing some basic dissipative gadgets which allow us to precisely initiate, trigger and time dissipative operations, while keeping the system Liouvillian time independent. These gadgets open up novel perspectives for thinking of timed, protected dissipative quantum information processing. As an example, we sketch how universal computation can be performed with geometrically local interactions. We also suggest that instances of dissipative error correction are possible, sketching models of topological error correction without any explicit time dependent control or measurement feedback, in fewer than 4 dimensions. b. Study of the robustness of code subspaces when stabilized by noisy quantum dissipative processes 1. Quantum memories based on engineered dissipation Authors: Fernando Pastawski, Lucas Clemente, Juan Ignacio Cirac Journal: Phys. Rev. A 83, 012304 (2011) [arXiv:1010.2901]. Storing quantum information for long times without disruptions is a major requirement for most quantum information technologies. A very appealing approach is to use self-correcting Hamiltonians, that is tailoring local interactions among the qubits such that when the system is weakly coupled to a cold bath the thermalization process takes a long time. Here we propose an alternative but more powerful approach in which the coupling to a bath is engineered, so that dissipation protects the encoded qubit against more general kinds of errors. We show that the method can be implemented locally in four-dimensional lattice geometries by means of a toric code and propose a simple two-dimensional setup for proof-of-principle experiments. 2. Limitations of Passive Protection of Quantum Information Journal: Quantum Information and Computation, Vol. 10, No. 7&8 (2010) 0580–0618 Authors: Fernando Pastawski, Alastair Kay, Norbert Schuch, Ignacio Cirac Abstract: The ability to protect quantum information from the effect of noise is one of the majorgoals of quantum information processing. In this article, we study limitations on the asymptotic stability of quantum information stored in passive N-qubit systems. We consider the effect of small imperfections in the implementation of the protecting Hamiltonian in the form of perturbations or weak coupling to a ground state environment. We prove that, regardless of the protecting Hamiltonian, there exists a perturbed evolution that necessitates a final error correcting step when the state of the memory is read. Such an error correction step is shown to require a finite error threshold, the lack thereof being exemplified by the 3D compass model. We go on to present explicit weak Hamiltonian perturbations which destroy the logical information stored in the 2D toric code in a time O(log(N)). c. New quantum algorithms 1. Martin Schwarz, Kristan Temme, Frank Verstraete, Contracting tensor networks and preparing PEPS on a quantum computer, Phys. Rev. Lett. 108, 110502 (2012) 2. Quantum Metropolis Sampling Authors: K. Temme, T.J. Osborne, K.G. Vollbrecht, D. Poulin, F. Verstraete Journal: Nature 471:87 (2011) [arXiv:0911.3635]. 4. WP4: Quantum effects driven by dissipation a. Characterize the phase diagram of non-equilibrium quantum models 1. Crossover between ballistic and diffusive transport: The Quantum Exclusion Process Author: Viktor Eisler Journal: J. Stat. Mech. P06007 (2011) [arXiv:1104.4050]. We study the evolution of a system of free fermions in one dimension under the simultaneous effects of coherent tunneling and stochastic Markovian noise. We identify a class of noise terms where a hierarchy of decoupled equations for the correlation functions emerges. In the special case of incoherent, nearest-neighbor hopping the equation for the two-point functions is solved explicitly. The Green's function for the particle density is obtained analytically and a time scale is identified where a crossover from ballistic to diffusive behavior takes place. The result can be interpreted as a competition between the two types of conduction channels where diffusion dominates on large timescales. 2. Entanglement spectrum and boundary theories with projected entangled-pair states Authors: J. Ignacio Cirac, Didier Poilblanc, Norbert Schuch, Frank Verstraete Journal: Phys. Rev. B 83, 245134 (2011) [arXiv:1103.3427]. In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated with their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using projected entangled-pair states. This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models: a deformed AKLT model [I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987)], an Ising-type model [F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)], and Kitaev’s toric code [A. Kitaev, Ann. Phys. 303, 2 (2003)], both in finite ladders and in infinite square lattices. In the second case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield nonlocal Hamiltonians. Because our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary. 3. An order parameter for symmetry-protected phases in one dimension Jutho Haegeman, David Perez-Garcia, Ignacio Cirac, Norbert Schuch Phys. Rev. Lett. (in press), arXiv:1201.4174 We introduce an order parameter for symmetry-protected phases in one dimension which allows to directly identify those phases. The order parameter consists of stringlike operators and swaps, but differs from conventional string order operators in that it only depends on the symmetry but not on the state. We verify our framework through numerical simulations for the SO(3) invariant spin-1 bilinear-biquadratic model which exhibits a dimerized and a Haldane phase, and find that the order parameter not only works very well for the dimerized and the Haldane phase, but it also returns a distinct signature for gapless phases. Finally, we discuss possible ways to measure the order parameter in experiments with cold atoms. 