Magic-Free Certification of Logical Error Rates in Universal Fault-Tolerant Circuits

Abstract

As quantum hardware enters the fault-tolerant regime, algorithms are beginning to be executed on encoded qubits, yet scalable certification of how well they run remains an open problem. Here we introduce magic-free certification, a certification protocol for universal fault-tolerant circuits that consumes no magic, the resource that generally places them beyond efficient classical simulation and is by far the most expensive element of a fault-tolerant computation. The protocol is code- and decoder-agnostic, runs interleaved with the target circuit on the same device, and has a sample complexity that grows linearly with the number of logical qubits and non-Clifford gates while remaining decoupled from the logical error rate itself. Given a predefined error tolerance $p_L^*$, the protocol determines at a chosen confidence level whether the device executes the target circuit at a logical error rate below $p_L^*$. The method relies on trap circuits, copies of the target with every magic state replaced by a stabilizer state, whose outcomes are deterministic and which, being indistinguishable from the target to stochastic Pauli noise, fail at the same rate. We illustrate the protocol in Steane-code simulations of a magic state injection gadget and a quantum Fourier transform.