基于编译非局域博弈的准线性资源量子计算经典验证

中文摘要 AI 辅助

计算自检验赋予经典验证者对单个计算受限证明者的量子寄存器的控制能力。我们利用这一框架，在电路模型中构建了首个具有准线性总资源需求的BQP论证系统。我们的论证系统基于带误差学习（LWE）假设，对于委托一个包含g个门的电路，总资源需求为$O(\mathrm{poly}(\lambda, \log g)\cdot g)$，其中$\lambda$为LWE安全参数。这是通过构建一个新的计算自检验来认证证明者的量子态，并利用该自检验对Broadbent（ToC 2018）的高效验证协议进行去量子化实现的。具体而言，该自检验能够实现对单量子比特Clifford可观测量$\sigma_X, \sigma_Y, \sigma_Z, (\sigma_Y-\sigma_X)/\sqrt{2}$和$(\sigma_Y+\sigma_X)/\sqrt{2}$的张量积态的可验证、随机远程态制备，且具有常数鲁棒性：验证误差与所制备的量子比特数量无关。该方法最初由Coladangelo等人（ToC 2024）在多证明者设置中提出。我们通过将Kalai等人（STOC 2023）提出的编译器——该编译器可将任意非局域博弈转化为单证明者论证系统——应用于其自检验的修改版本，在单证明者设置中复现了他们的结果。

英文摘要

Computational self-testing gives a classical verifier command over the quantum register of a single computationally bounded prover. We use this framework to construct the first argument system for BQP with quasilinear total resource requirements in the circuit model. Our argument system is based on the learning with errors (LWE) assumption and requires total resources of $O(\mathrm{poly}(λ, \log g)\cdot g)$ for delegating a circuit with $g$ gates, where $λ$ is the LWE security parameter. This is achieved by constructing a new computational self-test for certifying the prover's quantum state and using it to dequantize the efficient verification protocol of Broadbent (ToC 2018). Specifically, this self-test enables the verifiable, random remote state preparation of tensor product states of the single-qubit Clifford observables $σ_X, σ_Y, σ_Z, (σ_Y-σ_X)/\sqrt{2}$ and $(σ_Y+σ_X)/\sqrt{2}$, with constant robustness: the verification error is independent of the number of prepared qubits. This approach was first proposed by Coladangelo et al. (ToC 2024) in the multi-prover setting. We replicate their result in the single-prover setting by applying the compiler proposed by Kalai et al. (STOC 2023)---which turns any nonlocal game into a single-prover argument system---to a modified version of their self-test.

发表机构

• ETH Zurich（苏黎世联邦理工学院）
• MIT（麻省理工学院）

机构由 AI 辅助整理，请以论文原文为准。

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124 pages