Engineering nonlinear dissipation through parametric interactions is a key ingredient in autonomous quantum error correction. In ``cat'' qubits bit-flip errors may be exponentially suppressed using two-photon driven dissipation, but spurious dissipative channels appear, in a process that is poorly understood. The authors turn to high-order perturbation theory and exact numerical diagonalization to classify the possible decay mechanisms that reduce the coherence of such a qubit, bridging the gap between the microscopic parameters of the circuit and the lifetimes of the modes. Furthermore, engineering constraints on the surrounding apparatus are identified, to reduce decoherence.
Engineering nonlinear dissipation through parametric interactions is a key ingredient in autonomous quantum error correction. In ``cat'' qubits bit-flip errors may be exponentially suppressed using two-photon driven dissipation, but spurious dissipative channels appear, in a process that is poorly understood. The authors turn to high-order perturbation theory and exact numerical diagonalization to classify the possible decay mechanisms that reduce the coherence of such a qubit, bridging the gap between the microscopic parameters of the circuit and the lifetimes of the modes. Furthermore, engineering constraints on the surrounding apparatus are identified, to reduce decoherence.
Flux-pump induced degradation of T1 for dissipative cat qubits
Dissipative stabilization of cat qubits autonomously corrects for bit flip errors by ensuring that reservoir-engineered two-photon losses dominate over other mechanisms inducing phase flip errors. To describe the latter, we derive an effective master equation for an asymmetrically threaded SQUID based superconducting circuit used to stabilize a dissipative cat qubit. We analyze the dressing of relaxation processes under drives in time-dependent Schrieffer-Wolff perturbation theory for weakly anharmonic bosonic degrees of freedom, and in numerically exact Floquet theory. We find that spurious single-photon decay rates can increase under the action of the parametric pump that generates the required interactions for cat-qubit stabilization. Our analysis feeds into mitigation strategies that can inform current experiments, and the methods presented here can be extended to other circuit implementations.
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.
Cat qubits, a type of bosonic qubit encoded in a harmonic oscillator, can exhibit an exponential noise bias against bit-flip errors with increasing mean photon number. Here, we focus on cat qubits stabilized by two-photon dissipation, where pairs of photons are added and removed from a harmonic oscillator by an auxiliary, lossy buffer mode. This process requires a large loss rate and strong nonlinearities of the buffer mode that must not degrade the coherence and linearity of the oscillator. In this work, we show how to overcome this challenge by coloring the loss environment of the buffer mode with a multipole filter and optimizing the circuit to take into account additional inductances in the buffer mode. Using these techniques, we achieve near-ideal enhancement of cat-qubit bit-flip times with increasing photon number, reaching over 0.1 s with a mean photon number of only 4. Concurrently, our cat qubit remains highly phase coherent, with phase-flip times corresponding to an effective lifetime of T 1 , eff ≃ 70 μ s , comparable with the bare oscillator lifetime. We achieve this performance even in the presence of an ancilla transmon, used for reading out the cat-qubit states, by engineering a tunable oscillator-ancilla dispersive coupling. Furthermore, the low nonlinearity of the harmonic oscillator mode allows us to perform pulsed cat-qubit stabilization, an important control primitive, where the stabilization can remain off for a significant fraction (e.g., two-thirds) of a 3 μ s cycle without degrading bit-flip times. These advances are important for the realization of scalable error correction with cat qubits, where large noise bias and low phase-flip error rate enable the use of hardware-efficient outer error-correcting codes.
Autonomous quantum error correction (QEC) stabilizes a logical manifold through dissipative events that emit into output channels, which are typically accessible to measurement. These signals are often discarded, and whether they contain useful information about logical failures remains generally unclear. Using quantum trajectories, we show that in dissipatively stabilized cat qubits bit flips are not silent logical errors: each flip is accompanied by a strong, time-localized photon burst from the dissipative buffer. Photon counting and homodyne monitoring can therefore herald the loss of logical information without interrupting the autonomous stabilization: bit flips in dissipative cat qubits are erasures. More broadly, our results show that the emitted signals of engineered reservoirs can act as built-in failure monitors for autonomous QEC, turning rare logical faults into erasures available to a decoder and reducing fault-tolerance overhead. To this end, we develop a general framework, based on past quantum states and number-resolved master equations, to quantify the detectability of such logical failures in autonomous QEC from the emitted signal.
Cat qubits, for which logical |0⟩ and |1⟩ are coherent states |±α⟩ of a harmonic mode, offer a promising route towards quantum error correction. Using dissipation to our advantage so that photon pairs of the harmonic mode are exchanged with single photons of its environment, it is possible to stabilize the logical states and exponentially increase the bit-flip time of the cat qubit with the photon number |α|2 . A large two-photon dissipation rate κ2 ensures fast qubit manipulation and short error-correction cycles, which are instrumental to correct the remaining phase-flip errors in a repetition code of cat qubits. Here, we introduce and operate an autoparametric superconducting circuit that couples a mode containing the cat qubit to a lossy mode whose frequency is set at twice that of the cat mode. This passive coupling does not require a parametric pump, and it reaches a rate κ2/2π≈2 MHz . With such a strong two-photon dissipation, bit-flip errors of the autoparametric cat qubit are prevented for a characteristic time up to 0.3 s with only a mild impact on phase-flip errors. In addition, we illustrate how the phase of a quantum superposition between |α⟩ and |−α⟩ can be arbitrarily changed by driving the harmonic mode while keeping the engineered dissipation active. Published by the American Physical Society 2024
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.