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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/(log⁡2n) 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