Verification of Quantum Computations without Trusted Preparations or Measurements

TL;DR

This paper demonstrates that universal quantum computations can be verified with information-theoretic security without trusted state preparations or measurements, using only trusted gates and multi-qubit operations, advancing quantum verification protocols.

Contribution

It introduces a modular approach to verify quantum computations relying solely on trusted gates, eliminating the need for trusted preparations or measurements.

Findings

Verification reduces to trusted single-qubit rotations and bit flips.

It is possible to verify arbitrary quantum computations without trusted preparations or measurements.

The protocol requires multi-qubit gates on a fixed-size register independent of computation size.

Abstract

With the advent of delegated quantum computing as a service, verifying quantum computations is becoming a question of great importance. Existing information theoretically Secure Delegated Quantum Computing (SDQC) protocols require the client to possess the ability to perform either trusted state preparations or measurements. Whether it is possible to verify universal quantum computations with information-theoretic security without trusted preparations or measurements was an open question so far. In this paper, we settle this question in the affirmative by presenting a modular, composable, and efficient way to turn known verification schemes into protocols that rely only on trusted gates. Our first contribution is an extremely lightweight reduction of the problem of quantum verification for BQP to the trusted application of single-qubit rotations around the Z axis and bit flips. The second construction presented in this work shows that it is generally possible to information-theoretically verify arbitrary quantum computations with quantum output without trusted preparations or measurements. However, this second protocol requires the verifier to perform multi-qubit gates on a register whose size is independent of the size of the delegated computation.