Non-Markovian approach to quantum state fluctuations in noisy intermediate-scale quantum (NISQ) devices

Doyeol Ahn, Byeongyong Park

Published 2023-02-10Version 1

It is crucial to reduce the impact of errors and decoherence in near-term quantum computers, such as noisy intermediate-scale quantum (NISQ) devices. As these factors severely limit the feasibility of quantum algorithms, it is imperative to comprehend their physical causes in order to execute error mitigation procedures effectively. This paper presents a non-Markovian examination of quantum state fluctuations in NISQ devices interacting with an environment described by a set of simple harmonic oscillators as a noise source. The reduced density operator for the output quantum states is obtained in time-convolutionless form through the solution of the quantum Liouville equation using the projection operator formalism and advanced and retarded propagators in time. The output quantum state fluctuations for both identity and controlled-NOT (CNOT) gate operations are analyzed for different input states in a two-qubit operation and compared to experimental results from ion-trap and superconducting quantum computing systems. The study finds a strong correlation between the theoretical predictions and the experimental results for an ion-trap-based NISQ device.