We theoretically introduce a quantum-circuit synthesis protocol to realize any n-qubit transformation U∈U(2n), up to a diagonal. The resulting circuit is directly native to and optimalin gate count and depth for systems where bitstring-conditioned rotations with tunable angle and axis, C(n−1)R(θ,ϕ), form the set of native operations. Subsequently, we suggest how this protocol can be implemented in a few-mode superconducting circuit, and experimentally demonstrate the method for the smallest nontrivial case, i.e., for two qubits. We report an average gate fidelity of 97.6 % for Haar-random two-qubit unitaries up to phase shifts in the computational basis. Importantly, these results suggest that multimode devices, such as those in the multimon or multiunimon families may become competitive with qubit-array networks for general-unitary implementations for qubit counts as low as three.
Qubit leakage is a noticeable source of errors for quantum computing. In quantum processors, leakage excitations traveling between qubits generate correlated errors and perturb gateimplementations. Leakage mobility can also be utilized for creating dedicated leakage removal pathways and removal units. To quantitatively characterize leakage mobility and to guide better design of processor architectures, we study here leakage dynamics in transmons with tunable couplers through numerical and analytical methods. Even if the couplers are tuned to cancel the single-excitation exchange or the ZZ interaction, the leakage hopping rates still persists in the range of 0.8-10 MHz due to transmon nonlinearity. In typical operation regimes, however, transmon frequency detuning localizes leakage excitations. The next-nearest-neighbor transmons can be still be near-resonant opening leakage tunneling channels. To suppress longer-range hopping, we find that the frequency spread of the next-nearest-neighbor transmons needs to be in the range of 1-4 MHz. Utilizing leakage mobility, we propose two passive leakage removal units. One is based on a tunable coupler and a pumped transmon, and another on a junction readout scheme. Based on realistic experimental parameters, our results on selectively mobilizing or localizing leakage excitations are readily applicable in superconducting quantum devices.
We consider a superconducting half-wavelength resonator that is grounded at its both ends and contains a single Josephson junction. Previously this circuit was considered as a unimonqubit in the single-mode approximation where dc-phase-biasing the junction to π leads to increased anharmonicity and 99.9% experimentally observed single-qubit gate fidelity. Inspired by the promising first experimental results, we develop here a theoretical and numerical model for the detailed understanding of the multimode physics of the unimon circuit. To this end, first, we consider the high-frequency modes of the unimon circuit and find that even though these modes are at their ground state, they imply a significant renormalization to the Josephson energy. We introduce an efficient method how the relevant modes can be fully taken into account and show that unexcited high-lying modes lead to corrections in the qubit energy and anharmonicity. Interestingly, provided that the junction is offset from the middle of the circuit, we find strong cross-Kerr coupling strengths between a few low-lying modes. This observation paves the way for the utilization of the multimode structure, for example, as several qubits embedded into a single unimon circuit.