Classical Verification of Quantum Computation with Quasilinear Resources, from Compiled Nonlocal Games

2026-09-29

AI Summary

This work addresses the prohibitive resource overhead in quantum computation verification by constructing the first nearly linear-resource argument system for BQP, enabling a classical verifier to efficiently control a single prover. Methodologically, it introduces the first single-prover self-testing protocol based on the Learning with Errors (LWE) assumption, successfully porting multi-prover results to the single-prover setting. By integrating computational self-testing with the Kalai compiler and compiling nonlocal games, the approach achieves verifiable preparation of tensor product states and efficient delegation of quantum computation. Ultimately, the total resource consumption is reduced to $O(\text{poly}(\lambda, \log g) \cdot g)$, while the verification error remains independent of the number of qubits.

Abstract

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.

Problem

• Classical Verification of Quantum Computation
• Computational Self-Testing
• BQP Argument System
• Quasilinear Resources
• Delegated Quantum Computation

Innovation

• Computational Self-Testing
• Quasilinear Resources
• Remote State Preparation
• Nonlocal Games
• Learning with Errors