Logical accreditation: a framework for efficient certification of fault-tolerant computations

Abstract: As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification methods. In this work, we introduce logical accreditation, a framework for efficiently certifying quantum computations performed on logical qubits. Our protocol is robust against general noise models, far beyond those typically considered in performance analyses of quantum error-correcting codes. Through numerical simulations, we demonstrate that logical accreditation can scalably certify quantum advantage experiments and indicate the crossover point where encoded computations begin to outperform physical computations. Logical accreditation can also find application in evaluating whether logical circuit error rates are sufficiently low that error mitigation can be efficiently performed, extending the entropy benchmarking method to the regime of fault-tolerant computation, and upper-bounding the infidelity of the logical output state. Underpinning the framework is a novel randomised compiling scheme that converts arbitrary logical circuit noise into stochastic Pauli noise. This scheme includes a method for twirling non-transversal logical gates beyond the standard T-gate, resolving an open problem posed by Piveteau et al. [Piveteau et al. PRL 127, 200505 (2001)]. By bridging fault-tolerant computation and computational certification, logical accreditation offers a practical tool to assess the quality of computations performed on quantum hardware using encoded logical qubits.