Ahmed Hajr, Bingcheng Qing, Ke Wang, Gerwin Koolstra, Zahra Pedramrazi, Ziqi Kang, Larry Chen, Long B. Nguyen, Christian Jünger, Noah Goss, Irwin Huang, Bibek Bhandari, Nicholas Frattini, Shruti Puri, Justin Dressel, Andrew N. Jordan, David Santiago, Irfan A. Siddiqi
The Kerr-cat qubit is a bosonic qubit in which multiphoton Schrödinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressed bit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions necessary for stabilizing and controlling this qubit has traditionally required strong microwave drives that heat the qubit and degrade its performance. In contrast, increasing the coupling to the drive port removes the need for strong drives at the expense of large Purcell decay. By integrating an effective band-block filter on chip, we overcome this trade-off and realize a Kerr-cat qubit in a scalable 2D superconducting circuit with high coherence. This filter provides 30 dB of isolation at the qubit frequency with negligible attenuation at the frequencies required for stabilization and readout. We experimentally demonstrate quantum nondemolition readout fidelity of 99.6% for a cat with eight photons. Also, to have high-fidelity universal control over this qubit, we combine fast Rabi oscillations with a new demonstration of the X ( π / 2 ) gate through phase modulation of the stabilization drive. Finally, the lifetime in this architecture is examined as a function of the cat size of up to ten photons in the oscillator, achieving a bit-flip time higher than 1 ms and only a linear increase in the phase-flip rate, in good agreement with the theoretical analysis of the circuit. Our qubit shows promise as a building block for fault-tolerant quantum processors with a small footprint. Published by the American Physical Society 2024
The Kerr-cat qubit is a bosonic qubit in which multiphoton Schrödinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressed bit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions necessary for stabilizing and controlling this qubit has traditionally required strong microwave drives that heat the qubit and degrade its performance. In contrast, increasing the coupling to the drive port removes the need for strong drives at the expense of large Purcell decay. By integrating an effective band-block filter on chip, we overcome this trade-off and realize a Kerr-cat qubit in a scalable 2D superconducting circuit with high coherence. This filter provides 30 dB of isolation at the qubit frequency with negligible attenuation at the frequencies required for stabilization and readout. We experimentally demonstrate quantum nondemolition readout fidelity of 99.6% for a cat with eight photons. Also, to have high-fidelity universal control over this qubit, we combine fast Rabi oscillations with a new demonstration of the X ( π / 2 ) gate through phase modulation of the stabilization drive. Finally, the lifetime in this architecture is examined as a function of the cat size of up to ten photons in the oscillator, achieving a bit-flip time higher than 1 ms and only a linear increase in the phase-flip rate, in good agreement with the theoretical analysis of the circuit. Our qubit shows promise as a building block for fault-tolerant quantum processors with a small footprint. Published by the American Physical Society 2024
Quantum computing promises exponential advantages for simulating quantum systems and solving certain computational problems beyond the reach of classical computers, but the fragility of qubits and the resulting errors present a major challenge for scalable implementations. One promising approach is to engineer qubits whose physical noise processes are intrinsically biased, enabling more efficient quantum error correction. This dissertation investigates quantum computing with superconducting Kerr-cat qubits, a bosonic qubit architecture in which qubit states are encoded in coherent states of a nonlinear oscillator stabilized by a two-photon drive. This stabilization creates an effective double-well pseudo-potential that strongly suppresses bit-flip errors while enabling universal quantum control, leading to a noise-biased qubit. A superconducting device architecture based on SNAIL nonlinear oscillators is developed to realize Kerr-cat qubits with tunable parameters and high coherence, integrating readout resonators, dedicated filters, and microwave control lines for measurement and manipulation. Universal single-qubit gates are implemented using engineered single-photon and two-photon drives to deform the pseudo-potential, and a cat-quadrature readout method is employed to achieve high-fidelity quantum nondemolition measurement. The performance of the qubits is systematically characterized through lifetime measurements and benchmarking protocols, including quantum process tomography, gate set tomography, and dihedral randomized benchmarking, revealing a strongly biased noise structure with high performance. These results establish an experimental framework for the design, control, and characterization of Kerr-cat qubits and demonstrate their potential as hardware-efficient building blocks for scalable fault-tolerant quantum computing.
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.
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.
We present a systematic study of Schrödinger cat codes constructed from Kerr-type coherent states, including displaced Kerr coherent states and Barut--Girardello Kerr coherent states, each admitting two distinct families determined by the sign of the Kerr nonlinearity. By tuning the Kerr parameter and coherent-state amplitude, these states interpolate between su(2), su(1,1) coherent states, providing a unified and versatile foundation for this type of bosonic quantum error correction. Unlike standard two-component Schrödinger cat codes, where a single photon-loss event induces an uncorrectable bit-flip, the nonlinear phase-space structure of Kerr cat states enables simultaneous detection and correction of both photon-loss and dephasing errors within a unified recovery framework, with optimal recovery operations determined via convex optimization. We demonstrate that Kerr cat encodings significantly outperform conventional cat codes under combined loss and dephasing noise, and that judicious parameter optimization can suppress both error channels to a level that reduces the overhead of additional error correction layers. We further show that Kerr-deformed coherent-state manifolds under engineered two-photon driving emerge as effective steady states of driven-dissipative dynamics, with single-photon decoherence strongly suppressed and leakage outside the protected manifold appearing only as higher-order corrections in the deformation strength. Our extended formalism identifies generalized Kerr Schrödinger cat codes as promising candidates for fault-tolerant bosonic quantum computation in experimental platforms such as nonlinear photonics.
Cat qubits exhibit a strong noise bias, meaning that errors are predominantly confined to a single error channel, which can be corrected using a simple one-dimensional error correction code. As a result, cat qubits quadratically reduce the number of physical qubits required to realise a fully protected logical qubit compared with conventional surface codes. Recently a Kerr cat qubit was for the first time controlled with four-wave mixing in a SNAIL device. In this project we propose a circuit architecture adapted for four-wave mixing in the form of a capacitively shunted Josephson junction array which we call Kerr Josephson junction array oscillator (KJJA-oscillator). The device is fixed in frequency and not flux tunable, making it resilient to flux noise. Moreover the device strongly suppresses high order non-linearities, and therefore offers low intrinsic dephasing. The mathematical description of the KJJA-oscillator is developed, from which two KJJA-oscillators is designed. With four wave mixing the squeezing term of the Kerr Hamiltonian is realised with two separate drives slightly detuned from the cavity. This makes it possible to place cavities in the full frequency range of the signal generator. The Kerr is chosen as a neutral value in the trade-off between fast operations and long coherence times, based of previous results in the literature. The fabricated chip is characterised and found to exhibit low coherence times, most likely due to low fabrication quality. There is no known direct readout mechanism for four-wave mixing known to the author, instead an ancillary transmon was used to perform parity measurements. To showcase the readout mechanism Wigner-tomography of the vacuum state was measured. Due to the time constraints of the thesis there was not time to stabilise cats and show noise biasing properties. The chip will in the future be used to show how noise biasing scales with increasing cat state size and for demonstration of a universal single gate set.