Dual-rail encoding with superconducting cavities.

The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace, [Formula: see text], of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today's coherence times.

High-fidelity parametric beamsplitting with a parity-protected converter.

Fast, high-fidelity operations between microwave resonators are an important tool for bosonic quantum computation and simulation with superconducting circuits. An attractive approach for implementing these operations is to couple these resonators via a nonlinear converter and actuate parametric processes with RF drives. It can be challenging to make these processes simultaneously fast and high fidelity, since this requires introducing strong drives without activating parasitic processes or introducing additional decoherence channels. We show that in addition to a careful management of drive frequencies and the spectrum of environmental noise, leveraging the inbuilt symmetries of the converter Hamiltonian can suppress unwanted nonlinear interactions, preventing converter-induced decoherence. We demonstrate these principles using a differentially-driven DC-SQUID as our converter, coupled to two high-Q microwave cavities. Using this architecture, we engineer a highly-coherent beamsplitter and fast (~100 ns) swaps between the cavities, limited primarily by their intrinsic single-photon loss. We characterize this beamsplitter in the cavities' joint single-photon subspace, and show that we can detect and post-select photon loss events to achieve a beamsplitter gate fidelity exceeding 99.98%, which to our knowledge far surpasses the current state of the art.