Cat-state qubits, a prominent class of bosonic encodings, offer a promising pathway toward hardware-efficient fault-tolerant quantum computing. In this manuscript, we propose an optimally robust control protocol for the cat-state qubits which are stabilized by engineering two-photon dissipation. By deriving an effective two-level description in the cat-state subspace and applying shortcut-to-adiabaticity via inverse engineering, we design a robust protocol to achieve fast and high-fidelity state transfer in the cat-state qubit. We analyze the sensitivity to systematic control errors and identify an optimal robustness condition that strongly suppresses errors induced by imperfections in the driving fields. Furthermore, we show that dissipative confinement efficiently suppresses leakage out of the cat-state subspace caused by the pure dephasing, highlighting an intrinsic advantage of dissipative-cat qubits. This work establishes a robust and leakage-suppressing framework for high-fidelity bosonic qubit control, offering a promising route toward scalable fault-tolerant quantum computing.
Cat-state qubits, a prominent class of bosonic encodings, offer a promising pathway toward hardware-efficient fault-tolerant quantum computing. In this manuscript, we propose an optimally robust control protocol for the cat-state qubits which are stabilized by engineering two-photon dissipation. By deriving an effective two-level description in the cat-state subspace and applying shortcut-to-adiabaticity via inverse engineering, we design a robust protocol to achieve fast and high-fidelity state transfer in the cat-state qubit. We analyze the sensitivity to systematic control errors and identify an optimal robustness condition that strongly suppresses errors induced by imperfections in the driving fields. Furthermore, we show that dissipative confinement efficiently suppresses leakage out of the cat-state subspace caused by the pure dephasing, highlighting an intrinsic advantage of dissipative-cat qubits. This work establishes a robust and leakage-suppressing framework for high-fidelity bosonic qubit control, offering a promising route toward scalable fault-tolerant quantum computing.
Cat-state qubits formed by photonic coherent states are a promising candidate for realizing fault-tolerant quantum computing. Such logic qubits have a biased noise channel where the bit-flip error dominates over all the other errors. In this manuscript, we propose an optimally robust protocol using the control method of shortcuts to adiabaticity to realize a high-fidelity state transfer in a cat-state qubit. We construct a shortcut based on the Lewis-Riesenfeld invariant and examine the stability versus different types of perturbations for the fast and robust bit flipping. Numerical simulations demonstrate that the bit flipping can be robust against systematic errors in our protocol. Even when the parameter imperfection rate for bit-flip control is 20%, the final population of the target state can still reach ≥ 99%. The optimally robust control provides a feasible method for fault-tolerant and scalable quantum computation.
Quantum computing crucially relies on maintaining quantum coherence for the duration of a calculation. Bosonic quantum error correction protects this coherence by encoding qubits into superpositions of noise-resilient oscillator states. In the case of the Kerr-cat qubit (KCQ), these states derive their stability from being the quasi-degenerate ground states of an engineered Hamiltonian in a driven nonlinear oscillator. KCQs are experimentally compatible with on-chip architectures and high-fidelity operations, making them promising candidates for a scalable bosonic quantum processor. However, their bit-flip time must increase further to fully leverage these advantages. Here, we present direct evidence that the bit-flip time in a KCQ is limited by leakage out of the qubit manifold and experimentally mitigate this process. We coherently control the leakage population and measure it to be > 9%, twelve times higher than in the undriven system. We then cool this population back into the KCQ manifold with engineered dissipation, identify conditions under which this suppresses bit-flips, and demonstrate increased bit-flip times up to 3.6 milliseconds. By employing both Hamiltonian confinement and engineered dissipation, our experiment combines two paradigms for Schrödinger-cat qubit stabilization. Our results elucidate the interplay between these stabilization processes and indicate a path towards fully realizing the potential of these qubits for quantum error correction.
