We provide a systematic method for constructing effective dispersive Lindblad master equations to describe weakly-anharmonic superconducting circuits coupled by a generic dissipationlessnonreciprocal linear system, with effective coupling parameters and decay rates written in terms of the immittance parameters characterizing the coupler. This article extends the foundational work of Solgun et al. (2019) for linear reciprocal couplers described by an impedance response. Here, we expand the existing toolbox to incorporate nonreciprocal elements, account for direct stray coupling between immittance ports, circumvent potential singularities, and include dissipative interactions arising from interaction with a common bath. We illustrate the use of our results with a circuit of weakly-anharmonic Josephson junctions coupled to a multiport nonreciprocal environment and a dissipative port. The results obtained here can be used for the design of complex superconducting quantum processors with non-trivial routing of quantum information, as well as analog quantum simulators of condensed matter systems.
Quantum computers will require quantum error correction to reach the low error rates necessary for solving problems that surpass the capabilities of conventional computers. One of thedominant errors limiting the performance of quantum error correction codes across multiple technology platforms is leakage out of the computational subspace arising from the multi-level structure of qubit implementations. Here, we present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. This operation removes leakage down to our measurement accuracy of 7⋅10−4 in approximately 50ns with a low error of 2.5(1)⋅10−3 on the computational subspace, thereby reaching durations and fidelities comparable to those of single-qubit gates. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion to close to what can be achieved using leakage-rejection methods which do not scale. Our approach does neither require additional control electronics nor on-chip components and is applicable to both auxiliary and data qubits. These benefits make our method particularly attractive for mitigating leakage in large-scale quantum error correction circuits, a crucial requirement for the practical implementation of fault-tolerant quantum computation.