Euler-Milstein and relevant approaches for high-precision stochastic simulation of quantum trajectories

For quantum diffusive measurements, the system's dynamics can be described by the Itô stochastic master equation, which works well for an infinitesimal time resolution. However, in practical quantum experiments, one cannot make a time step to be infinitesimal, as it can introduce correlation of...

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Main Authors: Nattaphong Wonglakhon, Sujin Suwanna, Areeya Chantasri
Other Authors: Griffith University
Format: Conference or Workshop Item
Published: 2022
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Online Access:https://repository.li.mahidol.ac.th/handle/123456789/79024
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spelling th-mahidol.790242022-08-04T18:28:25Z Euler-Milstein and relevant approaches for high-precision stochastic simulation of quantum trajectories Nattaphong Wonglakhon Sujin Suwanna Areeya Chantasri Griffith University Mahidol University Physics and Astronomy For quantum diffusive measurements, the system's dynamics can be described by the Itô stochastic master equation, which works well for an infinitesimal time resolution. However, in practical quantum experiments, one cannot make a time step to be infinitesimal, as it can introduce correlation of noise in time, making the Markovian assumption invalid. On the other hand, increasing a time step can cause errors from non-commuting operations describing the system's dynamics. We therefore consider implementing the Euler-Milstein and relevant approaches, namely the Itô map, the high-order completely positive map, and the quantum Bayesian, to simulate quantum trajectory for a quantum system under diffusive continuous measurements. In particular, we numerically simulate trajectories for a qubit measurement in z basis. We show the comparison of individual trajectories and their averaged trajectories among these approaches. We find that the high-order completely positive map approach yields the most accurate averaged quantum trajectory. Furthermore, we also investigate the trace distance from true stochastic quantum trajectories, comparing the four approaches using the numerical simulation. We show that, for a realistic time resolution (as in a superconducting qubit experiment), the high-order map does give the most accurate estimate of the qubit trajectories. 2022-08-04T11:28:25Z 2022-08-04T11:28:25Z 2021-01-28 Conference Paper Journal of Physics: Conference Series. Vol.1719, No.1 (2021) 10.1088/1742-6596/1719/1/012099 17426596 17426588 2-s2.0-85100722912 https://repository.li.mahidol.ac.th/handle/123456789/79024 Mahidol University SCOPUS https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85100722912&origin=inward
institution Mahidol University
building Mahidol University Library
continent Asia
country Thailand
Thailand
content_provider Mahidol University Library
collection Mahidol University Institutional Repository
topic Physics and Astronomy
spellingShingle Physics and Astronomy
Nattaphong Wonglakhon
Sujin Suwanna
Areeya Chantasri
Euler-Milstein and relevant approaches for high-precision stochastic simulation of quantum trajectories
description For quantum diffusive measurements, the system's dynamics can be described by the Itô stochastic master equation, which works well for an infinitesimal time resolution. However, in practical quantum experiments, one cannot make a time step to be infinitesimal, as it can introduce correlation of noise in time, making the Markovian assumption invalid. On the other hand, increasing a time step can cause errors from non-commuting operations describing the system's dynamics. We therefore consider implementing the Euler-Milstein and relevant approaches, namely the Itô map, the high-order completely positive map, and the quantum Bayesian, to simulate quantum trajectory for a quantum system under diffusive continuous measurements. In particular, we numerically simulate trajectories for a qubit measurement in z basis. We show the comparison of individual trajectories and their averaged trajectories among these approaches. We find that the high-order completely positive map approach yields the most accurate averaged quantum trajectory. Furthermore, we also investigate the trace distance from true stochastic quantum trajectories, comparing the four approaches using the numerical simulation. We show that, for a realistic time resolution (as in a superconducting qubit experiment), the high-order map does give the most accurate estimate of the qubit trajectories.
author2 Griffith University
author_facet Griffith University
Nattaphong Wonglakhon
Sujin Suwanna
Areeya Chantasri
format Conference or Workshop Item
author Nattaphong Wonglakhon
Sujin Suwanna
Areeya Chantasri
author_sort Nattaphong Wonglakhon
title Euler-Milstein and relevant approaches for high-precision stochastic simulation of quantum trajectories
title_short Euler-Milstein and relevant approaches for high-precision stochastic simulation of quantum trajectories
title_full Euler-Milstein and relevant approaches for high-precision stochastic simulation of quantum trajectories
title_fullStr Euler-Milstein and relevant approaches for high-precision stochastic simulation of quantum trajectories
title_full_unstemmed Euler-Milstein and relevant approaches for high-precision stochastic simulation of quantum trajectories
title_sort euler-milstein and relevant approaches for high-precision stochastic simulation of quantum trajectories
publishDate 2022
url https://repository.li.mahidol.ac.th/handle/123456789/79024
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