4. Dissipative Phase Transition in Central Spin Systems, Eric M. Kessler, Geza Giedke, Atac Imamoglu, Susanne F. Yelin, Mikhail D. Lukin, J. Ignacio Cirac, Physical Review A 86, 012116 (2012), This paper analyzes the phase diagram for the steady state of the central spin model under dissipation. Its importance lies on three facts: (i) it describes experimentally accessible systems, like quantum dots or NV-centers; (ii) It developes theoretical techniques based on self-consistent Holstein-Primakoff approximation to derive the phase diagram; (iii) It describes irregularities in the gap of the Liouvilian, a phenomenon that up to our knowledge, is novel. b. Develop numerical renormalization group methods for simulating quantum dissipative processes 1. Continuous Matrix Product States for Quantum Fields Journal: Phys. Rev. Lett. 104, 190405 (2010) Authors: F. Verstraete, J.I. Cirac Abstract: We define matrix product states in the continuum limit, without any reference to an underlying lattice parameter. This allows us to extend the density matrix renormalization group and variational matrix product state formalism to quantum field theories and continuum models in 1 spatial dimension. We illustrate our procedure with the Lieb-Liniger model. 2. Holographic quantum states Authors: Tobias J. Osborne, Jens Eisert, Frank Verstraete Journal: Phys. Rev. Lett. 105, 260401 (2010) [arXiv:1005.1268]. We show how continuous matrix product states of quantum fields can be described in terms of the dissipative nonequilibrium dynamics of a lower-dimensional auxiliary boundary field by demonstrating that the spatial correlation functions of the bulk field correspond to the temporal statistics of the boundary field. This equivalence (1) illustrates an intimate connection between the theory of continuous quantum measurement and quantum field theory, (2) gives an explicit construction of the boundary field allowing the extension of real-space renormalization group methods to arbitrary dimensional quantum field theories without the introduction of a lattice parameter, and (3) yields a novel interpretation of recent cavity QED experiments in terms of quantum field theory, and hence paves the way toward observing genuine quantum phase transitions in such zero-dimensional driven quantum systems. c. Develop a real-space renormalization group formalism for non-equilibrium quantum dissipative processes 1. Stochastic Matrix Product States Authors: Kristan Temme, Frank Verstraete Journal-ref: Phys. Rev. Lett. 104, 210502 (2010) Abstract: The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows defining the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the entanglement entropy, the entropy cost $S_C$, and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state. We illustrate these concepts on the hand of the asymmetric exclusion process. 5. WP5: Experimental realizations a. Develop procedures for simulating quantum dissipative processes in ion traps 1. Dissipative preparation of entanglement in optical cavities Authors: M. J. Kastoryano, F. Reiter, A. S. Sørensen Journal: Phys. Rev. Lett. 106, 090502 (2011) [arXiv:1011.1441]. We propose a novel scheme for the preparation of a maximally entangled state of two atoms in an optical cavity. Starting from an arbitrary initial state, a singlet state is prepared as the unique fixed point of a dissipative quantum dynamical process. In our scheme, cavity decay is no longer undesirable, but plays an integral part in the dynamics. As a result, we get a qualitative improvement in the scaling of the fidelity with the cavity parameters. Our analysis indicates that dissipative state preparation is more than just a new conceptual approach, but can allow for significant improvement as compared to preparation protocols based on coherent unitary dynamics. 2. Quantum simulation of small-polaron formation with trapped ions Vladimir M. Stojanovic, Tao Shi, C. Bruder, J. Ignacio Cirac arXiv:1206.7010 We propose a method for simulating polaron physics using a one-dimensional system of trapped ions acted upon by off-resonant standing waves. This system, envisioned as an array of ion microtraps, in the single-excitation case provides a realization of the anti-adiabatic regime of the Holstein model. We show that the strong excitationphonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonondressed excitation. 3. Adiabatic Preparation of a Heisenberg Antiferromagnet Using an Optical Superlattice Michael Lubasch, Valentin Murg, Ulrich Schneider, J. Ignacio Cirac, Mari-Carmen Bañuls Phys. Rev. Lett. 107, 165301 (2011), arXiv:1106.1628 We analyze the possibility to prepare a Heisenberg antiferromagnet with cold fermions in optical lattices, starting from a band insulator and adiabatically changing the lattice potential. The numerical simulation of the dynamics in 1D allows us to identify the conditions for success, and to study the influence that the presence of holes in the initial state may have on the protocol. We also extend our results to twodimensional systems. b. Develop procedures for simulating quantum dissipative processes in neutral atoms 1. Simulating quantum-optical phenomena with cold atoms in optical lattices Authors: Carlos Navarrete-Benlloch, Inés de Vega, Diego Porras, J. Ignacio Cirac Journal: New J. Phys. 13 023024 (2011) [arXiv:1010.1730]. We propose a scheme involving cold atoms trapped in optical lattices to observe different phenomena traditionally linked to quantum-optical systems. The basic idea consists of connecting the trapped atomic state to a non-trapped state through a Raman scheme. The coupling between these two types of atoms (trapped and free) turns out to be similar to that describing light–matter interaction within the rotating- wave approximation, the role of matter and photons being played by the trapped and free atoms, respectively. We explain in particular how to observe phenomena arising from the collective spontaneous emission of atomic and harmonic oscillator samples, such as superradiance and directional emission. We also show how the same setup can simulate Bose–Hubbard Hamiltonians with extended hopping as well as Ising models with long-range interactions. We believe that this system can be realized with state of the art technology. c. Develop procedures for simulating quantum dissipative processes in atomic ensembles 1. Dissipatively driven entanglement of two macroscopic atomic ensembles Authors: C. A. Muschik, E. S. Polzik, J. I. Cirac Preprint: arXiv:1007.2209 Up to date, the life time of experimentally demonstrated entangled states has been limited, due to their fragility under decoherence and dissipation. Therefore, they are created under strict isolation conditions. In contrast, new approaches harness the coupling of the system to the environment, which drives the system into the desired state. Following these ideas, we present a robust method for generating steady state entanglement between two distant atomic ensembles. The proposed scheme relies on the interaction of the two atomic systems with the common vacuum modes of the electromagnetic field which act as an engineered environment. We develop the theoretical framework for two level systems including dipole-dipole interactions and complement these results by considering the implementation in multi-level ground states. 