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arXiv:2406.13957 · npj Quantum Information

Stabilization of Kerr-cat qubits with quantum circuit refrigerator

Shumpei Masuda, Shunsuke Kamimura, Tsuyoshi Yamamoto, Takaaki Aoki, Akiyoshi Tomonaga

Published Feb 15, 2025• 2 citations
arXivHTMLPDF

Abstract

A periodically driven superconducting nonlinear resonator can implement a Kerr-cat qubit, which provides a promising route to a quantum computer with a long lifetime. However, the system is vulnerable to pure dephasing, which causes unwanted excitations outside the qubit subspace. Therefore, we require a refrigeration technology that confines the system in the qubit subspace. We theoretically study on-chip refrigeration for Kerr-cat qubits based on photon-assisted electron tunneling at tunneling junctions, called quantum circuit refrigerators (QCR). Rates of QCR-induced deexcitations of the system can be changed by more than four orders of magnitude by tuning a bias voltage across the tunneling junctions. Unwanted QCR-induced bit flips are greatly suppressed due to quantum interference in the tunneling process, and thus the long lifetime is preserved. The QCR can serve as a tunable dissipation source that stabilizes Kerr-cat qubits.

DOI
10.1038/s41534-025-00974-6

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A periodically driven superconducting nonlinear resonator can implement a Kerr-cat qubit, which provides a promising route to a quantum computer with a long lifetime. However, the system is vulnerable to pure dephasing, which causes unwanted excitations outside the qubit subspace. Therefore, we require a refrigeration technology that confines the system in the qubit subspace. We theoretically study on-chip refrigeration for Kerr-cat qubits based on photon-assisted electron tunneling at tunneling junctions, called quantum circuit refrigerators (QCR). Rates of QCR-induced deexcitations of the system can be changed by more than four orders of magnitude by tuning a bias voltage across the tunneling junctions. Unwanted QCR-induced bit flips are greatly suppressed due to quantum interference in the tunneling process, and thus the long lifetime is preserved. The QCR can serve as a tunable dissipation source that stabilizes Kerr-cat qubits.
Kerr-cat qubits realized in periodically driven superconducting nonlinear resonators are a promising platform for quantum information processing with biased noise. Pure dephasing in such systems induces leakage out of the qubit subspace, motivating the use of quantum circuit refrigeration (QCR) to remove excess excitations. While conventional superconductor--insulator--normal-metal--insulator--superconductor (SINIS)-based QCRs can suppress leakage via single-photon absorption, they also enhance QCR-induced phase-flip errors. Here we investigate a QCR based on a superconductor--insulator--superconductor--insulator--superconductor (SISIS) junction coupled to a Kerr parametric oscillator (KPO). We show that a SISIS-based QCR can operate in a regime where single-photon processes are suppressed while two-photon absorption dominates. As a result, the proposed SISIS-based QCR achieves strong suppression of dephasing-induced leakage while substantially reducing the increase in phase-flip errors associated with QCR operation. These results demonstrate that the proposed SISIS-based QCR provides an effective approach for mitigating leakage while limiting QCR-induced phase-flip errors in Kerr-cat qubits.
We propose a quantum-circuit refrigerator (QCR) based on photon-assisted quasiparticle tunneling through a single normal-metal–insulator–superconductor (NIS) junction. In contrast to previous studies with multiple junctions and an additional charge island for the QCR, we directly connect the NIS junction to an inductively shunted electrode of a superconducting microwave resonator making the device immune to low-frequency charge noise. At low characteristic impedance of the resonator and parameters relevant to a recent experiment, we observe that a semiclassical impedance model of the NIS junction reproduces the bias voltage dependence of the QCR-induced damping rate and frequency shift. For high characteristic impedances, we derive a Born–Markov master equation and use it to observe significant non-linearities in the QCR-induced dissipation and frequency shift. We further demonstrate that, in this regime, the QCR can be used to initialize the linear resonator into a non-thermal state even in the absence of any microwave drive.
