Algebraic approach to interacting quantum systems
... [6]. It is well known that the XXZ model has an infinite number of symmetries which make it exactly solvable by the Bethe ansatz. Another example is provided by the family of spin Hamiltonians for which the ground state is a product of spin singlets. This family includes the Majumdar–Ghosh [9–11] mod ...
... [6]. It is well known that the XXZ model has an infinite number of symmetries which make it exactly solvable by the Bethe ansatz. Another example is provided by the family of spin Hamiltonians for which the ground state is a product of spin singlets. This family includes the Majumdar–Ghosh [9–11] mod ...
A Noncommutative Sigma Model by Mauritz van den Worm
... and norms squared are replaced by taking the trace of the product of an operator with its adjoint. We explore a finite dimensional σ-model based on the construction of the finite dimensional representation of the quantum torus. In this case we are able to determine an explicit partition function of ...
... and norms squared are replaced by taking the trace of the product of an operator with its adjoint. We explore a finite dimensional σ-model based on the construction of the finite dimensional representation of the quantum torus. In this case we are able to determine an explicit partition function of ...
entanglement properties of quantum many
... lines, driven by their tractability and by the equivalence of spin-1/2 with the qubit of quantum information theory. A is associated with a qualitative change of the ground state of a quantum many-body system as some parameter (e.g, density, pressure, doping, coupling constant) is varied. In contras ...
... lines, driven by their tractability and by the equivalence of spin-1/2 with the qubit of quantum information theory. A is associated with a qualitative change of the ground state of a quantum many-body system as some parameter (e.g, density, pressure, doping, coupling constant) is varied. In contras ...
ABSTRACT ADIABATIC QUANTUM COMPUTATION: NOISE IN THE ADIABATIC THEOREM AND USING THE JORDAN-WIGNER
... factoring may require more logic operations than classical computers will be able to perform. However, quantum mechanics gives us the potential for massively-parallel computing, so that some of these problems may be within reach of future quantum computers. The state of a classical register represen ...
... factoring may require more logic operations than classical computers will be able to perform. However, quantum mechanics gives us the potential for massively-parallel computing, so that some of these problems may be within reach of future quantum computers. The state of a classical register represen ...
Sparse-Graph Codes for Quantum Error-Correction
... Our aim in this paper is to create useful quantum error-correcting codes. To be useful, we think a quantum code must have a large blocklength, and it must be able to correct a large number of errors. From a theoretical point of view, we would especially like to find, for any rate R, a family of erro ...
... Our aim in this paper is to create useful quantum error-correcting codes. To be useful, we think a quantum code must have a large blocklength, and it must be able to correct a large number of errors. From a theoretical point of view, we would especially like to find, for any rate R, a family of erro ...
Emergence of a classical world from within quantum theory
... The starting point of this dissertation is that a quantum state represents the observer’s knowledge about the system of interest. As it has been pointed out several times by the opponents of this epistemic interpretation, it is difficult to reconcile this point of view with our common notion of “phy ...
... The starting point of this dissertation is that a quantum state represents the observer’s knowledge about the system of interest. As it has been pointed out several times by the opponents of this epistemic interpretation, it is difficult to reconcile this point of view with our common notion of “phy ...
"Rovelli's World"
... The observer can be any physical object having a definite state of motion. For instance, I say that my hand moves at a velocity v with respect to the lamp on my table. Velocity is a relational notion (in Galilean as well as in special relativistic physics), and thus it is always (explicitly or impli ...
... The observer can be any physical object having a definite state of motion. For instance, I say that my hand moves at a velocity v with respect to the lamp on my table. Velocity is a relational notion (in Galilean as well as in special relativistic physics), and thus it is always (explicitly or impli ...
Dynamics of Open Quantum Systems
... The use of the generally nonlinear QLE (2) is limited in practice for several reasons. More importantly, the application of the QLE bears some subtleties and pitfalls which must be observed when making approximations. These same subtleties typically also emerge with other approaches/methods to quant ...
... The use of the generally nonlinear QLE (2) is limited in practice for several reasons. More importantly, the application of the QLE bears some subtleties and pitfalls which must be observed when making approximations. These same subtleties typically also emerge with other approaches/methods to quant ...
MODULE MAPS OVER LOCALLY COMPACT QUANTUM GROUPS
... Let G = (L∞ (G), Γ, ϕ, ψ) be a von Neumann algebraic locally compact quantum group and let L1 (G) be the convolution quantum group algebra of G. If we let C0 (G) be the reduced C ∗ -algebra associated with G, then its operator dual M (G) is a faithful completely contractive Banach algebra containing ...
... Let G = (L∞ (G), Γ, ϕ, ψ) be a von Neumann algebraic locally compact quantum group and let L1 (G) be the convolution quantum group algebra of G. If we let C0 (G) be the reduced C ∗ -algebra associated with G, then its operator dual M (G) is a faithful completely contractive Banach algebra containing ...
Quantum computing
Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits (qubits), which can be in superpositions of states. A quantum Turing machine is a theoretical model of such a computer, and is also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers. The field of quantum computing was initiated by the work of Yuri Manin in 1980, Richard Feynman in 1982, and David Deutsch in 1985. A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968.As of 2015, the development of actual quantum computers is still in its infancy, but experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits. Both practical and theoretical research continues, and many national governments and military agencies are funding quantum computing research in an effort to develop quantum computers for civilian, business, trade, and national security purposes, such as cryptanalysis.Large-scale quantum computers will be able to solve certain problems much more quickly than any classical computers that use even the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible probabilistic classical algorithm.Given sufficient computational resources, however, a classical computer could be made to simulate any quantum algorithm, as quantum computation does not violate the Church–Turing thesis.