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

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Mathematical models of quantum noise

Yu. I. Bogdanov, Andrey Yu. Chernyavskiy, Alexander Semenovich Holevo, Vladimir F. Lukichev, Alexander A. Orlikovsky

Published Jan 8, 2013• 8 citations
Publisher

Abstract

This paper presents a review of different ways of quantum operation descriptions, including operator-sums, unitary representations, Choi-Jamiolkowski state representations and the corresponding chi-matrices, as well as quantum system evolution operators. These models are equivalent, but each one is useful in different applications. The main application of these models is simulation and analysis of quantum computer noisy gates.

DOI
10.1117/12.2017396

Related papers

Creating, maintaining, and breaking of quantum entanglement in quantum operations

Yu. I. Bogdanov, Andrey Yu. Chernyavskiy, Alexander Semenovich Holevo +3 more

We study the evolution of entanglement in quantum gates in terms of Choi-Jamiolkowski relative states negativity. SQiSW (generated by XY-interaction), CNOT and CZ gates are considered in ideal case and under amplitude and phase relaxation. In addition, we consider an important task of analyzing entanglement of “pure” noise, which is obtained by deducting an ideal gate from a noisy one.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 8, 2013•1 citation

Mathematical modeling and experimental study of polarization echo in optically anisotropic media

Yu. I. Bogdanov, Alexander A. Kalinkin, S. P. Kulik +3 more

As optical systems are one of the candidates for implementation of a scalable quantum computer, it is important to develop an adequate method of description of both quantum states of light and operations performed by optical elements. Using the concept of chi-matrix representation of quantum operations and Choi-Jamiolkowski isomorphism we expand Jones calculus to allow description of evolution of mixed polarization states in linear optical systems. The developed method is then used to give a full description of polarization echo effect, which was described in 1 based on an analogy between the effects of polarization optics and spin dynamics. Theoretical predictions are confirmed by reconstructing operations performed by a series of quartz waveplates using quantum process tomography protocols.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 8, 2013•1 citation

Reduced Dynamical Maps in Finite Temperature Vibronic Coupling Models via Choi Matrices: Numerical Methods and Applications

Raffaele Borrelli, Hideaki Takahashi

We present a streamlined implementation of a computational framework for constructing and analyzing reduced dynamical maps for complex system--bath models at finite temperature. The methodology is based on three established ingredients of quantum dynamics: the Choi--Jamiołkowski isomorphism for the representation of quantum channels, thermofield (TFD) purification of thermal environments, and tensor-train (TT) propagation of the resulting enlarged pure state. The reduced map is obtained from a single unitary propagation in a thermofield-doubled Hilbert space and represented in matrix form through the Choi--Jamiołkowski isomorphism. The TFD evolution is implemented in the TT representation, enabling efficient propagation of high-dimensional purified thermal states. We illustrate the methodology for exciton transfer in the Fenna--Matthews--Olson complex with site-dependent structured spectral densities represented by discretized bosonic environments. The resulting maps are used to analyze decoherence, relaxation, and finite-memory effects, and to assess the crossover to an effectively time-local description. The proposed approach provides a route to compute reduced propagators and to post-process them into memory kernels, transfer tensors, and effective kinetic rate descriptions for complex molecular systems.

quant-pharXiv:2605.22459•The Journal of Chemical Physics•May 22, 2026•0 citations

Quantum Noise

Binayak Samadder Choudhury, Soumen Samanta

This chapter is on quantum noise. The origin of noise as a part of interaction with the environment is discussed. The Kraus operator formulation of noise along with various special types of noises are presented. References [ 14 , 32 , 44 , 77 , 109 , 113 , 115 , 131 ] are helpful to understand different aspects of quantum noise.

Chapman & Hall/CRC eBooks•Dec 10, 2025•0 citations

On Open Quantum Systems and Mathematical Modeling of Quantum Noise

Andrzej Jamiokowski

In modeling of physical systems for which time behaviour can be represented by stochastic processes one assumes that a system in question is described by certain mathematical model, for example, by random variables in classical case or by sets of non-commuting observables in quantum case, acting on an abstract probability space. In most cases our assumptions are not believed to be a fully realistic model of the physical reality, but nevertheless very often it turns out to be extremely useful.

InTech eBooks•Jul 24, 2013•1 citation

Models of quantum computation and quantum programming languages

Jarosław Adam Miszczak

Models of quantum computation and quantum programming languages The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.

arXiv:1012.6035•Bulletin of the Polish Academy of Sciences Technical Sciences•Sep 1, 2011•34 citations
This paper presents a review of different ways of quantum operation descriptions, including operator-sums, unitary representations, Choi-Jamiolkowski state representations and the corresponding chi-matrices, as well as quantum system evolution operators. These models are equivalent, but each one is useful in different applications. The main application of these models is simulation and analysis of quantum computer noisy gates.
As optical systems are one of the candidates for implementation of a scalable quantum computer, it is important to develop an adequate method of description of both quantum states of light and operations performed by optical elements. Using the concept of chi-matrix representation of quantum operations and Choi-Jamiolkowski isomorphism we expand Jones calculus to allow description of evolution of mixed polarization states in linear optical systems. The developed method is then used to give a full description of polarization echo effect, which was described in 1 based on an analogy between the effects of polarization optics and spin dynamics. Theoretical predictions are confirmed by reconstructing operations performed by a series of quartz waveplates using quantum process tomography protocols.
We present a streamlined implementation of a computational framework for constructing and analyzing reduced dynamical maps for complex system--bath models at finite temperature. The methodology is based on three established ingredients of quantum dynamics: the Choi--Jamiołkowski isomorphism for the representation of quantum channels, thermofield (TFD) purification of thermal environments, and tensor-train (TT) propagation of the resulting enlarged pure state. The reduced map is obtained from a single unitary propagation in a thermofield-doubled Hilbert space and represented in matrix form through the Choi--Jamiołkowski isomorphism. The TFD evolution is implemented in the TT representation, enabling efficient propagation of high-dimensional purified thermal states. We illustrate the methodology for exciton transfer in the Fenna--Matthews--Olson complex with site-dependent structured spectral densities represented by discretized bosonic environments. The resulting maps are used to analyze decoherence, relaxation, and finite-memory effects, and to assess the crossover to an effectively time-local description. The proposed approach provides a route to compute reduced propagators and to post-process them into memory kernels, transfer tensors, and effective kinetic rate descriptions for complex molecular systems.
Models of quantum computation and quantum programming languages The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.