2. Entanglement generated by dissipation Authors: Hanna Krauter, Christine A. Muschik, Kasper Jensen, Wojciech Wasilewski, Jonas M. Petersen, J. Ignacio Cirac, Eugene S. Polzik Preprint: arXiv:1006.4344 Entanglement is not only one of the most striking features of Quantum Mechanics but also an essential ingredient in most applications in the field of Quantum Information. Unfortunately, this property is very fragile. In experiments conducted so far, coupling of the system to a quantum mechanical environment, commonly referred to as dissipation, either inhibits entanglement or prevents its generation. In this Letter, we report on an experiment in which dissipation induces entanglement between two atomic objects rather than impairing it. This counter-intuitive effect is achieved by engineering the dissipation by means of laser- and magnetic fields, and leads to entanglement which is very robust and therefore long-lived. Our system consists of two distant macroscopic ensembles containing about 10^{12} atoms coupled to the environment composed of the vacuum modes of the electromagnetic field. The two atomic objects are kept entangled by dissipation at room temperature for about 0.015s. The prospects of using this method to obtain extremely long-lived entanglement in a steady state are discussed. 3. Robust entanglement generation by reservoir engineering Authors: Christine A. Muschik, Hanna Krauter, Kasper Jensen, Jonas M. Petersen, J. Ignacio Cirac, Eugene S. Polzik Journal: J. Phys. B: At. Mol. Opt. Phys. 45, 124021 (2012), arXiv:1203.4785 Following a recent proposal [C. Muschik et. al., Phys. Rev. A 83, 052312 (2011)], engineered dissipative processes have been used for the generation of stable entanglement between two macroscopic atomic ensembles at room temperature [H. Krauter et. al., Phys. Rev. Lett. 107, 080503 (2011)]. This experiment included the preparation of entangled states which are continuously available during a time interval of one hour. Here, we present additional material, further-reaching data and an extension of the theory developed in [C. Muschik et. al., Phys. Rev. A 83, 052312 (2011)]. In particular, we show how the combination of the entangling dissipative mechanism with measurements can give rise to a substantial improvement of the generated entanglement in the presence of noise. 4. Driving two atoms in an optical cavity into an entangled steady state using engineered decay Journal: New J. Phys. 14, 053022 (2012) Authors: F. Reiter, M. J. Kastoryano, A. Sorensen Abstract: We propose various schemes for the dissipative preparation of a maximally entangled steady state of two atoms in an optical cavity. Harnessing the natural decay processes of cavity photon loss and spontaneous emission, we use an effective operator formalism to identify and engineer effective decay processes, which reach an entangled steady state of two atoms as the unique fixed point of the dissipative time evolution. We investigate various aspects that are crucial for the experimental implementation of our schemes in present-day and future cavity quantum electrodynamics systems and analytically derive the optimal parameters, the error scaling and the speed of convergence of our protocols. Our study shows promising performance of our schemes for existing cavity experiments and favourable scaling of fidelity and speed with respect to the cavity parameters. 4.1.4: Potential impact and main dissemination activities. The main impact of the work performed during the QUEVADIS project is situated in the domain of quantum information theory. The study of dissipative phenomena will necessarily remain an integral part of research on the field of quantum computation and simulations, and this project aimed first at all at doing research on the novel effects that can arise as a consequence of this, and secondly at identifying experimental set-ups that can be used to implement those. This has led to a deeper understanding of completely positive maps on the one hand, and to a variety of novel quantum algorithms aimed at the simulation of strongly correlated quantum many-body systems. The main dissemination activities were certainly the publication of papers in prestigious journals, the corresponding press coverage, and most importantly the presentation of our results on multiple workshops and conferences. 4.1.5: Website. The internet address of our website is www.quevadis.at 4.2 Use and dissemination of foreground A plan for use and dissemination of foreground (including socio-economic impact and target groups for the results of the research) shall be established at the end of the project. It should, where appropriate, be an update of the initial plan in Annex I for use and dissemination of foreground and be consistent with the report on societal implications on the use and dissemination of foreground (section 4.3 – H). The plan should consist of: Section A This section should describe the dissemination measures, including any scientific publications relating to foreground. Its content will be made available in the public domain thus demonstrating the added-value and positive impact of the project on the European Union. Section B This section should specify the exploitable foreground and provide the plans for exploitation. All these data can be public or confidential; the report must clearly mark non-publishable (confidential) parts that will be treated as such by the Commission. Information under Section B that is not marked as confidential will be made available in the public domain thus demonstrating the added-value and positive impact of the project on the European Union. Section A (public) This section includes two templates Template A1: List of all scientific (peer reviewed) publications relating to the foreground of the project. Template A2: List of all dissemination activities (publications, conferences, workshops, web sites/applications, press