Verifying commuting quantum computations via fidelity estimation of weighted graph states

TL;DR

This paper develops efficient fidelity estimation protocols for verifying weighted graph states in IQP quantum circuits, enabling practical validation of quantum advantage demonstrations with minimal quantum operations.

Contribution

It introduces the first polynomial-time verification protocols for weighted graph states in IQP models, covering various measurement restrictions and adaptive capabilities.

Findings

Protocols work without i.i.d. assumptions

Verifier only needs single-qubit measurements

Applicable to multiple measurement scenarios

Abstract

The instantaneous quantum polynomial time model (or the IQP model) is one of promising models to demonstrate a quantum computational advantage over classical computers. If the IQP model can be efficiently simulated by a classical computer, an unlikely consequence in computer science can be obtained (under some unproven conjectures). In order to experimentally demonstrate the advantage using medium or large-scale IQP circuits, it is inevitable to efficiently verify whether the constructed IQP circuits faithfully work. There exists two types of IQP models, each of which is the sampling on hypergraph states or weighted graph states. For the first-type IQP model, polynomial-time verification protocols have already been proposed. In this paper, we propose verification protocols for the second-type IQP model. To this end, we propose polynomial-time fidelity estimation protocols of weighted graph states for each of the following four situations where a verifier can (i) choose any measurement basis and perform adaptive measurements, (ii) only choose restricted measurement bases and perform adaptive measurements, (iii) choose any measurement basis and only perform non-adaptive measurements, and (iv) only choose restricted measurement bases and only perform non-adaptive measurements. In all of our verification protocols, the verifier's quantum operations are only single-qubit measurements. Since we assume no i.i.d. property on quantum states, our protocols work in any situation.