Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1907.05807 · Physical Review X

When Is a Non-Markovian Quantum Process Classical?

Simon Milz, Dario Egloff, Philip Taranto, Thomas Theurer, Martin Bodo Plenio, Andrea Smirne, Susana F. Huelga

Published Dec 10, 2020• 101 citations
arXivHTMLPDF

Abstract

A new paradigm for separating what is inherently quantum from what is classical relies solely on observable quantities and makes it possible to identify the mechanisms leading to nonclassicality in a wide range of situations.
DOI
10.1103/physrevx.10.041049

Related papers

Automatic generation of test circuits for the verification of Quantum deterministic algorithms

Antonio García de la Barrera, Manuel Serrano, Ignacio García‐Rodríguez de Guzmán +2 more

Quantum computing will make it possible to exponentially accelerate the performance of a wide range of computational problems, such as cryptography, machine learning or chemical simulation. However, the quantum potential is not only a matter of hardware, but also of software. Therefore, this new paradigm has an impact yet to be explored on software development processes and techniques, and the adaptation of classical software engineering to the new classical/quantum hybrid systems raises a number of important challenges: a new Quantum Software Engineering is therefore needed. Specifically, and focusing on quantum software quality, software verification remains an open research question, as its novelty and complexity make quantum software development a particularly error-prone process. Most current approaches to test-driven verification rely heavily on simulations, which is a problem due to the lack of scalability of simulators running on classical computers. To address this shortcoming, we define the concept of a "Quantum Test Case", and then present a method to test quantum circuits on real machines, without using simulation test functionalities such as amplitude calculation or non-destructive measurement. This is achieved by automatically generating a Quantum Test Case, which wraps the circuit under test and performs the verification. We also present the process to run a set of tests on a circuit with this method, along with an example to illustrate the technique.

•Nov 7, 2022•7 citations

Quantum physical systems as classical systems

Antonio Cassa

A physical system showing a classical (deterministic) behavior to an observer can appear to be a quantum system to another observer unable to distinguish between some distinct states.

arXiv:quant-ph/0111070•Journal of Mathematical Physics•Nov 1, 2001•3 citations

Semiclassical formulation of non-Markovian quantum Brownian motion

Werner Koch, Frank Großmann, Joachim Ankerhold +1 more

Physica E Low-dimensional Systems and Nanostructures•Jun 25, 2009•1 citation

Non-Markovianity of photon dynamics in a birefringent crystal

Kai-Hung Wang, Shih-Hsuan Chen, Yu‐Cheng Lin +1 more

The way a principle system and its environment interact characterizes the non-Markovianity of the dynamics. Herein, we investigate the non-Markovian dynamics of photon polarization in a birefringent crystal. We consider the so-called ``quantity of quantum-mechanical process'' first defined by Hsieh et al. [Sci. Rep. 7, 13588 (2017)]. The non-Markovianity of the photon dynamics is evaluated by examining the quantity of quantum-mechanical process varying with time, and the difference between the quantity of quantum-mechanical process in a complete dynamics and that in a process composed of two subprocesses. We show that all of the processes identified as Markovian in the seminal study of Liu et al. [Nat. Phys. 7, 931 (2011)] can actually be identified as non-Markovian. The presented method enables us to classify non-Markovianity in the dynamical processes that are classified as Markovian by existing verification criteria. Overall, the results confirm the feasibility of performing the experimental characterization of photon dynamics using an all-optical setup and provide a useful insight into enhancing the accuracy and control of quantum system designs for quantum engineering applications.

arXiv:1810.03829•Physical Review A•Oct 29, 2018•5 citations

Evolution Equations for Quantum Semi-Markov Dynamics

Nina Megier, Andrea Smirne, Bassano Vacchini

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the corresponding classical concept, guarantees mathematically well-defined master equations, while accounting for a wide range of phenomena, possibly in the non-Markovian regime. In particular, we analyse the emergence of a dephasing term when moving from one type of master equation to the other, by means of several examples. We also investigate the corresponding Redfield-like approximated dynamics, which are obtained after a coarse graining in time. Relying on general properties of the associated classical random process, we conclude that such an approximation always leads to a Markovian evolution for the considered class of dynamics.

arXiv:2007.11276•Entropy•Jul 21, 2020•13 citations

Non-Markovian quantum stochastic processes and their entropy

Göran Lindblad

Communications in Mathematical Physics•Oct 1, 1979•122 citations
Quantum computing will make it possible to exponentially accelerate the performance of a wide range of computational problems, such as cryptography, machine learning or chemical simulation. However, the quantum potential is not only a matter of hardware, but also of software. Therefore, this new paradigm has an impact yet to be explored on software development processes and techniques, and the adaptation of classical software engineering to the new classical/quantum hybrid systems raises a number of important challenges: a new Quantum Software Engineering is therefore needed. Specifically, and focusing on quantum software quality, software verification remains an open research question, as its novelty and complexity make quantum software development a particularly error-prone process. Most current approaches to test-driven verification rely heavily on simulations, which is a problem due to the lack of scalability of simulators running on classical computers. To address this shortcoming, we define the concept of a "Quantum Test Case", and then present a method to test quantum circuits on real machines, without using simulation test functionalities such as amplitude calculation or non-destructive measurement. This is achieved by automatically generating a Quantum Test Case, which wraps the circuit under test and performs the verification. We also present the process to run a set of tests on a circuit with this method, along with an example to illustrate the technique.
The way a principle system and its environment interact characterizes the non-Markovianity of the dynamics. Herein, we investigate the non-Markovian dynamics of photon polarization in a birefringent crystal. We consider the so-called ``quantity of quantum-mechanical process'' first defined by Hsieh et al. [Sci. Rep. 7, 13588 (2017)]. The non-Markovianity of the photon dynamics is evaluated by examining the quantity of quantum-mechanical process varying with time, and the difference between the quantity of quantum-mechanical process in a complete dynamics and that in a process composed of two subprocesses. We show that all of the processes identified as Markovian in the seminal study of Liu et al. [Nat. Phys. 7, 931 (2011)] can actually be identified as non-Markovian. The presented method enables us to classify non-Markovianity in the dynamical processes that are classified as Markovian by existing verification criteria. Overall, the results confirm the feasibility of performing the experimental characterization of photon dynamics using an all-optical setup and provide a useful insight into enhancing the accuracy and control of quantum system designs for quantum engineering applications.
Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the corresponding classical concept, guarantees mathematically well-defined master equations, while accounting for a wide range of phenomena, possibly in the non-Markovian regime. In particular, we analyse the emergence of a dephasing term when moving from one type of master equation to the other, by means of several examples. We also investigate the corresponding Redfield-like approximated dynamics, which are obtained after a coarse graining in time. Relying on general properties of the associated classical random process, we conclude that such an approximation always leads to a Markovian evolution for the considered class of dynamics.