releases, flyers, articles published in the popular press, videos, media briefings, presentations, exhibitions, thesis, interviews, films, TV clips, posters). These tables are cumulative, which means that they should always show all publications and activities from the beginning until after the end of the project. Updates are possible at any time. TEMPLATE A1: LIST OF SCIENTIFIC (PEER REVIEWED) PUBLICATIONS, STARTING WITH THE MOST IMPORTANT ONES NO. 1 2 Title Quantum Metropolis Sampling Quantum computation, quantum state engineering, and quantum phase 2 Permanent Is/Will open 2 identifiers access3 provided (if to this publication? available) Title of the periodical or the series Number, date or frequency K. Temme Nature 471 - 87 2011 arXiv:0911.3635 F. Verstraete Nature Physics 5 - 633 2009 arXiv:0803.1447 Main author Publisher Place of Year of publication publication Relevant pages A permanent identifier should be a persistent link to the published version full text if open access or abstract if article is pay per view) or to the final manuscript accepted for publication (link to article in repository). 3 Open Access is defined as free of charge access for anyone via Internet. Please answer "yes" if the open access to the publication is already established and also if the embargo period for open access is not yet over but you intend to establish open access afterwards. 3 4 5 6 7 8 9 10 11 transitions driven by dissipation Computational complexity of interacting electrons and fundamental limitations of density functional theory Extracting dynamical equations from experimental data is NPhard An order parameter for symmetry-protected phases in one dimension Laughlin spin liquid states on lattices obtained from conformal field theory Contracting tensor net5works and preparing PEPS on a quantum computer Dissipative preparation of entanglement in optical cavities Entanglement distillation by dissipation and continuous quantum repeaters Entanglement can completely defeat quantum noise Adiabatic Preparation of a Heisenberg Antiferromagnet Using an Norbert Schuch Nature Physics 5 - 732 2009 Toby S. Cubitt Phys. Rev. Lett. 108 – 120503 2012 Jutho Haegeman Phys. Rev. Lett. (in press) 2012 Anne E. B. Nielsen Phys. Rev. Lett. 108 – 257206 2012 arXiv:1201.3096 Martin Schwarz Phys. Rev. Lett. 108 – 110502 2012 arXiv:1104.1410 M. J. Phys. Rev. Kastoryano Lett. 106 – 090502 2011 arXiv:1011.1441 Karl Gerd H. Vollbrecht Phys. Rev. Lett. 107 – 120502 2011 arXiv:1011.4115 Jianxin Chen Phys. Rev. Lett. 107 – 250504 2011 M. Lubasch Phys. Rev. Lett. 107 – 165301 2011 arXiv:1201.4174 arXiv:1106.1628 12 13 14 15 16 17 18 19 20 21 22 Optical Superlattice Optical pumping into many-body entanglement Strong and weak thermalization of infinite non-integrable quantum systems Nuclear spin cooling using Overhauser field selective coherent population trapping Continuous Matrix Product States for Quantum Fields Holographic quantum states Applying the variational principle to (1+1)dimensional quantum field theories Pfaffian State Generation by Strong Three-Body Dissipation Stochastic Matrix Product States Operator Space Theory: A Natural Framework for Bell Inequalities How Long Can a Quantum Memory Withstand Depolarizing Noise? Assessing Quantum Dimensionality from Observable Dynamics Dissipative Phase J. Cho Phys. Rev. Lett. Phys. Rev. Lett. 106 – 020504 2011 arXiv:1008.4088 106 - 050405 2011 arXiv:1007.3957 Mena Issler Phys. Rev. Lett. 105 – 267202 2010 arXiv:1008.3507 F. Verstraete Phys. Rev. Lett. 104 – 190405 2010 arXiv:1002.1824 Tobias J. Osborne Jutho Haegeman Phys. Rev. Lett. Phys. Rev. Lett. 105 – 260401 2010 arXiv:1005.1268 105 – 251601 2010 arXiv:1006.2409 M. Roncaglia Phys. Rev. Lett. 104 – 096803 2010 arXiv:0905.1247 Kristan Temme M. Junge Phys. Rev. Lett. Phys. Rev. Lett. 104 – 210502 2010 104 – 170405 2010 Fernando Pastawski Phys. Rev. Lett. 103 – 080501 2009 arXiv:0904.4861 M. M. Wolf Phys. Rev. Lett. 102 – 190504 2009 arXiv:0901.2542 Eric M. Physical 86 – 012116 2012 arXiv:1205.3341 Mari Carmen Bañuls 23 24 25 26 27 28 29 30 31 32 33 Transition in Central Spin Systems A Cutoff Phenomenon for Quantum Markov Chains The Algebraic Bethe Ansatz and Tensor Networks Robust entanglement generation by reservoir engineering Stochastic exclusion processes versus coherent transport Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems Driving two atoms in an optical cavity into an entangled state using engineered decay Finite-temperature mutual information in a simple phase transition Hilbert's projective metric in quantum information theory Quantum memories based on engineered dissipation Classifying quantum phases using Matrix Product States and PEPS Entanglement spectrum Kessler Review A Michael J. Phys. A: Kastoryano Math. Theor. Valentin Phys. Rev. B Murg 45 – 075307 2012 86 – 045125 2012 Christine A. Muschik Phys. B: Mol. Opt. Phys. 45 – 124021 2012 K. Temme New J. Phys. 14 – 075004 2012 Alexander MüllerHermes New J. Phys. 14 – 075003 2012 arXiv:1204.5080 F. Reiter New J. Phys. 14 – 053022 2012 arxiv:1110.1024 J. Wilms Stat. Mech. P01023 2012 David Reeb Math. Phys. (in press) 2012 arXiv:1102.5170 Fernando Pastawski Phys. Rev. A 83 – 012304 2011 arXiv:1010.2901 Norbert Schuch Phys. Rev. B 84 – 165139 2011 arXiv:1010.3732 Ignacio Phys. Rev. B 83 – 245134 2011 arXiv:1103.3427 arXiv:1203.4785 34 35 36 37 38 39 40 41 42 43 and boundary theories with projected entangledpair states The inverse eigenvalue problem for quantum channels Connes' embedding problem and Tsirelson's problem Crossover between ballistic and diffusive transport: The Quantum Exclusion Process Quantum spin Hamiltonians for the SU(2)_k WZW model Sequential Strong Measurements and Heat Vision Simulating quantumoptical phenomena with cold atoms in optical lattices Fermionic projected entangled pair states Infinite matrix product states, Conformal Field Theory and the HaldaneShastry model Simulating two- and three-dimensional frustrated quantum systems with string-bond states Unbounded violations of Cirac Michael M. Math.Phys. Wolf 2011 arXiv:1005.4545 M. Junge Math.Phys. 52 – 012102 2011 arXiv:1008.1142 Viktor Eisler Stat. Mech. P06007 2011 arXiv:1104.4050 Anne E. B. Nielsen Stat. Mech. P11014 2011 arXiv:1109.5470 Miguel Navascues New J. Phys. 13 – 113038 2011 arXiv:1010.4983 Carlos NavarreteBenlloch New J. Phys. 13 – 023024 2011 