Publicly verifiable delegation is a well-known problem involving a user who wishes to outsource a resource-intensive computational task to a more powerful but potentially untrusted server such that any other party is able to efficiently check the veracity of the computation's result. This problem has been extensively studied in the classical domain where the user and server are both non-quantum machines. However, the problem becomes more challenging when the classical user wants to delegate a quantum circuit to a single prover with quantum-computing capabilities. Previous solutions have resorted to using impractical or non-standard cryptographic solutions (e.g. indistinguishability obfuscation) to achieve this requirement. In this work, we relax the requirement to have time-delayed publicly verifiable proofs, where the verification key is made known to the public only when the computation (and its proof) are guaranteed to have been completed. We propose a practical non-interactive scheme leveraging commitment schemes and time-lock puzzles, which can be efficiently realized through well-established and standard post-quantum assumptions. The main idea of our technique lies in using time-lock puzzles to compile a 2-round privately verifiable scheme into a non-interactive publicly verifiable scheme with timestamped proofs, outsourcing not only the quantum computation but the puzzle solving as well. Security is proven in the quantum random oracle model with a common reference string (CRS).

翻译：公开可验证委托是一个著名问题，涉及用户希望将资源密集的计算任务外包给更强大但可能不可信的服务器，使得任何第三方能够高效地验证计算结果的正确性。该问题在经典领域已得到广泛研究，其中用户和服务器均为非量子机器。然而，当经典用户希望委托单个具有量子计算能力的证明者执行量子电路时，问题变得更具挑战性。以往的解决方案依赖不实用或非标准的密码学方法（例如不可区分混淆）来实现这一需求。本研究放宽了要求，提出耗时公开可验证证明方案，即仅在计算（及其证明）保证完成时，才向公众公开验证密钥。我们提出了一种实用的非交互式方案，该方案利用承诺方案和时限谜题，可通过成熟且标准的后量子假设高效实现。本技术的核心思想在于使用时限谜题，将两轮私有可验证方案编译为带时间戳证明的非交互式公开可验证方案，同时外包量子计算与谜题求解。安全性在带公共参考字符串（CRS）的量子随机预言机模型中得到证明。