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arXiv:2502.07892

Enhancing dissipative cat qubit protection by squeezing

Rousseau, Rémi, Diego Ruiz, Emanuele Albertinale, Pol d'Avezac, D. Banys, Ugo Blandin, Nicolas Bourdaud, Giulio Campanaro, Cardoso, Gil, Nathanaël Cottet, Charlotte Cullip, S. Deléglise, Louise Devanz, Adam Devulder, Antoine Essig, Pierre Février, Adrien Gicquel, Élie Gouzien, Antoine Gras, Jérémie Guillaud, Efe Gümüs, Mattis Hallén, Jacob, Anissa, Paul Magnard, Antoine Marquet, Salim Miklass, Théau Peronnin, Stéphane Polis, Rautschke, Felix, Ulysse Réglade, Julien Roul, Jeremy Stevens, Jeanne Solard, Thomas, Alexandre, Jean-Loup Ville, Pierre Wan-Fat, Raphaël Lescanne, Zaki Leghtas, Joachim Cohen, S. Jézouin, Anil Murani

Published Feb 11, 2025• 0 citations
arXivHTMLPDF

Abstract

Dissipative cat-qubits are a promising architecture for quantum processors due to their built-in quantum error correction. By leveraging two-photon stabilization, they achieve an exponentially suppressed bit-flip error rate as the distance in phase-space between their basis states increases, incurring only a linear increase in phase-flip rate. This property substantially reduces the number of qubits required for fault-tolerant quantum computation. Here, we implement a squeezing deformation of the cat qubit basis states, further extending the bit-flip time while minimally affecting the phase-flip rate. We demonstrate a steep reduction in the bit-flip error rate with increasing mean photon number, characterized by a scaling exponent $γ=4.3$, rising by a factor of 74 per added photon. Specifically, we measure bit-flip times of 22 seconds for a phase-flip time of 1.3 $μ$s in a squeezed cat qubit with an average photon number $\bar{n}=4.1$, a 160-fold improvement in bit-flip time compared to a standard cat. Moreover, we demonstrate a two-fold reduction in $Z$-gate infidelity, with an estimated phase-flip probability of $ε_X = 0.085$ and a bit-flip probability of $ε_Z = 2.65 \cdot 10^{-9}$ which confirms the gate bias-preserving property. This simple yet effective technique enhances cat qubit performances without requiring design modification, moving multi-cat architectures closer to fault-tolerant quantum computation.

DOI
10.48550/arxiv.2502.07892

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Dissipative cat-qubits are a promising architecture for quantum processors due to their built-in quantum error correction. By leveraging two-photon stabilization, they achieve an exponentially suppressed bit-flip error rate as the distance in phase-space between their basis states increases, incurring only a linear increase in phase-flip rate. This property substantially reduces the number of qubits required for fault-tolerant quantum computation. Here, we implement a squeezing deformation of the cat qubit basis states, further extending the bit-flip time while minimally affecting the phase-flip rate. We demonstrate a steep reduction in the bit-flip error rate with increasing mean photon number, characterized by a scaling exponent γ=4.3γ=4.3γ=4.3, rising by a factor of 74 per added photon. Specifically, we measure bit-flip times of 22 seconds for a phase-flip time of 1.3 μμμs in a squeezed cat qubit with an average photon number nˉ=4.1\bar{n}=4.1nˉ=4.1, a 160-fold improvement in bit-flip time compared to a standard cat. Moreover, we demonstrate a two-fold reduction in ZZZ-gate infidelity, with an estimated phase-flip probability of εX=0.085ε_X = 0.085εX​=0.085 and a bit-flip probability of εZ=2.65⋅10−9ε_Z = 2.65 \cdot 10^{-9}εZ​=2.65⋅10−9 which confirms the gate bias-preserving property. This simple yet effective technique enhances cat qubit performances without requiring design modification, moving multi-cat architectures closer to fault-tolerant quantum computation.
Bosonic qubits implement error correction by harnessing the high-dimensional Hilbert space of a harmonic oscillator to redundantly encode logical quantum information. Squeezing of quantum states — a cornerstone of precision metrology — redistributes uncertainty between conjugate quadratures to enhance sensitivity in one variable at the expense of the other. In bosonic codes, decoherence can be seen as the environment performing an unwanted measurement on a noise-sensitive quadrature, collapsing superpositions and inducing errors. By redistributing uncertainty to that quadrature, squeezing can be leveraged to reduce the environment’s measurement strength, thereby prolonging coherence. Here, we exploit this insight to implement a squeezing deformation of the simplest bosonic code — the cat qubit — extending the bit-flip time with minimal impact on the phase-flip rate. We observe a dramatic reduction in bit-flip errors, achieving a 160-fold improvement over standard cat qubits and bringing multi-cat architectures closer to fault-tolerant quantum computation. In bosonic codes, decoherence can be seen as the environment performing an unwanted measurement on a noise-sensitive quadrature, collapsing superpositions and inducing errors. Here, the authors show how to use squeezing to further protect bosonic codes from noise, extending the bit-flip times of the cat qubit by two orders of magnitude without reducing phase-flip times.
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.
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.
Noise-biased qubits are a promising route toward significantly reducing the hardware overhead associated with quantum error correction. The squeezed-cat code, a nonlocal encoding in phase space based on squeezed coherent states, is an example of a noise-biased (bosonic) qubit with exponential error bias. Here we propose and analyze the error correction performance of a dissipatively stabilized squeezed-cat qubit. We find that for moderate squeezing the bit-flip error rate gets significantly reduced in comparison with the ordinary cat qubit while leaving the phase-flip rate unchanged. Additionally, we find that the squeezing enables faster and higher-fidelity gates.
Noise-biased qubits have bit-flip errors that are exponentially suppressed relative to phase-flip errors, and offer a promising route toward fault-tolerant quantum computing. However, this bias can be compromised during gate operations with non-biased control qubits. To address this limitation, we propose a "0-n" Fock qubit architecture that maintains the noise bias by encoding information in the ground state and n-th excited state of a nonlinear multi-level system, such as a transmon. This encoding is achieved via a dissipative stabilization that acts as decay and gain for lower and upper intermediate levels, respectively. We first analytically demonstrate that bit-flip errors are exponentially suppressed with the number of levels. Then, we present a practical implementation using a multi-mode lossy filter to achieve the frequency-selective dissipation. Finally, we numerically demonstrate that bit-flip probabilities approaching 10−810^{-8}10−8 are achievable for controlled-X gates on cat qubits using the 0-n qubit as an ancilla with n≥9n \geq 9n≥9 (i.e. ten or more levels), for realistic experimental parameters. Building on this, we simulate syndrome extraction in a repetition code, achieving logical error rates in the megaquop regime with only a distance of d=9d=9d=9.