Stabilized cat qubits that possess biased noise channel with bit-flip errors exponentially smaller than phase-flip errors. Together with a set of bias-preserving (BP) gates, cat qubits are a promising candidate for realizing hardware efficient quantum error correction and fault-tolerant quantum computing. Compared to dissipatively stabilized cat qubits, the Kerr cat qubits can in principle support faster gate operations with higher gate fidelity, benefiting from the large energy gap that protects the code space. However, the leakage of the Kerr cats can increase the minor type of errors and compromise the noise bias. Both the fast implementation of gates and the interaction with environment can lead to such detrimental leakage if no sophisticated controls are applied. In this work, we introduce new fine-control techniques to overcome the above obstacles for Kerr cat qubits. To suppress the gate leakage, we use the derivative-based transition suppression technique to design derivative-based controls for the Kerr BP gates. We show that the fine-controlled gates can simultaneously have high gate fidelity and high noise bias and when applied to concatenated quantum error correction, can not only improve the logical error rate but also reduce resource overhead. To suppress the environment-induced leakage, we introduce colored single-photon dissipation, which can continuously cool the Kerr cats and suppress the minor errors while not enhancing the major errors.
Dissipatively stabilized cat qubits provide a promising route toward fault-tolerant quantum computation, exhibiting exponential suppression of bit-flip errors with increasing phase-space separation of the logical states, while incurring only a linear increase in phase-flip errors. Existing implementations rely on engineered two-photon dissipation via nonlinear coupling to a lossy environment, an approach largely confined to superconducting platforms and limited by spurious decay channels and finite dissipation rates. Here, we propose a fundamentally different stabilization paradigm based on repeated interactions with an auxiliary two-level system mediated by a quadratic Hamiltonian, enabling dissipative stabilization without reservoir engineering. Our approach overcomes key limitations of existing schemes and is compatible with a wider class of experimental platforms. Furthermore, it preserves the noise bias and extends to squeezed cat qubits, rendering single-photon loss errors partially correctable.
Encoding quantum information onto bosonic systems is a promising route to quantum error correction. In a cat code, this encoding relies on the confinement of the system's dynamics onto the two-dimensional manifold spanned by Schrödinger cats of opposite parity. In dissipative cat qubits, an engineered dissipation scheme combining two-photon drive and loss has been used to autonomously stabilize this manifold, ensuring passive protection against bit-flip errors, regardless of their origin. In Kerr cat qubits, where highly-performing gates can be engineered, two-photon drive and Kerr nonlinearity cooperate to confine the system to a two-fold degenerate ground state manifold spanned by cats of opposite parity. Dissipative, Hamiltonian, and hybrid confinements have been investigated at resonance. Here, we propose a critical cat code, where both two-photon loss and Kerr nonlinearity are present, and the two-photon drive is allowed to be out of resonance. The performance of this code is assessed via the spectral theory of Liouvillians in all configurations, from the purely dissipative to the Kerr limit. We show that large detunings and small, but non-negligible, two-photon loss rates are fundamental to achieve optimal performance. We demonstrate that the competition between nonlinearity and detuning results in a first-order dissipative phase transition, leading to a squeezed vacuum steady state. To achieve the maximal suppression of the logical bit-flip rate requires initializing the system in the metastable state emerging from the first-order transition, and we detail a protocol to do so. Efficiently operating over a broad range of detuning values, the critical cat code is particularly resistant to random frequency shifts characterizing multiple-qubit operations, opening venues for the realization of reliable protocols for scalable and concatenated bosonic qubit architectures.
We propose a framework for the direct generation of flying cat-qubit states from vacuum using time-dependent two-photon drives in nonlinear bosonic systems. We study both Kerr-based and two-photon-dissipation-based generation. By engineering Kerr nonlinearity, two-photon driving, and dissipation, we demonstrate logical control of a cat qubit during its generation and emission, while its quantum information is simultaneously shared between the nonlinear system and the propagating output field. We further analyze the effects of photon loss and pure dephasing, showing that both the state generation and logical control remain robust under realistic noise conditions. These results provide a route toward programmable bosonic quantum networks and future propagating error-correctable encodings.