Mathematical modeling of quantum noise and the quality of hardware components of quantum computers

TL;DR

This paper develops methods for modeling quantum operations in quantum computer circuits, analyzing quantum gates under noise, and exploring error correction to improve quantum information processing.

Contribution

It introduces comprehensive modeling techniques for quantum gates considering decoherence and noise, and discusses error correction and entanglement management.

Findings

Modeling of quantum gates under various noise mechanisms.

Analysis of decoherence effects on quantum gate fidelity.

Strategies for error correction and entanglement preservation.

Abstract

In the present paper methods and algorithms of modeling quantum operations for quantum computer integrated circuits design are developed. We examine 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. The results of modeling of practically important quantum gates: SQiSW (square root of i-SWAP gate), controlled-NOT (CNOT), and controlled Z-transform (CZ) subject to different decoherence mechanisms are presented. These mechanisms include analysis of depolarizing quantum noise and processes of amplitude and phase relaxation. Finally, we consider error correction of phase flip, and the tasks of creating and maintaining the entanglement, as well as its breaking for two- and multi-qubit realizations of quantum operations. Importance of the present analysis for the quality and efficiency of quantum information technologies in practical applications is discussed.