Given that reliable cloud quantum computers are becoming closer to reality, the concept of delegation of quantum computations and its verifiability is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a single round. In addition, during a set-up phase, the client specifies the size $n$ of the computation and receives an untrusted, off-the-shelf (OTS) quantum device that is used to report the outcome of a single constant-sized measurement from a predetermined logarithmic-sized input. In the OTS model, we thus picture that a single quantum server does the bulk of the computations, while the OTS device is used as an untrusted and generic verification device, all in a single round. We show how to delegate polynomial-time quantum computations in the OTS model. Scaling up the technique also yields an interactive proof system for all of QMA, which, furthermore, we show can be accomplished in statistical zero-knowledge. This yields the first relativistic (one-round), two-prover zero-knowledge proof system for QMA. As a proof approach, we provide a new self-test for $n$-EPR pairs using only constant-sized Pauli measurements, and show how it provides a new avenue for the use of simulatable codes for local Hamiltonian verification. Along the way, we also provide an enhanced version of a well-known stability result due to Gowers and Hatami and show how it completes a common argument used in self-testing.

翻译：鉴于可靠的云端量子计算机正逐渐成为现实，量子计算的委托概念及其可验证性已成为关注焦点。已有多种模型被提出，各具优缺点。本文提出一种新模型：客户端仅信任其经典处理能力，不依赖任何计算假设，并与量子服务器进行单轮交互。此外，在设置阶段，客户端指定计算规模$n$，并接收一个不可信的现成（OTS）量子设备，该设备用于从预定的对数规模输入中报告单次常数规模测量的结果。在OTS模型中，我们设想单个量子服务器承担主要计算任务，而OTS设备作为不可信的通用验证设备，所有这些均在单轮中完成。我们展示了如何在该模型下委托多项式时间的量子计算。进一步扩展该技术，还可为QMA（量子马林-施特劳斯复杂度类）构建交互式证明系统，且能实现统计零知识性。这为QMA提供了首个相对论性（单轮）双证明者零知识证明系统。作为证明方法，我们提出了一种仅使用常数规模泡利测量的$n$-EPR对自检验新方案，并展示了该方案如何为使用可模拟编码进行局部哈密顿量验证开辟新途径。与此同时，我们改进了戈尔斯-哈塔米稳定性结果的一个经典版本，并展示其如何完善自检验中常用的论证方法。