Robust Implementation of Discrete-time Quantum Walks in Any Finite-dimensional Quantum System

TL;DR

This paper presents a method to implement discrete-time quantum walks efficiently on finite-dimensional quantum systems, reducing circuit complexity and enabling more reliable quantum computations without ancilla qubits.

Contribution

The authors introduce a new approach that halves circuit cost and extends implementation to any finite-dimensional quantum system using intermediate qudits, improving scalability and efficiency.

Findings

Circuit cost reduced by 50% compared to previous methods

Implementation successful in any finite-dimensional quantum system

Supports reliable quantum walk execution on NISQ devices

Abstract

Research has shown that quantum walks can accelerate certain quantum algorithms and act as a universal paradigm for quantum processing. The discrete-time quantum walk (DTQW) model, owing to its discrete nature, stands out as one of the most suitable choices for circuit implementation. Nevertheless, most current implementations are characterized by extensive, multi-layered quantum circuits, leading to higher computational expenses and a notable decrease in the number of confidently executable time steps on current quantum computers. Since quantum computers are not scalable enough in this NISQ era, we also must confine ourselves to the ancilla-free frontier zone. Therefore, in this paper, we have successfully cut down the circuit cost concerning gate count and circuit depth by half through our proposed methodology in qubit systems as compared to the state-of-the-art increment-decrement approach. Furthermore, for the engineering excellence of our proposed approach, we implement DTQW in any finite-dimensional quantum system with akin efficiency. To ensure an efficient implementation of quantum walks without requiring ancilla, we have incorporated an intermediate qudit technique for decomposing multi-qubit gates. Experimental outcomes hold significance far beyond the realm of just a few time steps, laying the groundwork for dependable implementation and utilization on quantum computers.