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Threshold theorem in isolated quantum dynamics with stochastic control errors.

Threshold theorem in isolated quantum dynamics with stochastic control errors.

Authors :
Okuyama, Manaka
Ohki, Kentaro
Ohzeki, Masayuki
Source :
Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences. 1/23/2023, Vol. 381 Issue 2241, p1-7. 7p.
Publication Year :
2023

Abstract

We investigate the effect of stochastic control errors in the time-dependent Hamiltonian on isolated quantum dynamics. The control errors are formulated as time-dependent stochastic noise in the Schrödinger equation. For a class of stochastic control errors, we establish a threshold theorem that provides a sufficient condition to obtain the target state, which should be determined in noiseless isolated quantum dynamics, as a relation between the number of measurements and noise strength. The theorem guarantees that if the sum of the noise strengths is less than the inverse of computational time, the target state can be obtained through a constant-order number of measurements. If the opposite is true, the number of measurements to guarantee obtaining the target state increases exponentially with computational time. Our threshold theorem can be applied to any isolated quantum dynamics such as quantum annealing and adiabatic quantum computation. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
1364503X
Volume :
381
Issue :
2241
Database :
Academic Search Index
Journal :
Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
Publication Type :
Academic Journal
Accession number :
161137962
Full Text :
https://doi.org/10.1098/rsta.2021.0412