Engineering error-detectable gates on logical qubits

Superconducting cavities coupled to transmon ancillae is a promising platform for fault-tolerant quantum computation. This pairing produces universal control over a long-lived bosonic mode, in whose many levels we encode a logical qubit. The resources required for fault-tolerance are high and likely require multiple layers of error correction. In this work, we construct a universal set of SNAP-based (Selective Number-dependent Arbitrary Phase [1]) quantum gates on a logical qubit whose dominant transmon errors are detectable. These gates use three levels of the ancilla whose final state heralds the success of the logical operation. Single ancilla X and Z errors correspond to unique ancilla states at the end of the SNAP gate. Our ancilla readout is single-shot and high fidelity, enabling us to accurately detect and discard shots with an error. Postselection increases the fidelity of resulting gate sequences, at the cost of reduced success rate. We show that this cost is small and substantially improves logical gate fidelity.

[1] Krastanov et. al., Phys. Rev. A (2015)