arXiv:1010.1730 Christina V. Kraus J.I. Cirac Phys. Rev. A 81 - 052338 2010 Phys. Rev. B 81 – 104431 2010 Alessandro Sfondrini Phys. Rev. B 81 - 214426 2010 M. Junge Math. Phys. 81 – 214426 2010 44 45 46 47 48 49 bipartite Bell Inequalities via Operator Space theory The $\chi^2$ - divergence and Mixing times of quantum Markov processes Characterizing symmetries in Projected Entangled Pair States Matrix product operator representations PEPS as ground states: degeneracy and topology Non-disturbing quantum measurements Limitations of Passive Protection of Quantum Information K. Temme Math. Phys. 51 – 122201 2010 arXiv:1005.2358 D. PérezGarcía New J. Phys. 12 – 025010 2010 arXiv:0908.1674 B Pirvu New J. Phys. 12 – 025012 2010 N. Schuch Annals of Physics Math.Phys. 325 – 2153 2010 arXiv:1001.3807 51 – 092201 2010 arXiv:1005.5659 Teiko Heinosaari Fernando Pastawski 50 The semigroup structure of Gaussian channels T. Heinosaari 51 Renormalization and tensor product states in spin chains and lattices Ground-state properties of quantum many-body systems: entangledplaquette states and variational Monte Carlo A quantum version of Wielandt’s inequality J. Ignacio Cirac 52 53 Quantum Vol. 10, No. 7&8 Information and Computation Quantum Vol. 10 Information and Computation Phys. A: 42 – 504004 Math. Theor. F New J. Phys. Mezzacapo M. Sanz IEEE Trans. Inf. Theory 11 – 083026 2010 pp. 580–618 2010 pp. 619-635 2009 2009 2009 arXiv:0911.3843 54 55 56 57 58 59 60 61 62 63 64 65 Matrix Product States: Symmetries and TwoBody Hamiltonians Inverting the central limit theorem Entangling dynamics beyond quantum theory Joint system quantum descriptions arising from local quantumness Quantum Steering and Space-Like Separation Quantum logarithmic Sobolev inequalities and rapid mixing A constructive commutative quantum Lovasz Local Lemma, and beyond Are problems in Quantum Information Theory (un)decidable? Extending quantum operations Matrix Product States with long-range Localizable Entanglement Cluster update for tensor network states Spin-liquid phase in spin1/2 square J1-J2 Heisenberg model: A tensor product state approach Quantum Chi-Squared M. Sanz 2009 arXiv:0901.2223 Miguel Navascues Lluis Masanes Tom Cooney 2012 arXiv:1110.2394v2 2012 arXiv:1111.4060v1 2012 arXiv:1205.4110 Miguel Navascues Michael J. Kastoryano 2012 arXiv:1204.6220 2012 arXiv:1207.3261 Toby S. Cubitt 2012 arXiv:1112.1413 Michael M. Wolf 2012 arXiv:1111.5425v1 Teiko Heinosaari Thorsten B. Wahl 2012 arXiv:1205.0641 2012 arXiv:1206.4254 Ling Wang 2012 arXiv:1110.4362v1 Ling Wang 2012 arXiv:1112.3331 K. Temme 2012 arXiv:1112.6343 Phys. Rev. A 79 – 042308 66 67 68 69 70 71 72 73 74 75 76 77 and Goodness of Fit Testing Precisely timing dissipative quantum information processing Resonating valence bond states in the PEPS formalism Gapless Hamiltonians for the toric code using the PEPS formalism Quantum simulation of small-polaron formation with trapped ions Dissipative spin chains: implementation with cold atoms and steady state properties Superradiance-like Electron Transport through a Quantum Dot Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy A physical approach to Tsirelson's problem Entanglement generated by dissipation Determining dynamical equations is hard A dissipative quantum Church-Turing theorem Simulating open quantum M.J. Kastoryano 2012 arXiv:1205.0985 Norbert Schuch 2012 arXiv:1203.4816 Carlos FernándezGonzález V. Stojanovic 2012 arXiv:1111.5817 2012 arXiv:1206.7010 H. Schwager 2012 arXiv:1207.5768 M. J. A. Schuetz 2012 arXiv:1206.2573 Benoit Collins To be published in CMP 2012 arXiv:1201.6324v1 Miguel Navascues to be published in Found. Phys. 2012 arXiv:1105.3373 Hanna Krauter Toby S. Cubitt M. Kliesch 2011 arXiv:1006.4344 2011 arXiv:1005.0005 2011 arXiv:1105.3986 M. Mueller 2011 arXiv:1104.2507 78 79 80 systems: from many-body interactions to stabilizer pumping Quantum Information at the Interface of Light with Mesoscopic Objects Dissipatively driven entanglement of two macroscopic atomic ensembles Perturbation Bounds for Quantum Markov Processes and their Fixed Points C. A. Muschik 2011 arXiv:1105.2947 C. A. Muschik 2010 arXiv:1007.2209 O. Szehr 2012 arXiv:1210.1171 TEMPLATE A2: LIST OF DISSEMINATION ACTIVITIES NO. Type of activities4 Main leader Title Date/Period 1 Workshop F. Verstraete Quantum metropolis sampling 1/12/2009 2 Seminar F. Verstraete Quantum Simulation of manybody systems 9/12/2009 Place Santa Barbara Princeton Size of audience Type of audience5 Physicists 60 Physicists 50 4 A drop down list allows choosing the dissemination activity: publications, conferences, workshops, web, press releases, flyers, articles published in the popular press, videos, media briefings, presentations, exhibitions, thesis, interviews, films, TV clips, posters, Other. 5 A drop down list allows choosing the type of public: Scientific Community (higher education, Research), Industry, Civil Society, Policy makers, Medias, Other ('multiple choices' is possible). 3 F. Verstraete Quantum Simulation of manybody systems 11/02/2010 Karpacz Physicists 100 4 Karpacz Winter School Conference F. Verstraete 13/04/2010 Leeds Physicists 150 5 Conference F. Verstraete Simulating quantum manybody systems on a quantum computer Variational wavefunctions for quantum field theories 27/05/2010 Physicists 100 6 APS meeting F. Verstraete 28/05/2010 Physicists 400 7 Workshop F. Verstraete 9/06/2010 Obergurgl Physicists 100 8 9 Seminar Conference K. Temme F. Verstraete 10/05/2010 16/06/2010 MIT Trieste Physicists Physicists 50 100 10 Conference: Qmath11 F. Verstraete 8/9/2010 Czech Repulblic Physicists 200 11 Conference F. Verstraete 24/09/2010 Mainz Conference F. Verstraete 30/01/2012 Coogee Physicists and Chemists Physicists 100 12 13 Conference F. Verstraete 7/06/2012 Slovakei Physicists 100 14 15 Workshop Conference D. Pérez-García D. Pérez-García 02/07/2012 26/06/2012 Seefeld Roscoff Physicists Mathematicians 70 80 16 17 Seminar Conference D. Pérez-García M. Schwarz Dissipative processes for quantum simulation and computation Dissipative processes for quantum simulation and computation Quantum Metropolis Sampling Dissipative processes for quantum simulation and computation Dissipative processes for quantum simulation and computation Entanglement and complexity of many-body wavefunctions Quantum chi-square and goodness of fit testing Quantum