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Noise-Robustness for Delegated Quantum Computation in the Circuit Model

Anne Broadbent, Joshua Nevin

TL;DR

This work extends the circuit-based verifiable quantum computation framework to settings with server-side noise, building on Bro18 by interleaving computation and test rounds in a way that remains indistinguishable to the prover. The authors prove a noise-robust, N-round protocol for a BQP prover with inherent error probability $q$, achieving a tolerable noise level of $p^{\text{noise}} = (1- O(1/\sqrt{N})) \frac{2q-1}{2q-2}$, approaching the ideal bound as $N$ grows. The analysis reduces to a combinatorial $(\alpha,w)$-avoidance game, with a rigorous mapping from the quantum verification setting to probabilistic bounds via Hoeffding-type inequalities and careful handling of abort conditions. The results improve practical verifiability prospects for near-term quantum devices and offer a transparent, probabilistic security proof that lifts the noise tolerance from Bro18's perfect hardware setting to realistic noisy servers. The work suggests natural directions for refining noise models, exploring more detailed component-wise tolerances, and bridging toward experimental demonstrations of noise-resilient verifiable delegation.

Abstract

Cloud-based quantum computing, coupled with the rapid progress in quantum algorithms, brings to the forefront the question of verifiability in delegated quantum computations. In the current landscape of noisy quantum devices, this question must be addressed alongside noise tolerance. In this work, we revisit the circuit-based framework for verifiable quantum computation introduced by Broadbent [Theory of Computing, 2018], and extend it to the setting of server-side noise. Our contribution is an improved upper bound on the noise-tolerance threshold, achieved through a protocol that interleaves computation and test rounds in an indistinguishable manner. This structure enables a concise security proof against arbitrary deviations by the server, while ensuring robustness to realistic noise.

Noise-Robustness for Delegated Quantum Computation in the Circuit Model

TL;DR

This work extends the circuit-based verifiable quantum computation framework to settings with server-side noise, building on Bro18 by interleaving computation and test rounds in a way that remains indistinguishable to the prover. The authors prove a noise-robust, N-round protocol for a BQP prover with inherent error probability , achieving a tolerable noise level of , approaching the ideal bound as grows. The analysis reduces to a combinatorial -avoidance game, with a rigorous mapping from the quantum verification setting to probabilistic bounds via Hoeffding-type inequalities and careful handling of abort conditions. The results improve practical verifiability prospects for near-term quantum devices and offer a transparent, probabilistic security proof that lifts the noise tolerance from Bro18's perfect hardware setting to realistic noisy servers. The work suggests natural directions for refining noise models, exploring more detailed component-wise tolerances, and bridging toward experimental demonstrations of noise-resilient verifiable delegation.

Abstract

Cloud-based quantum computing, coupled with the rapid progress in quantum algorithms, brings to the forefront the question of verifiability in delegated quantum computations. In the current landscape of noisy quantum devices, this question must be addressed alongside noise tolerance. In this work, we revisit the circuit-based framework for verifiable quantum computation introduced by Broadbent [Theory of Computing, 2018], and extend it to the setting of server-side noise. Our contribution is an improved upper bound on the noise-tolerance threshold, achieved through a protocol that interleaves computation and test rounds in an indistinguishable manner. This structure enables a concise security proof against arbitrary deviations by the server, while ensuring robustness to realistic noise.

Paper Structure

This paper contains 19 sections, 9 theorems, 63 equations.

Table of Contents

  1. Introduction
  2. Contributions and Techniques
  3. Related Work
  4. The Perfect-Hardware Protocol of Bro18
  5. Classical Proof Systems
  6. Quantum Interactive Proofs in the Circuit Model
  7. A Brief Overview of the Protocol of Bro18
  8. Completeness and Soundness Parameters for Bro18
  9. The Multi-Round Run of the protocol of Bro18 as a Combinatorial Game
  10. IPSk with abort conditions
  11. The $(\alpha, w)$-avoidance game
  12. Modelling Attacks from the Prover
  13. Strategies against the $(\alpha, w)$-avoidance game for the malicious prover
  14. Attacks on single rounds in Bro18
  15. Basic Probability Notions
  16. ...and 4 more sections

Key Result

Theorem 4.6

Let Then there is an $(\mathcal{S}, \frac{8}{9}, \frac{7}{9})$-quantum interactive proof system for the promise problem Q-CIRCUIT$_{\frac{1}{3}}$. Thus, for any fixed constants $c,s$ with $c>s$, we have $\emph{BQP}=\emph{QPIP}_{c,s}$.

Theorems & Definitions (31)

  • Definition 2.1
  • Definition 4.1
  • Definition 4.2
  • Definition 4.3
  • Definition 4.4
  • Definition 4.5
  • Theorem 4.6
  • Proposition 4.7
  • Definition 5.1
  • Definition 5.2
  • ...and 21 more