Circuits demonstrating flags for multiple cases. In (a.) we show a general flag gadget for a general n-qubit unitary U. In (b.) we show that for a Clifford subcircuit (here shown surrounded by T-gates) this can be simplified to Pauli flags. In (c.) we show how Pauli flags can be used for a circuit with non-Clifford elements. Lastly in (d.) we show how multiple flags can be used to verify a single circuit.
Flag verification techniques are useful in quantum error correction for detecting critical faults. Here we present an application of flag-verification techniques for improving postselected performance of near-term algorithms. We extend the definition of what constitutes a flag by creating error-detection gadgets based on known transformations of unitary operators. In the case of Clifford or near-Clifford circuits, these unitary operators can be chosen to be controlled Pauli gates, leading to gadgets which require only a small number of additional Clifford gates. We show that such flags can improve circuit fidelities by up to a factor of 2 after postselection, and demonstrate their effectiveness over error models featuring single-qubit depolarizing noise, crosstalk, and two-qubit coherent overrotation. doi: 10.1103/PhysRevA.102.052409
Debroy, Dripto M.;Brown, Kenneth R.,
