Shallow unitary decompositions of quantum Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging

Author:

M. Q. Cruz Pedro123ORCID,Murta Bruno14ORCID

Affiliation:

1. International Iberian Nanotechnology Laboratory (INL) 1 , 4715-330 Braga, Portugal

2. ICFO–Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology 2 , 08860 Castelldefels, Spain

3. Departamento de Ciência de Computadores, Universidade do Porto 3 , 4169-007 Porto, Portugal

4. Departamento de Física, Universidade do Minho 4 , 4710-057 Braga, Portugal

Abstract

The controlled-swap and controlled-controlled-not gates are at the heart of the original proposal of reversible classical computation by Fredkin and Toffoli. Their widespread use in quantum computation, both in the implementation of classical logic subroutines of quantum algorithms and in quantum schemes with no direct classical counterparts, has made it imperative early on to pursue their efficient decomposition in terms of the lower-level gate sets native to different physical platforms. Here, we add to this body of literature by providing several logically equivalent circuits for the Toffoli and Fredkin gates under all-to-all and linear qubit connectivity, the latter with two different routings for control and target qubits. Besides achieving the lowest cnot counts in the literature for all these configurations, we also demonstrate the remarkable effectiveness of the obtained decompositions at mitigating coherent errors on near-term quantum computers via equivalent circuit averaging. We first quantify the performance of the method in silico with a coherent-noise model before validating it experimentally on a superconducting quantum processor. In addition, we consider the case where the three qubits on which the Toffoli or Fredkin gates act nontrivially are not adjacent, proposing a novel scheme to reorder them that saves one cnot for every swap. This scheme also finds use in the shallow implementation of long-range cnots. Our results highlight the importance of considering different entangling gate structures and connectivity constraints when designing efficient quantum circuits.

Funder

Fundação para a Ciência e a Tecnologia

Fundación Cellex

Fundació Privada Mir-Puig

Generalitat de-Catalunya

AXA Research Fund

Publisher

AIP Publishing

Reference94 articles.

1. Conservative logic;Int. J. Theor. Phys.,1982

2. Both Toffoli and controlled-NOT need little help to do universal quantum computation;Quantum Infor. Comput.,2002

3. D. Aharonov , “A simple proof that Toffoli and Hadamard are quantum universal,” arXiv:quant-ph/0301040 (2003).

4. Elementary gates for quantum computation;Phys. Rev. A,1995

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Block encodings of discrete subgroups on a quantum computer;Physical Review D;2024-09-09

2. MIRAGE: Quantum Circuit Decomposition and Routing Collaborative Design Using Mirror Gates;2024 IEEE International Symposium on High-Performance Computer Architecture (HPCA);2024-03-02

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3