Reducing resources for verification of quantum computations

TL;DR

This paper introduces two efficient quantum verification protocols that use minimal noise-free operations and achieve linear overhead, marking a significant step towards reducing quantum resource requirements for verifying quantum computations.

Contribution

The paper presents the first verification protocols with minimal quantum operations that still achieve linear overhead, improving practicality in quantum verification.

Findings

Protocols rely on minimal noise-free operations

Achieve linear overhead in verification

Represent the least demanding techniques for such verification

Abstract

We present two verification protocols where the correctness of a "target" computation is checked by means of "trap" computations that can be efficiently simulated on a classical computer. Our protocols rely on a minimal set of noise-free operations (preparation of eight single-qubit states or measurement of four observables, both on a single plane of the Bloch sphere) and achieve linear overhead. To the best of our knowledge, our protocols are the least demanding techniques able to achieve linear overhead. They represent a step towards further reducing the quantum requirements for verification.