chi-squared and goodness of fit testing RVB using PEPS Random Matrix Product States and the Principle of Maximum Entropy RVB using PEPS Preparing PEPS on a quantum computer Perimeter Institute, Waterloo Houston 25/01/2012 16/12/2011 Caltech QIP2012 Montreal Physicists Physicists 100 350 60 18 Conference T. Cubitt Three Proofs of a Constructive Commuting Quantum Lovasz Local Lemma Tensor Network States: an easy description of exotic states of matter Symmetries in PEPS A quantum version of Wielandt's inequality Constructing topological quantum states on a quantum computer Constructing topological quantum states on a quantum computer Looking for signs of microscopic quantization Inverting the central limit theorem Is physics (NP)-hard? It is official: Physics is hard Engineered dissipation and quantum information 13/12/2011 QIP2012 Montreal Physicists 350 19 Workshop D. Pérez-García 18/11/2011 Toulouse Mathematicians 50 20 21 Workshop Seminar D. Pérez-García D. Pérez-García 30/01/2010 16/02/2010 Munich Bristol Physicists 80 Computer Science 30 22 Workshop T. Cubitt 02/07/2012 Seefeld Physicists 70 23 Workshop T. Cubitt 15/05/2012 Benasque Physicists 80 24 Conference M. Navascués 10/06/2012 Slovakia Physicists 70 25 Seminar M. Navascués 03/11/2011 Cambridge Mathematicians 50 26 27 28 Conference TV Conference T. Cubitt T. Cubitt I. Cirac 26/05/2012 24/04/2012 06/09/2011 Finland TVE news Zurich Computer Science 70 General 2600000 Physicists 100 29 Colloquium I. Cirac Dissipation: a new tool in quantum information Science 08/11/2011 Hanover Physicists 100 30 Colloquium I. Cirac Dissipation: a new tool in quantum information Science 07/02/2012 Stanford Physicists 200 31 Colloquium I. Cirac Dissipation: a new tool in quantum information Science 20/02/2012 Maryland Physicists 200 32 Colloquium I. Cirac Dissipation: a new tool in 16/04/2012 Barcelona Physicists 140 quantum information Science 33 Conference – Poster M. Kastoryano 34 D. Reeb 35 Conference – Poster Conference 36 Seminar M. Kastoryano 37 Seminar M. Kastoryano 38 Conference D. Reeb 39 Seminar D. Reeb 40 Conference D. Reeb 41 Conference – Poster Workshop M. Kastoryano Conference – Poster Conference – Poster D. Reeb 45 Seminar D. Reeb 46 Conference – Poster Conference D. Reeb 42 43 44 47 D. Reeb D. Reeb M. Kastoryano M.Wolf The chi-squared distance and mixing times of quantum Markov processes Hilbert’s projective metric in quantum information theory Extension theorems for quantum operations Hilbert’s projective metric in quantum information theory Dissipative preparation of entanglement in optical cavities Hilbert’s projective metric in quantum information theory Hilbert’s projective metric in quantum information theory Extending quantum operations A cutoff phenomenon for quantum Markov chains Convergence behaviour of quantum Markov chains Extending quantum operations Timer Gadgets and geometrically local dissipative quantum computing A cutoff phenomenon for quantum Markov chains Extending quantum operation Partial quantum information 5/10/2010 Stockholm Physicists 300 11/01/2011 Singapore 300 14/03/2011 Dresden Physicists and Mathematicians Physicists 6/04/2011 Vienna Physicists 20 29/03/2011 Berlin Physicists 30 2/06/2011 Physicists 70 15/08/2011 Czech Republic Finland Physicists 20 9/09/2011 Zurich Physicists 50 7/09/2011 Zurich Physicists 300 9/10/2011 Physicists 30 12/12/2011 Bavaria/Ge rmany Canada 300 18/05/2012 Tokyo Physicists and Mathematicians Physicists 18/06/2012 Physicists 20 2/07/2012 Heidelberg /Germany Austria 150 4/07/2012 Austria Physicists and Mathematicians Physicists 50 200 150 48 49 Conference Conference M.Wolf M. Wolf 50 51 Conference Conference M. Wolf M. Wolf Partial quantum information Advances in quantum information Quantum Markov processes Quantum Channels 18/05/2012 04/08/2010 Tokyo Bavaria Physicists Physicists 200 150 28/07/2010 01/03/2012 Zurich Göttingen Physicists Physicists 50 100 Section B (Confidential6 or public: confidential information to be marked clearly) Part B1 No applications for patents, trademarks or registered designs were made. Part B2 Please complete the table hereafter: Type of Exploitable Foreground7 Description of exploitable foreground Confidential Click on YES/NO Foreseen embargo date dd/mm/yyyy Novel type of quantum computing and quantum simulation architecture Exploitable product(s) or measure(s) Supercomputing Sector(s) of application8 Timetable, commercial or any other use Patents or other IPR exploitation (licences) Owner & Other Beneficiary(s) involved Many-body physics Quantum Chemistry The research in the QUEVADIS project will first of all have an impact on the way quantum computers will be build and used for quantum simulation. On the other hand, the study of dissipative dynamics turns out to be very relevant for the description of quantum many-body systems; there seems to be a certain duality between equilibrium physics in d dimensions and non-equilibrium (dissipative) physics in d-1 dimensions. 6 Note to be confused with the "EU CONFIDENTIAL" classification for some security research projects. 19 A drop down list allows choosing the type of foreground: General advancement of knowledge, Commercial exploitation of R&D results, Exploitation of R&D results via standards, exploitation of results through EU policies, exploitation of results through (social) innovation. 8 A drop down list allows choosing the type sector (NACE nomenclature) : http://ec.europa.eu/competition/mergers/cases/index/nace_all.html 4.3 Report on societal implications Replies to the following questions will assist the Commission to obtain statistics and indicators on societal and socio-economic issues addressed by projects. The questions are arranged in a number of key themes. As well as producing certain statistics, the replies will also help identify those projects that have shown a real engagement with wider societal issues, and thereby identify interesting approaches to these issues and best practices. The replies for individual projects will not be made public. A General Information (completed automatically when Grant Agreement number is entered. Grant Agreement Number: Title of Project: Name and Title of Coordinator: B 233859 quevadis Frank Verstraete, Professor Ethics 1. Did your project undergo an Ethics Review (and/or Screening)? * If Yes: have you described the progress of