We draw analogies between protected superconducting qubits and bosonic qubits by studying the fluxonium Hamiltonian in its Fock basis. The mean-field phase diagram of fluxonium (atthe sweet spot) is identified, with a region in parameter space that is characterized by ℤ2-symmetry-broken ground states. In the heavy fluxonium limit, these ground states are well approximated by squeezed coherent states in a Fock basis (corresponding to persistent current states with definite flux but indefinite charge), and simple expressions are provided for them in terms of the circuit parameters. We study the noise bias in fluxonium via a universal Lindblad master equation and find that the bit-flip rate is exponentially small in Ej/(kBT), while the phase-flip rate does not get worse with this ratio. Analogous behavior is found in cos(2θ) qubits. We discuss first steps towards generating an Ising interaction between protected superconducting qubits on a two-dimensional lattice, with the aim of achieving a passive quantum memory by coupling a static Hamiltonian to a generic thermal bath.
The conditional displacement (CD) gate between an oscillator and a discrete-variable ancilla plays a key role in quantum information processing tasks, such as enabling universal controlof the oscillator and longitudinal readout of the qubit. However, the gate is unprotected against the propagation of ancilla decay errors and hence not fault-tolerant. Here, we propose a CD gate scheme with fluxonium as the ancilla, which has been experimentally demonstrated to have a large noise bias and millisecond-level lifetimes. The proposed gate is applied cross-resonantly by modulating the external flux of the fluxonium at the frequency of the target oscillator, which requires minimal hardware overhead and does not increase sensitivity to decoherence mechanisms like dephasing. We further provide a perturbative description of the gate mechanism and identify the error budget. Additionally, we develop an approximate procedure for choosing device and gate parameters that optimizes gate performance. Following the procedure for multiple sets of fluxonium parameters from the literature, we numerically demonstrate CD gates with unitary fidelity exceeding 99.9% and gate times of hundreds of nanoseconds.
We take a bottom-up, first-principles approach to design a two-qubit gate between fluxonium qubits for minimal error, speed, and control simplicity. Our proposed architecture consistsof two fluxoniums coupled via a linear resonator. Using a linear coupler introduces the possibility of material optimization for suppressing its loss, enables efficient driving of state-selective transitions through its large charge zero point fluctuation, reduces sensitivity to junction aging, and partially mitigates coherent coupling to two-level systems. Crucially, a resonator-as-coupler approach also suggests a clear path to increased connectivity between fluxonium qubits, by reducing capacitive loading when the coupler has a high impedance. After performing analytic and numeric analyses of the circuit Hamiltonian and gate dynamics, we tune circuit parameters to destructively interfere sources of coherent error, revealing an efficient, fourth-order scaling of coherent error with gate duration. For component properties from the literature, we predict an open-system average CZ gate infidelity of 1.86×10−4 in 70ns.