The effect of quantum noise on algorithmic perfect quantum state transfer on NISQ processors

TL;DR

This paper examines how various quantum noise sources impact the fidelity and timing of perfect state transfer in quantum walks on NISQ devices, proposing error mitigation techniques to improve transfer accuracy.

Contribution

It provides a detailed simulation of noise effects on quantum walk-based state transfer and introduces an error mitigation method for noisy quantum processors.

Findings

Pauli noise reduces transfer fidelity peak

Crosstalk affects hitting time significantly

Error mitigation improves transfer results

Abstract

Quantum walks are an analog of classical random walks in quantum systems. Quantum walks have smaller hitting times compared to classical random walks on certain types of graphs, leading to a quantum advantage of quantum-walks-based algorithms. An important feature of quantum walks is that they are accompanied by the excitation transfer from one site to another, and a moment of hitting the destination site is characterized by the maximum probability amplitude of observing the excitation on this site. It is therefore prospective to consider such problems as candidates for quantum advantage demonstration, since gate errors can smear out a peak in the transfer probability as a function of time, nevertheless leaving it distinguishable. We investigate the influence of quantum noise on hitting time and fidelity of a typical quantum walk problem - a perfect state transfer (PST) over a qubit chain. We simulate dynamics of a single excitation over the chain of qubits in the presence of typical noises of a quantum processor (homogeneous and inhomogeneous Pauli noise, crosstalk noise, thermal relaxation, and dephasing noise). We find that Pauli noise mostly smears out a peak in the fidelity of excitation transfer, while crosstalks between qubits mostly affect the hitting time. Knowledge about these noise patterns allows us to propose an error mitigation procedure, which we use to refine the results of running the PST on a simulator of a noisy quantum processor.