For useful quantum computation, error-corrected machines are required that can dramatically reduce the inevitable errors experienced by physical qubits. While significant progress hasbeen made in approaching and exceeding the surface-code threshold in superconducting platforms, large gains in the logical error rate with increasing system size remain out of reach. This is due both to the large number of required physical qubits and the need to operate far below threshold. Importantly, by exploiting the biases and structure of the physical errors, this threshold can be raised. Erasure qubits achieve this by detecting certain errors at the hardware level. Dual-rail qubits encoded in superconducting cavities are a promising erasure qubit wherein the dominant error, photon loss, can be detected and converted to an erasure. In these approaches, the complete set of operations, including two qubit gates, must be high performance and preserve as much of the desirable hierarchy or bias in the errors as possible. Here, we design and realize a novel two-qubit gate for dual-rail erasure qubits based on superconducting microwave cavities. The gate is high-speed (∼500 ns duration), and yields a residual gate infidelity after error detection below 0.1%. Moreover, we experimentally demonstrate that this gate largely preserves the favorable error structure of idling dual-rail qubits, making it ideal for error correction. We measure low erasure rates of ∼0.5% per gate, as well as low and asymmetric dephasing errors that occur at least three times more frequently on control qubits compared to target qubits. Bit-flip errors are practically nonexistent, bounded at the few parts per million level. This error asymmetry has not been well explored but is extremely useful in quantum error correction and flag-qubit contexts, where it can create a faster path to effective error-corrected systems.
Quantum computation will rely on quantum error correction to counteract decoherence. Successfully implementing an error correction protocol requires the fidelity of qubit operationsto be well-above error correction thresholds. In superconducting quantum computers, measurement of the qubit state remains the lowest-fidelity operation. For the transmon, a prototypical superconducting qubit, measurement is carried out by scattering a microwave tone off the qubit. Conventionally, the frequency of this tone is of the same order as the transmon frequency. The measurement fidelity in this approach is limited by multi-excitation resonances in the transmon spectrum which are activated at high readout power. These resonances excite the qubit outside of the computational basis, violating the desired quantum non-demolition character of the measurement. Here, we find that strongly detuning the readout frequency from that of the transmon exponentially suppresses the strength of spurious multi-excitation resonances. By increasing the readout frequency up to twelve times the transmon frequency, we achieve a quantum non-demolition measurement fidelity of 99.93% with a residual probability of leakage to non-computational states of only 0.02%.
We present a general approach for analyzing arbitrary parametric processes in Josephson circuits within a single degree of freedom approximation. Introducing a systematic normal-orderedexpansion for the Hamiltonian of parametrically driven superconducting circuits we present a flexible procedure to describe parametric processes and to compare different circuit designs for particular applications. We obtain formally exact amplitudes (`supercoefficients‘) of these parametric processes for driven SNAIL-based and SQUID-based circuits. The corresponding amplitudes contain complete information about the circuit topology, the form of the nonlinearity, and the parametric drive, making them, in particular, well-suited for the study of the strong drive regime. We present a closed-form expression for supercoefficients describing circuits without stray inductors and a tractable formulation for those with it. We demonstrate the versatility of the approach by applying it to the estimation of Kerr-cat qubit Hamiltonian parameters and by examining the criterion for the emergence of chaos in Kerr-cat qubits. Additionally, we extend the approach to multi-degree-of-freedom circuits comprising multiple linear modes weakly coupled to a single nonlinear mode. We apply this generalized framework to study the activation of a beam-splitter interaction between two cavities coupled via driven nonlinear elements. Finally, utilizing the flexibility of the proposed approach, we separately derive supercoefficients for the higher-harmonics model of Josephson junctions, circuits with multiple drives, and the expansion of the Hamiltonian in the exact eigenstate basis for Josephson circuits with specific symmetries.