委托量子计算验证方法研究综述

doi:10.11871/jfdc.issn.2096-742X.2025.06.006

数据与计算发展前沿 ›› 2025, Vol. 7 ›› Issue (6): 55-67.

CSTR: 32002.14.jfdc.CN10-1649/TP.2025.06.006

doi: 10.11871/jfdc.issn.2096-742X.2025.06.006

• 专刊：第40次全国计算机安全学术交流会征文 • 上一篇下一篇

委托量子计算验证方法研究综述

袁梓萌^1,²(),龙春^1,^2,^*(),李婧²,杨帆²,付豫豪²,魏金侠^1,²,万巍^1,²

1.中国科学院大学，北京 100190
2.中国科学院计算机网络信息中心，北京 100083

收稿日期:2025-08-01 出版日期:2025-12-20 发布日期:2025-12-17
通讯作者: 龙春
作者简介:袁梓萌，中国科学院计算机网络信息中心，博士研究生，主要研究方向为量子信息处理。
本文承担工作为：文献调研与分析，论文撰写。
YUAN Zimeng is a Ph.D. student at the Computer Network Information Center, Chinese Academy of Sciences. His main research interest is quantum information processing.
In this paper, he is mainly responsible for literature research, analysis, and manuscript writing.
E-mail: zmyuan@cnic.cn|龙春，中国科学院计算机网络信息中心，正高级工程师，博士生导师。中国计算机学会安全专委会委员，中国互联网协会青年专家。主要研究方向为智能网络安全保障、安全大数据挖掘与深度分析等。
本文承担工作为：课题背景支撑，论文框架指导。
LONG Chun is a professorate senior engineer and PhD supervisor at the Computer Network Information Center, Chinese Academy of Sciences. He is also a member of the Technical Committee on Security, China Computer Federation (CCF), and a young expert of the China Internet Association. His main research interests are intelligent cybersecurity assurance, security big data mining, and deep analytics.
In this paper, he is mainly responsible for providing background support and guidance on the overall framework.
E-mail: anquanip@cnic.cn
基金资助:
中国科学院网络安全和信息化专项(CAS-WX2022GC-04);中国科学院青年创新促进会项目(2022170)

Survey of Verification Methods for Delegated Quantum Computation

YUAN Zimeng^1,²(),LONG Chun^1,^2,^*(),LI Jing²,YANG Fan²,FU Yuhao²,WEI Jinxia^1,²,WAN Wei^1,²

1. University of Chinese Academy of Sciences, Beijing 100190, China
2. Computer Network Information Center, Chinese Academy of Sciences, Beijing 100083, China

Received:2025-08-01 Online:2025-12-20 Published:2025-12-17
Contact: LONG Chun

摘要/Abstract

摘要：

【目的】系统梳理和分析委托量子计算验证方法的研究进展与现状。【文献范围】本文调研了1994年至2025年主流会议与期刊的74篇文献，涵盖量子计算验证领域的核心成果与最新进展。【方法】以客户端量子能力需求为主线，将验证方法分为三类（弱量子能力、纠缠、计算假设），构建分类框架；通过对比通信模式、资源开销、容错性等维度，提炼方法演进规律与优劣。【结果】发现三类方法形成互补格局：弱量子方案最成熟但需客户端具备量子能力；纠缠方案仅要求经典客户端但需多服务器协同；计算假设方案通信最简单但依赖后量子密码学。资源开销从指数级降至近线性，但理论优化渐近瓶颈。【结论】研究重心正从理论优化转向应用落地，亟需跨平台实验验证与多方委托计算场景标准化协议。

关键词: 量子计算, 委托计算, 可验证计算, 量子密码学

Abstract:

[Objective] This paper systematically reviews and analyzes the research progress and current status of the verification methods for delegated quantum computation. [Coverage] This paper surveys 74 publications from mainstream conferences and journals spanning 1994 to 2025, covering core achievements and cutting-edge developments in quantum computing verification. [Methods] Classifying verification methods into three categories (weak quantum capability, entanglement, computational assumptions) based on client-side quantum capability requirements, we establish a taxonomy framework. By comparing communication patterns, overhead and fault tolerance, we distill evolutionary trends and comparative advantages of these approaches. [Results] Three complementary patterns emerge: weak-quantum-client schemes offer maturity but require client-side quantum capabilities; entanglement-based schemes need only classical clients but require multi-server collaboration; computational-assumption schemes feature minimal communication yet rely on post-quantum cryptography. Overhead decreases from exponential to near-linear complexity, though theoretical optimization is approaching asymptotic bottlenecks. [Conclusions] Research focus is shifting from theoretical optimization to practical deployment, urgently demanding cross-platform experimental validation and standardized protocols for multi-party delegated computation scenarios.

Key words: quantum computation, delegated computation, verification of computation, quantum cryptography

袁梓萌,龙春,李婧,杨帆,付豫豪,魏金侠,万巍. 委托量子计算验证方法研究综述[J]. 数据与计算发展前沿, 2025, 7(6): 55-67.

YUAN Zimeng,LONG Chun,LI Jing,YANG Fan,FU Yuhao,WEI Jinxia,WAN Wei. Survey of Verification Methods for Delegated Quantum Computation[J]. Frontiers of Data and Computing, 2025, 7(6): 55-67, https://cstr.cn/32002.14.jfdc.CN10-1649/TP.2025.06.006.

图/表 10

图1

图2

图3

图4

表1

基于陷阱的委托量子计算验证方案对比"

验证方案	特点	容错性	资源开销
Fitzsimons与Kashefi^[23]	利用RHG方案^[24]插入陷阱	有	$O n 2$
Kashefi与Wallden^[25]	利用“三倍点缀”方法插入陷阱	无	线性级别
Ferracin等人^[26]	将资源态的某些量子比特替换为陷阱	无	线性级别
Leichtle等人^[27]	在Ferracin等人方案的基础上引入多数投票机制	有	线性级别

表1

图5

表2

基于稳定子检测的委托量子计算验证方案对比"

验证方案	验证的资源态类型	资源开销
Morimae^[31]	RHG态^[24]	指数级别
Hayashi与Morimae^[32]	一般图态	指数级别
Miller与Miyake^[33]	Union Jack态（超图态）	指数级别
Morimae等人^[34]	超边度数为2或3的超图态	$O n 21$
Takeuchi与Morimae^[35]	一般超图态	$O n 21$
Takeuchi等人^[36]	一般超图态	$O n 5 l o g n$
Zhu与Hayashi^[37]	一般超图态	$O n 2 l o g n$
Zhu与Hayashi^[38]	一般量子态	$O n 2 l o g n$
Tao等人^[39]	m-染色超图态	$O n 21$
Li等人^[40]	一般图态	$O n l o g n$

表2

图6

图7

表3

三类委托量子计算验证方法对比"

验证方法	通信需求	客户端能力需求	服务器数目	计算假设需求	安全性	效率	实现难度
基于弱量子能力	受限量子通信、经典通信	弱量子客户端	$1$	无	强	高	适中
基于纠缠	经典通信	经典客户端	$≥ 2$	无	强	低	困难
基于计算假设	经典通信	经典客户端	$1$	量子计算难题	适中	中	简单

表3

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委托量子计算验证方法研究综述

Survey of Verification Methods for Delegated Quantum Computation

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