Composable Verification in the Circuit-Model via Magic-Blindness

TL;DR

This work develops a complete framework for verifiable delegation of quantum computations in circuit-model architectures that use Clifford gates augmented with Magic-State Injection (MSI). By introducing a refined blindness notion called magic-blindness, the authors construct composable resources that hide only the non-Clifford content (magic states) while exposing the public Clifford structure, allowing efficient verification with quantum communication scaling as $n+t$. They design a trap-based verification protocol that interleaves computation rounds with classically simulable, stabilizer-test rounds, and prove exponential security against arbitrary malicious behavior through a Reduction to Pauli Deviations and careful trap design. The framework bridges MBQC verification ideas with circuit-model implementations, enabling modular trap design, trap merging, and a general pathway to hardware-aware verification strategies with near-term applicability. Overall, the work advances practical, composable, and noise-robust verification for near-term quantum devices by enabling circuit-model verification with significantly reduced quantum communication and strong security guarantees.

Abstract

As quantum computing machines move towards the utility regime, it is essential that users are able to verify their delegated quantum computations with security guarantees that are (i) robust to noise, (ii) composable with other secure protocols, and (iii) exponentially stronger as the number of resources dedicated to security increases. Previous works that achieve these guarantees and provide modularity necessary to optimization of protocols to real-world hardware are most often expressed in the Measurement-Based Quantum Computation (MBQC) model. This leaves architectures based on the circuit model -- in particular those using the Magic State Injection (MSI) -- with fewer options to verify their computations or with the need to compile their circuits in MBQC leading to overheads. This paper introduces a family of noise robust, composable and efficient verification protocols for Clifford + MSI circuits that are secure against arbitrary malicious behavior. This family contains the verification protocol of Broadbent (ToC, 2018), extends its security guarantees while also bridging the modularity gap between MBQC and circuit-based protocols, and reducing quantum communication costs. As a result, it opens the prospect of rapid implementation for near-term quantum devices. Our technique is based on a refined notion of blindness, called magic-blindness, which hides only the injected magic states -- the sole source of non-Clifford computational power. This enables verification by randomly interleaving computation rounds with classically simulable, magic-free test rounds, leading to a trap-based framework for verification. As a result, circuit-based quantum verification attains the same level of security and robustness previously known only in MBQC. It also optimizes the quantum communication cost as transmitted qubits are required only at the locations of state injection.

Figures (6)

• Figure 1: The Test/Computation paradigm. On the left picture, a blinding protocol embeds a computation $C$ in a class of computations $\mathfrak C$ which contains the initial computation (denoted by a red star) and other instances that are classically simulable (denoted by green circles), which are all indistinguishable when delegated under the protocol. Among those instances, those which provide deterministic measurement outcomes are named traps. In the Verification protocol, traps and computation are blindly delegated to the Server: the trap outcomes are checked by the Client to yield the acceptance/rejection decision, while the computation outcomes are aggregated via a majority vote.
• Figure 2: Same protocol paradigm as Figure \ref{['fig:verif-canvas']}, but with the definition of generalized traps, the Client has more freedom to design traps. Choosing one appropriate set of traps (that detects all Server deviaions) is enough to proceed with verification.
• Figure 3: Quantum Computation described in the Clifford $+\mathsf{T}$ model, with $t$ non-Clifford steps represented by $\mathsf{T}-$gates.
• Figure 4: Magic-State Injection, to implement a $\mathsf{T}-$gate.
• Figure 5: Quantum Computation in the Clifford $+$ MSI model, with $t$ non-Clifford steps represented by Magic-State Injection.

Theorems & Definitions (41)

• Theorem 5: Security of Magic-Blind DQC, informal
• Theorem 6: Security of Verified DQC, informal
• Lemma 1: Pauli Twirl DCEL09exact
• Definition 1: Statistical Indistinguishability of Resources
• Definition 2: Construction of Resources
• Theorem 1: General Composition of Resources MR11abstract
• Theorem 2
• proof : Proof of correctness (sketch, formal in \ref{['appendix: correctness of blind-gate']})
• proof : Security proof
• Theorem 3