Quantum margulis expanders

2008 ◽  
Vol 8 (8&9) ◽  
pp. 722-733
Author(s):  
D. Gross ◽  
J. Eisert
Keyword(s):  
Phase Space ◽  
Probability Distributions ◽  
Continuous Variable ◽  
Continuous Phase ◽  
Classical Counterpart ◽  
Essential Properties ◽  
Quantum Version ◽  
Phase Space Methods ◽  
Continuous Phase Space ◽  
Complete Analogy

We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The quantum version shares all essential properties of the classical counterpart, e.g., it has the same degree and spectrum. Unlike previous constructions of quantum expanders, our method does not rely on non-Abelian harmonic analysis. Analogues for continuous variable systems are mentioned. Indeed, the construction seems one of the few instances where applications based on discrete and continuous phase space methods can be developed in complete analogy.

scholarly journals Efficiency of molecular machines with continuous phase space

2012 ◽  
Vol 97 (6) ◽  
pp. 60005 ◽  
Author(s):  
N. Golubeva ◽  
A. Imparato ◽  
L. Peliti
Keyword(s):  
Phase Space ◽  
Molecular Machines ◽  
Continuous Phase ◽  
Continuous Phase Space

scholarly journals Entropy Production in Continuous Phase Space Systems

2013 ◽  
Vol 153 (5) ◽  
pp. 828-841 ◽  
Author(s):  
David Luposchainsky ◽  
Haye Hinrichsen
Keyword(s):  
Phase Space ◽  
Entropy Production ◽  
Continuous Phase ◽  
Space Systems ◽  
Continuous Phase Space

A New Uncertainty Analysis-Based Framework for Data-Driven Computational Mechanics

2021 ◽  
pp. 1-22
Author(s):  
Xu Guo ◽  
Zongliang Du ◽  
Chang Liu ◽  
Shan Tang
Keyword(s):  
Phase Space ◽  
Uncertainty Analysis ◽  
Distinctive Feature ◽  
Computational Mechanics ◽  
Problem Formulation ◽  
Solution Set ◽  
Data Driven ◽  
Data Set ◽  
Classical Counterpart ◽  
Single Solution

Abstract In the present paper, a new uncertainty analysis-based framework for data-driven computational mechanics (DDCM) is established. Compared with its practical classical counterpart, the distinctive feature of this framework is that uncertainty analysis is introduced into the corresponding problem formulation explicitly. Instated of only focusing on a single solution in phase space, a solution set is sought for in order to account for the influence of the multi-source uncertainties associated with the data set on the data-driven solutions. An illustrative example provided shows that the proposed framework is not only conceptually new, but also has the potential of circumventing the intrinsic numerical difficulties pertaining to the classical DDCM framework.

scholarly journals Nonequilibrium dynamics of spin-boson models from phase-space methods

2017 ◽  
Vol 96 (3) ◽  
Author(s):  
Asier Piñeiro Orioli ◽  
Arghavan Safavi-Naini ◽  
Michael L. Wall ◽  
Ana Maria Rey
Keyword(s):  
Phase Space ◽  
Nonequilibrium Dynamics ◽  
Phase Space Methods

scholarly journals Coherent representation of fields and deformation quantization

2020 ◽  
Vol 17 (11) ◽  
pp. 2050166 ◽  
Author(s):  
Jasel Berra-Montiel ◽  
Alberto Molgado
Keyword(s):  
Phase Space ◽  
Deformation Quantization ◽  
Probability Distributions ◽  
Series Representation ◽  
Quantum Field ◽  
Husimi Distribution ◽  
Normal Star ◽  
Holomorphic Representation ◽  
Functional Distribution ◽  
Space Description

Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution associated with a normal ordered operator. This relation also allows to establish a [Formula: see text]-equivalence between the Moyal and the normal star-products. In addition, by writing the density operator in terms of coherent states we are able to directly introduce a series representation of the Wigner functional distribution, which may be convenient in order to calculate probability distributions of quantum field observables without performing formal phase space integrals at all.

scholarly journals Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Agung Budiyono ◽  
Hermawan K. Dipojono
Keyword(s):  
Phase Space ◽  
Continuous Variable ◽  
Complex Hilbert Space ◽  
Quantum Circuits ◽  
Space Distribution ◽  
Space Representation ◽  
Specific Class ◽  
Expectation Values ◽  
Conceptual Tool ◽  
Quantum Uncertainty

Abstract We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable—after the Heisenberg evolution associated with the circuits—is at most second order in momentum. The classical computational algorithm exploits a specific epistemic restriction in classical phase space which directly captures the quantum uncertainty relation, to transform the quantum circuits in the complex Hilbert space into classical albeit unconventional stochastic processes in the phase space. The resulting multidimensional integral is then evaluated using the Monte Carlo sampling method. The convergence rate of the classical sampling algorithm is determined by the variance of the classical physical quantity over the epistemically restricted phase space distribution. The work shows that for the specific class of computational schemes, Wigner negativity is not a sufficient resource for quantum speedup. It highlights the potential role of the epistemic restriction as an intuitive conceptual tool which may be used to study the boundary between quantum and classical computations.

scholarly journals Fidelity of Gaussian Channels

2004 ◽  
Vol 11 (04) ◽  
pp. 309-323 ◽  
Author(s):  
Carlton M. Caves ◽  
Krzysztof Wódkiewicz
Keyword(s):  
Phase Space ◽  
Scaling Law ◽  
Continuous Variable ◽  
Gaussian Channel ◽  
Quantum Cloning ◽  
Field Mode ◽  
Universal Scaling ◽  
Input Field ◽  
Gaussian Channels ◽  
Initial States

A noisy Gaussian channel is defined as a channel in which an input field mode is subjected to random Gaussian displacements in phase space. We introduce the quantum fidelity of a Gaussian channel for pure and mixed input states, and we derive a universal scaling law of the fidelity for pure initial states. We also find the maximum fidelity of a Gaussian channel over all input states. Quantum cloning and continuous-variable teleportation are presented as physical examples of Gaussian channels to which the fidelity results can be applied.

Sign in / Sign up

Export Citation Format

Share Document