Efficient Sparse State Preparation via Quantum Walks

TL;DR

This paper introduces a quantum algorithm that leverages dynamic continuous-time quantum walks to efficiently prepare sparse quantum states, reducing gate complexity compared to existing methods.

Contribution

It develops a novel framework converting dynamic CTQWs into gate models, enabling more efficient sparse state preparation with fewer controlled gates.

Findings

Reduces the number of CX gates needed for sparse state preparation.

Reformulates existing ancilla-free methods within the CTQW framework.

Offers an alternative to the uniform controlled rotation method with better gate efficiency.

Abstract

Continuous-time quantum walks (CTQWs) on dynamic graphs, referred to as dynamic CTQWs, are a recently introduced universal model of computation that offers a new paradigm in which to envision quantum algorithms. In this work we develop an algorithm that converts single-edge and self-loop dynamic CTQWs to the gate model of computation. We use this mapping to introduce an efficient sparse quantum state preparation framework based on dynamic CTQWs. Our approach utilizes combinatorics techniques such as minimal hitting sets, minimum spanning trees, and shortest Hamiltonian paths to reduce the number of controlled gates required to prepare sparse states. We show that our framework encompasses the current state of the art ancilla free sparse state preparation method by reformulating this method as a CTQW. This CTQW-based framework offers an alternative to the uniformly controlled rotation method used by Qiskit by requiring fewer CX gates when the target state has a polynomial number of non-zero amplitudes.