Interactive Proofs For Quantum Computations

TL;DR

This paper introduces Quantum Prover Interactive Proofs (QPIP), enabling classical verifiers with limited quantum capabilities to verify quantum computations, demonstrating that all BQP problems have fault-tolerant interactive proof protocols.

Contribution

It establishes that any BQP problem admits a fault-tolerant quantum interactive proof system, using novel quantum authentication schemes and fault-tolerance techniques.

Findings

Any BQP problem has a QPIP protocol

A fault-tolerant QPIP protocol is constructed

Protocols can be made blind to protect input and computation

Abstract

The widely held belief that BQP strictly contains BPP raises fundamental questions: Upcoming generations of quantum computers might already be too large to be simulated classically. Is it possible to experimentally test that these systems perform as they should, if we cannot efficiently compute predictions for their behavior? Vazirani has asked: If predicting Quantum Mechanical systems requires exponential resources, is QM a falsifiable theory? In cryptographic settings, an untrusted future company wants to sell a quantum computer or perform a delegated quantum computation. Can the customer be convinced of correctness without the ability to compare results to predictions? To answer these questions, we define Quantum Prover Interactive Proofs (QPIP). Whereas in standard Interactive Proofs the prover is computationally unbounded, here our prover is in BQP, representing a quantum computer. The verifier models our current computational capabilities: it is a BPP machine, with access to few qubits. Our main theorem can be roughly stated as: "Any language in BQP has a QPIP, and moreover, a fault tolerant one". We provide two proofs. The simpler one uses a new (possibly of independent interest) quantum authentication scheme (QAS) based on random Clifford elements. This QPIP however, is not fault tolerant. Our second protocol uses polynomial codes QAS due to BCGHS, combined with quantum fault tolerance and multiparty quantum computation techniques. A slight modification of our constructions makes the protocol "blind": the quantum computation and input are unknown to the prover. After we have derived the results, we have learned that Broadbent at al. have independently derived "universal blind quantum computation" using completely different methods. Their construction implicitly implies similar implications.