Composable Verification in the Circuit-Model via Magic-Blindness

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.