1Alice&Bob, 53 boulevard du Général Martial Valin, 75015 Paris
2Laboratoire de Physique de l’Ecole Normale Supérieure, Ecole normale supérieure, MINES Paris, Université PSL, Sorbonne Université, CNRS, Inria, 75005 Paris
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Abstract
Bosonic cat qubits stabilized by two-photon driven dissipation benefit from exponential suppression of bit-flip errors and an extensive set of gates preserving this protection. These properties make them promising building blocks of a hardware-efficient and fault-tolerant quantum processor. In this paper, we propose a performance optimization of the repetition cat code architecture using fast but noisy CNOT gates for stabilizer measurements. This optimization leads to high thresholds for the physical figure of merit, given as the ratio between intrinsic single-photon loss rate of the bosonic mode and the engineered two-photon loss rate, as well as a very interesting scaling below threshold of the required overhead, to reach an expected level of logical error rate. Relying on the specific error models for cat qubit operations, this optimization exploits fast parity measurements, using accelerated low-fidelity CNOT gates, combined with fast ancilla parity-check qubits. The significant enhancement in the performance is explained by: 1- the highly asymmetric error model of cat qubit CNOT gates with a major component on control (ancilla) qubits, and 2- the robustness of the error correction performance in presence of the leakage induced by fast operations. In order to demonstrate these performances, we develop a method to sample the repetition code under circuit-level noise that also takes into account cat qubit state leakage.
Featured image: QEC circuit for the distance-$d$ repetition cat code.
(a) a repetition cat code consists of a 1D array of stabilized cat qubits, where the phase-flip error correction is performed by repetitive $XX$ parity measurements between neighboring cat qubits.
(b) The QEC on a distance-$d$ phase-flip repetition code is performed by repeated $XX$ parity measurements.
(c) Each QEC cycle is composed of $d-1$ $XX$ parity checks between neighboring cat qubits. Each parity check is performed by applying bias-preserving CNOT gates between the two associated data cat qubits (as targets) and one ancilla cat qubit (as control). The ancilla cat qubit is finally measured in its $X$ basis.
(d) The measurement of an ancilla cat qubit in the $X$ basis is performed through a photon number parity measurement. This is done by turning off the two-photon dissipation mechanism on the ancilla cat qubit and following a Ramsey type experiment. In this scheme the ancilla cat mode is coupled dispersively to a qubit, e.g. a transmon, where the interaction Hamiltonian is given by $hat{H}_{mathrm{int}}=hbar frac{chi}{2} hat{sigma}_z hat{a}^{dagger} hat{a}$. The Ramsey sequence consists then of applying two $pi/2$-pulses on the qubit separated by a waiting time of $pi/chi$. During the waiting time, the qubit accumulates a phase of $0$ or $pi$ depending on the photon number parity of the cat mode. The final readout of the qubit thus measures this observable.
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Cited by
[1] Adrian Copetudo, Clara Yun Fontaine, Fernando Valadares, and Yvonne Y. Gao, “Shaping photons: quantum computation with bosonic cQED”, arXiv:2311.03846, (2023).
[2] Ofir Milul, Barkay Guttel, Uri Goldblatt, Sergey Hazanov, Lalit M. Joshi, Daniel Chausovsky, Nitzan Kahn, Engin çiftyürek, Fabien Lafont, and Serge Rosenblum, “Superconducting Cavity Qubit with Tens of Milliseconds Single-Photon Coherence Time”, PRX Quantum 4 3, 030336 (2023).
[3] Élie Gouzien, Diego Ruiz, Francois-Marie Le Régent, Jérémie Guillaud, and Nicolas Sangouard, “Performance Analysis of a Repetition Cat Code Architecture: Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126 133 Cat Qubits”, Physical Review Letters 131 4, 040602 (2023).
[4] Ronan Gautier, Mazyar Mirrahimi, and Alain Sarlette, “Designing High-Fidelity Zeno Gates for Dissipative Cat Qubits”, PRX Quantum 4 4, 040316 (2023).
[5] Shubham P. Jain, Joseph T. Iosue, Alexander Barg, and Victor V. Albert, “Quantum spherical codes”, arXiv:2302.11593, (2023).
[6] Antoine Marquet, Antoine Essig, Joachim Cohen, Nathanaël Cottet, Anil Murani, Emanuele Abertinale, Simon Dupouy, Audrey Bienfait, Théau Peronnin, Sébastien Jezouin, Raphaël Lescanne, and Benjamin Huard, “Autoparametric resonance extending the bit-flip time of a cat qubit up to 0.3 s”, arXiv:2307.06761, (2023).
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The above citations are from SAO/NASA ADS (last updated successfully 2023-12-06 09:57:51). The list may be incomplete as not all publishers provide suitable and complete citation data.
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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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