Error-Detectable Bosonic Entangling Gates with a Noisy Ancilla

Abstract

Bosonic quantum error correction has proven to be a successful approach for extending the coherence\nof quantum memories, but to execute deep quantum circuits, high-fidelity gates between encoded qubits\nare needed. To that end, we present a family of error-detectable two-qubit gates for a variety of bosonic\nencodings. From a new geometric framework based on a “Bloch sphere” of bosonic operators, we construct ZZL(θ ) and exponential-SWAP(θ ) gates for the binomial, four-legged cat, dual-rail, and several other\nbosonic codes. The gate Hamiltonian is simple to engineer, requiring only a programmable beam splitter\nbetween two bosonic qubits and an ancilla dispersively coupled to one qubit. This Hamiltonian can be\nrealized in circuit QED hardware with ancilla transmons and microwave cavities. The proposed theoretical framework was developed for circuit QED but is generalizable to any platform that can effectively\ngenerate this Hamiltonian. Crucially, one can also detect first-order errors in the ancilla and the bosonic\nqubits during the gates. We show that this allows one to reach error-detected gate fidelities at the 0.01%\nlevel with today’s hardware, limited only by second-order hardware errors.