Noisy simulations of Quantum Walk and Quantum Walk search via Quantum Cellular Automata on a semiconducting spin processor emulator

TL;DR

This paper explores the implementation and simulation of quantum walks and search algorithms using Quantum Cellular Automata on a cQED-based semiconducting spin processor emulator, highlighting their potential for NISQ-era quantum computing.

Contribution

It introduces a mapping of QCA to cQED hardware, performs both noiseless and noisy simulations, and develops a circuit for W state preparation without ancillas, advancing NISQ-compatible quantum algorithms.

Findings

QCA framework is promising for NISQ quantum algorithms

Successful simulation of quantum walk and search on emulator

Performance metrics indicate viability of the approach

Abstract

In this work we map NISQ-friendly implementations of the non-interacting QCA to a circuit Quantum Electrodynamics (cQED) hardware. We perform both noiseless and noisy simulations of the QCA one particle sector, namely the Quantum Walk, on $N$-cycles and $N \times N$ torus graphs. Moreover, within this framework, we also investigate the search problem and present a circuit for preparing the W state (i.e., the Dicke state with hamming weight one) using only N-1 $\sqrt{\text{iSWAP}}$ gates and no ancilla qubits. The noiseless simulations are conducted with the Qiskit Aer simulator, while the noisy simulations with C12 Quantum Electronics' in-house noisy emulator, \textit{Callisto}. We benchmark the performance of our implementations by analyzing the simulations via relevant metrics and quantities such as the state count distributions, the Hellinger Fidelity, the $\ell^{1}$ distance, the hitting time, and success probability. Our results demonstrate that the QCA framework, in combination with cQED processors, holds promise as an effective platform for early NISQ implementations of Quantum Walk and Quantum Walk Search algorithms.