compliance with the relevant Ethics Review/Screening Requirements in the frame of the periodic/final project reports? No Special Reminder: the progress of compliance with the Ethics Review/Screening Requirements should be described in the Period/Final Project Reports under the Section 3.2.2 'Work Progress and Achievements' 2. Please indicate whether your project involved any of the following issues (tick box) : RESEARCH ON HUMANS * Did the project involve children? * Did the project involve patients? * Did the project involve persons not able to give consent? * Did the project involve adult healthy volunteers? * Did the project involve Human genetic material? Did the project involve Human biological samples? Did the project involve Human data collection? RESEARCH ON HUMAN EMBRYO/FOETUS * Did the project involve Human Embryos? * Did the project involve Human Foetal Tissue / Cells? * Did the project involve Human Embryonic Stem Cells (hESCs)? * Did the project on human Embryonic Stem Cells involve cells in culture? * Did the project on human Embryonic Stem Cells involve the derivation of cells from Embryos? PRIVACY * Did the project involve processing of genetic information or personal data (eg. health, sexual lifestyle, ethnicity, political opinion, religious or philosophical conviction)? * Did the project involve tracking the location or observation of people? RESEARCH ON ANIMALS * Did the project involve research on animals? * Were those animals transgenic small laboratory animals? * Were those animals transgenic farm animals? * Were those animals cloned farm animals? YES * Were those animals non-human primates? RESEARCH INVOLVING DEVELOPING COUNTRIES * Did the project involve the use of local resources (genetic, animal, plant etc)? * Was the project of benefit to local community (capacity building, access to healthcare, education etc)? DUAL USE Research having direct military use * Research having the potential for terrorist abuse 0 Yes 0 No C Workforce Statistics 3. Workforce statistics for the project: Please indicate in the table below the number of people who worked on the project (on a headcount basis). Type of Position Number of Women Number of Men Scientific Coordinator Work package leaders Experienced researchers (i.e. PhD holders) PhD Students Other 0 0 1 4 4. How many additional researchers (in companies and universities) were recruited specifically for this project? Of which, indicate the number of men: D Gender Aspects 5. No Did you carry out specific Gender Equality Actions under the project? 6. Which of the following actions did you carry out and how effective were they? Not at all effective Design and implement an equal opportunity policy Set targets to achieve a gender balance in the workforce Organise conferences and workshops on gender Actions to improve work-life balance Very effective Other: Was there a gender dimension associated with the research content – i.e. wherever people were 7. the focus of the research as, for example, consumers, users, patients or in trials, was the issue of gender considered and addressed? Yes- please specify X No E Synergies with Science Education 8. Did your project involve working with students and/or school pupils (e.g. open days, participation in science festivals and events, prizes/competitions or joint projects)? Yes- please specify X 9. No Did the project generate any science education material (e.g. kits, websites, explanatory booklets, DVDs)? Yes- please specify X No F Interdisciplinarity 10. Which disciplines (see list below) are involved in your project? Main discipline9: 1.2 Associated discipline9:1.3 Associated discipline9:1.1 G Engaging with Civil society and policy makers 11a Did your project engage with societal actors beyond the research community? (if 'No', go to Question 14) X Yes No 11b If yes, did you engage with citizens (citizens' panels / juries) or organised civil society (NGOs, patients' groups etc.)? No Yes- in determining what research should be performed Yes - in implementing the research Yes, in communicating /disseminating / using the results of the project 9 Insert number from list below (Frascati Manual). Yes 11c In doing so, did your project involve actors whose role is mainly to No organise the dialogue with citizens and organised civil society (e.g. professional mediator; communication company, science museums)? 12. Did you engage with government / public bodies or policy makers (including international organisations) No Yes- in framing the research agenda Yes - in implementing the research agenda Yes, in communicating /disseminating / using the results of the project 13a Will the project generate outputs (expertise or scientific advice) which could be used by policy makers? Yes – as a primary objective (please indicate areas below- multiple answers possible) Yes – as a secondary objective (please indicate areas below - multiple answer possible) No 13b If Yes, in which fields? Agriculture Audiovisual and Media Budget Competition Consumers Culture Customs Development Economic and Monetary Affairs Education, Training, Youth Employment and Social Affairs Energy Enlargement Enterprise Environment External Relations External Trade Fisheries and Maritime Affairs Food Safety Foreign and Security Policy Fraud Humanitarian aid Human rights Information Society Institutional affairs Internal Market Justice, freedom and security Public Health Regional Policy Research and Innovation Space Taxation Transport 13c If Yes, at which level? Local / regional levels National level European level International level H Use and dissemination 14. How many Articles were published/accepted for publication in peer-reviewed journals? To how many of these is open access10 provided? 53 53 How many of these are published in open access journals? 11 How many of these are published in open repositories? 53 To how many of these is open access not provided? 0 Please check all applicable reasons for not providing open access: publisher's licensing agreement would not permit publishing in a repository no suitable repository available no suitable open access journal available no funds available to publish in an open access journal lack of time and resources lack of information on open access other11: …………… How many new patent applications (‘priority filings’) have been made? 15. 