Gate-Based Circuit Designs For Quantum Adder Inspired Quantum Random Walks on Superconducting Qubits

TL;DR

This paper explores implementing Coin Quantum Random Walks on superconducting qubits using a quantum adder-based shift operator, analyzing circuit efficiency and demonstrating feasibility on IBM's NISQ device.

Contribution

It introduces a novel quantum circuit design for quantum walks with boundary conditions on superconducting qubits, including experimental fidelity results.

Findings

Circuit depth and gate count are manageable for current NISQ devices.

Boundary condition implementation is effective in 1D and 2D.

Quantum walks can be run with reasonable fidelity on IBM's quantum hardware.

Abstract

Quantum Random Walks, which have drawn much attention over the past few decades for their distinctly non-classical behavior, is a promising subfield within Quantum Computing. Theoretical framework and applications for these walks have seen many great mathematical advances, with experimental demonstrations now catching up. In this study, we examine the viability of implementing Coin Quantum Random Walks using a Quantum Adder based Shift Operator, with quantum circuit designs specifically for superconducting qubits. We focus on the strengths and weaknesses of these walks, particularly circuit depth, gate count, connectivity requirements, and scalability. We propose and analyze a novel approach to implementing boundary conditions for these walks, demonstrating the technique explicitly in one and two dimensions. And finally, we present several fidelity results from running our circuits on IBM's quantum volume 32 `Toronto' chip, showcasing the extent to which these NISQ devices can currently handle quantum walks.