Efficient sparse state preparation via quantum walks

IF 8.3 1区 物理与天体物理 Q1 PHYSICS, APPLIED
Alvin Gonzales, Rebekah Herrman, Colin Campbell, Igor Gaidai, Ji Liu, Teague Tomesh, Zain H. Saleem
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引用次数: 0

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.

Abstract Image

基于量子行走的高效稀疏态制备
动态图上的连续时间量子行走(ctqw),被称为动态ctqw,是最近引入的一种通用计算模型,它提供了一种设想量子算法的新范式。在这项工作中,我们开发了一种将单边和自环动态ctqw转换为计算门模型的算法。我们利用这种映射引入了一种高效的基于动态ctqw的稀疏量子态制备框架。我们的方法利用组合学技术,如最小命中集、最小生成树和最短哈密顿路径来减少准备稀疏状态所需的受控门的数量。我们通过将该方法重新表述为CTQW,表明我们的框架包含了当前最先进的无辅助稀疏状态制备方法。这种基于ctqw的框架提供了Qiskit使用的均匀控制旋转方法的替代方案,当目标状态具有多项式个数的非零振幅时,需要更少的CX门。
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来源期刊
npj Quantum Information
npj Quantum Information Computer Science-Computer Science (miscellaneous)
CiteScore
13.70
自引率
3.90%
发文量
130
审稿时长
29 weeks
期刊介绍: The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.
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