0 ("Technologically unique": multiple applications for the same invention in different jurisdictions should be counted as just one application of grant). 16. 17. Indicate how many of the following Intellectual Property Rights were applied for (give number in each box). Trademark 0 Registered design 0 Other 0 How many spin-off companies were created / are planned as a direct result of the project? 0 Indicate the approximate number of additional jobs in these companies: 18. Please indicate whether your project has a potential impact on employment, in comparison with the situation before your project: In small & medium-sized enterprises Increase in employment, or Safeguard employment, or In large companies X None of the above / not relevant to the project Decrease in employment, Difficult to estimate / not possible to quantify Indicate figure: 19. For your project partnership please estimate the employment effect resulting directly from your participation in Full Time Equivalent (FTE = one person working fulltime for a year) jobs: 10 Open Access is defined as free of charge access for anyone via Internet. 11 For instance: classification for security project. X Difficult to estimate / not possible to quantify I Media and Communication to the general public 20. As part of the project, were any of the beneficiaries professionals in communication or media relations? Yes X No 21. As part of the project, have any beneficiaries received professional media / communication training / advice to improve communication with the general public? Yes X No 22 Which of the following have been used to communicate information about your project to the general public, or have resulted from your project? X 23 Press Release Media briefing TV coverage / report Radio coverage / report Brochures /posters / flyers DVD /Film /Multimedia X X X Coverage in specialist press Coverage in general (non-specialist) press Coverage in national press Coverage in international press Website for the general public / internet Event targeting general public (festival, conference, exhibition, science café) In which languages are the information products for the general public produced? X Language of the coordinator Other language(s) X English Question F-10: Classification of Scientific Disciplines according to the Frascati Manual 2002 (Proposed Standard Practice for Surveys on Research and Experimental Development, OECD 2002): FIELDS OF SCIENCE AND TECHNOLOGY 1. 1.1 1.2 1.3 1.4 1.5 2 2.1 2.2 2.3. NATURAL SCIENCES Mathematics and computer sciences [mathematics and other allied fields: computer sciences and other allied subjects (software development only; hardware development should be classified in the engineering fields)] Physical sciences (astronomy and space sciences, physics and other allied subjects) Chemical sciences (chemistry, other allied subjects) Earth and related environmental sciences (geology, geophysics, mineralogy, physical geography and other geosciences, meteorology and other atmospheric sciences including climatic research, oceanography, volcanology, paleoecology, other allied sciences) Biological sciences (biology, botany, bacteriology, microbiology, zoology, entomology, genetics, biochemistry, biophysics, other allied sciences, excluding clinical and veterinary sciences) ENGINEERING AND TECHNOLOGY Civil engineering (architecture engineering, building science and engineering, construction engineering, municipal and structural engineering and other allied subjects) Electrical engineering, electronics [electrical engineering, electronics, communication engineering and systems, computer engineering (hardware only) and other allied subjects] Other engineering sciences (such as chemical, aeronautical and space, mechanical, metallurgical and materials engineering, and their specialised subdivisions; forest products; applied sciences such as geodesy, industrial chemistry, etc.; the science and technology of food production; specialised technologies of interdisciplinary fields, e.g. systems analysis, metallurgy, mining, textile technology and other applied subjects) 3. 3.1 3.2 3.3 4. 4.1 4.2 MEDICAL SCIENCES Basic medicine (anatomy, cytology, physiology, genetics, pharmacy, pharmacology, toxicology, immunology and immunohaematology, clinical chemistry, clinical microbiology, pathology) Clinical medicine (anaesthesiology, paediatrics, obstetrics and gynaecology, internal medicine, surgery, dentistry, neurology, psychiatry, radiology, therapeutics, otorhinolaryngology, ophthalmology) Health sciences (public health services, social medicine, hygiene, nursing, epidemiology) AGRICULTURAL SCIENCES Agriculture, forestry, fisheries and allied sciences (agronomy, animal husbandry, fisheries, forestry, horticulture, other allied subjects) Veterinary medicine 5. 5.1 5.2 5.3 5.4 SOCIAL SCIENCES Psychology Economics Educational sciences (education and training and other allied subjects) Other social sciences [anthropology (social and cultural) and ethnology, demography, geography (human, economic and social), town and country planning, management, law, linguistics, political sciences, sociology, organisation and methods, miscellaneous social sciences and interdisciplinary , methodological and historical S1T activities relating to subjects in this group. Physical anthropology, physical geography and psychophysiology should normally be classified with the natural sciences]. 6. 6.1 HUMANITIES History (history, prehistory and history, together with auxiliary historical disciplines such as archaeology, numismatics, palaeography, genealogy, etc.) Languages and literature (ancient and modern) Other humanities [philosophy (including the history of science and technology) arts, history of art, art criticism, painting, sculpture, musicology, dramatic art excluding artistic "research" of any kind, religion, theology, other fields and subjects pertaining to the humanities, methodological, historical and other S1T activities relating to the subjects in this group] 6.2 6.3 2. FINAL REPORT ON THE DISTRIBUTION OF THE EUROPEAN UNION FINANCIAL CONTRIBUTION This report shall be submitted to the Commission within 30 days after receipt of the final payment of the European Union financial contribution. Report on the distribution of the European Union financial contribution between beneficiaries Name of beneficiary 1. 2. n Total Final amount of EU beneficiary in Euros contribution per