Benjamin Anker

It has previously been shown that fault-tolerant syndrome can be enabled with flag gadgets. In essence, this relies upon the fact that syndrome extraction circuits are Clifford circuits. In this work we extend our previous framework to produce flag gadgets for syndrome extraction to a framework to flag any Clifford circuit. The construction we present allows a Clifford circuit including n two-qubit gates acting upon physical qubits in a code of distance d to be made fault tolerant to distance d using O(d^2 log(nd^2 log n)) ancilla qubits and O(nd^2 log(nd^2 log n)) extra CNOTs. This framework opens new pathways to universal fault-tolerance, for instance by allowing T gates to be implemented transversally while (a subset of) Clifford gates are fault-tolerantly implemented using flags, or by creating higher-reliability magic states using a flagged preparation circuit.