Echoed Conditional Displacement (ECD) gates constitute a fundamental building block for quantum control of harmonic oscillator modes. However, bit-flips of the auxiliary qubit remaina dominant error mechanism for this kind of bosonic control. In this work, we present a numerical case study of a bit-flip protected fluxonium operating as the control qubit and numerically implement ECD gates in a single-mode resonator-fluxonium device, demonstrating that fidelities exceeding 99.9% are possible. We systematically investigate the resonator dynamics using a combination of semiclassical trajectories and master equation simulations, numerically revealing asymptotic saturation of the dispersive shift in the strongly driven regime of the resonator. We develop an efficient technique to numerically simulate the strongly driven regime of the resonator using a semiclassical formulation that maps the full perturbation series in the dispersive expansion as order-by-order frequency shifts. This provides a compact polynomial description of the resonator which is intuitive and remains valid throughout the dispersive regime. Furthermore, we propose an improved ECD sequence that accounts for the effects of photon loss and spurious nonlinear terms on resonator trajectories.
Binary classical information is routinely encoded in the two metastable states of a dynamical system. Since these states may exhibit macroscopic lifetimes, the encoded information inheritsa strong protection against bit-flips. A recent qubit – the cat-qubit – is encoded in the manifold of metastable states of a quantum dynamical system, thereby acquiring bit-flip protection. An outstanding challenge is to gain quantum control over such a system without breaking its protection. If this challenge is met, significant shortcuts in hardware overhead are forecast for quantum computing. In this experiment, we implement a cat-qubit with bit-flip times exceeding ten seconds. This is a four order of magnitude improvement over previous cat-qubit implementations, and six orders of magnitude enhancement over the single photon lifetime that compose this dynamical qubit. This was achieved by introducing a quantum tomography protocol that does not break bit-flip protection. We prepare and image quantum superposition states, and measure phase-flip times above 490 nanoseconds. Most importantly, we control the phase of these superpositions while maintaining the bit-flip time above ten seconds. This work demonstrates quantum operations that preserve macroscopic bit-flip times, a necessary step to scale these dynamical qubits into fully protected hardware-efficient architectures.
We propose a novel approach to generate, protect and control GKP qubits. It employs a microwave frequency comb parametrically modulating a Josephson circuit to enforce a dissipativedynamics of a high impedance circuit mode, autonomously stabilizing the finite-energy GKP code. The encoded GKP qubit is robustly protected against all dominant decoherence channels plaguing superconducting circuits but quasi-particle poisoning. In particular, noise from ancillary modes leveraged for dissipation engineering does not propagate at the logical level. In a state-of-the-art experimental setup, we estimate that the encoded qubit lifetime could extend two orders of magnitude beyond the break-even point, with substantial margin for improvement through progress in fabrication and control electronics. Qubit initialization, readout and control via Clifford gates can be performed while maintaining the code stabilization, paving the way toward the assembly of GKP qubits in a fault-tolerant quantum computing architecture.