Error-detectable bosonic entangling gates with a noisy ancilla

TL;DR

This paper introduces a family of error-detectable two-qubit bosonic gates suitable for various encodings, enabling high-fidelity quantum operations with error detection capabilities in circuit QED systems.

Contribution

It presents a new geometric framework for bosonic gates, designs simple Hamiltonians for implementation, and demonstrates error detection during gates to improve fidelity.

Findings

Error-detectable gates achieve fidelities at the 10^{-4} level.

The framework is applicable to multiple bosonic encodings.

Implementation is feasible with current circuit QED hardware.

Abstract

Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates between encoded qubits are needed. To that end, we present a family of error-detectable two-qubit gates for a variety of bosonic encodings. From a new geometric framework based on a "Bloch sphere" of bosonic operators, we construct $ZZ_L(\theta)$ and $\text{eSWAP}(\theta)$ gates for the binomial, 4-legged cat, dual-rail and several other bosonic codes. The gate Hamiltonian is simple to engineer, requiring only a programmable beamsplitter between two bosonic qubits and an ancilla dispersively coupled to one qubit. This Hamiltonian can be realized 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 generate this Hamiltonian. Crucially, one can also detect first-order errors in the ancilla and the bosonic qubits during the gates. We show that this allows one to reach error-detected gate fidelities at the $10^{-4}$ level with today's hardware, limited only by second-order hardware errors.