A simple protocol for fault tolerant verification of quantum computation

TL;DR

This paper introduces a straightforward protocol for verifying quantum computations that remains reliable despite device noise, eliminating the need for additional assumptions, and demonstrates its effectiveness through simulation.

Contribution

It presents a novel, simple verification protocol for noisy quantum devices that does not rely on extra assumptions, advancing practical quantum verification methods.

Findings

Protocol tolerates noise without extra assumptions

Simulation shows error thresholds with repetition and Steane codes

Effective for one-qubit quantum computations

Abstract

With experimental quantum computing technologies now in their infancy, the search for efficient means of testing the correctness of these quantum computations is becoming more pressing. An approach to the verification of quantum computation within the framework of interactive proofs has been fruitful for addressing this problem. Specifically, an untrusted agent (prover) alleging to perform quantum computations can have his claims verified by another agent (verifier) who only has access to classical computation and a small quantum device for preparing or measuring single qubits. However, when this quantum device is prone to errors, verification becomes challenging and often existing protocols address this by adding extra assumptions, such as requiring the noise in the device to be uncorrelated with the noise on the prover's devices. In this paper, we present a simple protocol for verifying quantum computations, in the presence of noisy devices, with no extra assumptions. This protocol is based on post hoc techniques for verification, which allow for the prover to know the desired quantum computation and its input. We also perform a simulation of the protocol, for a one-qubit computation, and find the error thresholds when using the qubit repetition code as well as the Steane code.