Recent advancements in circuit quantum electrodynamics have enabled precise manipulation and detection of the single energy quantum in quantum systems. A quantum circuit refrigerator (QCR) is capable of electrically cooling the excited population of quantum systems, such as superconducting resonators and qubits, through photon-assisted tunneling of quasi-particles within a superconductor-insulator-normal metal junction. In this study, we demonstrated instantaneous QCR in the quantum regime. We performed the time-resolved measurement of the QCR-induced cooling of photon number inside the superconducting resonator by harnessing a qubit as a photon detector. From the enhanced photon loss rate of the resonator estimated from the amount of the AC Stark shift, the QCR was shown to have a cooling power of approximately 300 aW. Furthermore, even below the single energy quantum, the QCR can reduce the number of photons inside the resonator with 100 ns pulse from thermal equilibrium. Numerical calculations based on the Lindblad master equation successfully reproduced these experimental results.
Superconducting microwave circuits are promising candidates for a variety of different applications, ranging from extremely sensitive photon detectors to large-scale quantum computer. Thus, they may revolutionize our everyday lives in the future through substantial technological development. Superconducting quantum circuits typically operate at low power levels and consist of linear and nonlinear resonators. In order to enhance their operation fidelity, they need to be cooled efficiently, and the dissipation of the circuit needs to be well engineered. In this chapter, we describe a refrigerator for electric quantum circuits based on photon-assisted electron tunneling in hybrid superconductor–insulator–normal-metal junctions. Furthermore, such junctions can also serve as incoherent microwave sources. Importantly, the photon absorption and emission rates can be tuned over several orders of magnitude. In addition, these junctions are used for refrigeration and heating of the normal-metal electrons as well as for probing the electron temperature. Here, we present their operation principle and provide insight to their potential applications as well as briefly describe fabrication methods.
Abstract The recent progress in direct active cooling of the quantum‐electric degrees of freedom in engineered circuits, or quantum‐circuit refrigeration is reviewed. In 2017, the discovery of a quantum‐circuit refrigerator (QCR) based on photon‐assisted tunneling of quasiparticles through normal‐metal–insulator–superconductor junctions inspired a series of experimental studies demonstrating the following main properties: i) the direct‐current (dc) bias voltage of the junction can change the QCR‐induced damping rate of a superconducting microwave resonator by orders of magnitude and give rise to nontrivial Lamb shifts, ii) the damping rate can be controlled in nanosecond time scales, and ii) the dc bias can be replaced by a microwave excitation, the amplitude of which controls the induced damping rate. Theoretically, it is predicted that state‐of‐the‐art superconducting resonators and qubits can be reset with an infidelity lower than 10−4 in tens of nanoseconds using experimentally feasible parameters. A QCR‐equipped resonator has also been demonstrated as an incoherent photon source with an output temperature above 1 K yet operating at millikelvin. This source has been used to calibrate cryogenic amplification chains. In the future, the QCR may be experimentally used to quickly reset superconducting qubits, and hence assist in the great challenge of building a practical quantum computer.
Previous studies of photon-assisted tunneling through normal-metal–insulator–superconductor junctions have exhibited potential for providing a convenient tool to control the dissipation of quantum-electric circuits in situ. However, the current literature on such a quantum-circuit refrigerator (QCR) does not present a detailed description for the charge dynamics of the tunneling processes or the phase coherence of the open quantum system. Here, we derive a master equation describing both quantum-electric and charge degrees of freedom, and discover that typical experimental parameters of low temperature and yet lower charging energy yield a separation of time scales for the charge and quantum dynamics. Consequently, the minor effect of the different charge states can be taken into account by averaging over the charge distribution. We also consider applying an ac voltage to the tunnel junction, which enables control of the decay rate of a superconducting qubit over four orders of magnitude by changing the drive amplitude; we find an order-of-magnitude drop in the qubit excitation in 40 ns and a residual reset infidelity below 10−4. Furthermore, for the normal island, we consider the case of charging energy and single-particle level spacing large compared to the superconducting gap, i.e., a quantum dot. Although the decay rates arising from such a dot QCR appear low for use in qubit reset, the device can provide effective negative damping (gain) to the coupled microwave resonator. The Fano factor of such a millikelvin microwave source may be smaller than unity, with the latter value being reached close to the maximum attainable power.