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.
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.
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 is a relatively new computing paradigm that leverages entanglement to implement algorithms beyond the reach of classical hardware. Superconducting quantum circuits have emerged as a platform to build quantum processors, with demonstrations of quantum supremacy over classical supercomputers and quantum error correction beyond fault tolerance. However, current noisy devices require significant improvements to unlock the full potential of quantum algorithms.This thesis investigates intrinsic noise channels in superconducting circuits and the design of noise-resilient qubits. By characterizing high-quality superconducting resonators, we identify lossy dielectric materials at the interfaces as the dominant loss mechanism, which we mitigate via targeted surface treatments. Subsequently, we leverage Josephson junction nonlinearity to engineer noise-biased qubits utilizing the Kerr parametric oscillator (KPO). By analyzing the efficiency of strong, far-off-resonance driving to facilitate three- and four-wave mixing processes, we demonstrate high-fidelity operations on Fock, Kerr-cat, and dual-rail qubits. For the Kerr-cat qubit, we introduce a novel 2D architecture that enables strong light-matter coupling with suppressed Purcell decay, yielding millisecond-scale bit-flip lifetimes. Within this same architecture, we demonstrate a longitudinal qubit readout with a 99.6% quantum nondemolition score, alongside a high-fidelity universal single-qubit gate set, all while maintaining bit-flip error suppression. Finally, we exploit the efficient wave-mixing of strongly coupled, far-detuned KPOs to realize a dynamically protected dual-rail qubit exhibiting both erasure bias and high-fidelity single-qubit gates.
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
DC-voltage-biased Josephson junctions have been recently employed in superconducting circuits for Hamiltonian engineering, demonstrating microwave amplification, single photon sources and entangled photon generation. Compared to more conventional approaches based on parametric pumps, this solution typically enables larger interaction strengths. In the context of quantum information, a two-to-one photon interaction can stabilize cat qubits, where bit-flip errors are exponentially suppressed, promising significant resource savings for quantum error correction. This work investigates how the DC bias approach to Hamiltonian engineering can benefit cat qubits. We find a simple circuit design that is predicted to showcase a two-to-one photon exchange rate larger than that of the parametric pump-based implementation while dynamically averaging typically resonant parasitic terms such as Kerr and cross Kerr. In addition to addressing qubit stabilization, we propose to use injection locking with a cat-qubit adapted frequency filter to prevent long-term drifts of the cat qubit angle associated to DC voltage noise. The whole scheme is simulated without rotating-wave approximations, highlighting for the first time the amplitude of related oscillatory effects in cat-qubit stabilization schemes. This study lays the groundwork for the experimental realization of such a circuit.
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.
Kerr-cat qubits are bosonic qubits offering autonomous bit-flip protection, traditionally studied using driven superconducting nonlinear asymmetric inductive element (SNAIL) oscillators. Here, we theoretically explore an alternative circuit for Kerr-cat qubits based on symmetrically threaded superconducting quantum interference devices (SQUIDs). The symmetrically threaded SQUID (STS) architecture employs a simplified flux-pumped design that suppresses two-photon dissipation, a dominant loss mechanism in high-Kerr regimes, by engineering the drive Hamiltonian’s flux operator to generate only even-order harmonics. By fulfilling two critical criteria for practical Kerr-cat qubit operation, the STS emerges as an ideal platform: (1) a static Hamiltonian with diluted Kerr nonlinearity (achieved via the STS’s middle branch) and (2) a drive Hamiltonian restricted to even harmonics, which ensures robust two-photon driving with reduced dissipation. For weak Kerr nonlinearity, we find that the coherent state lifetime ( T α ) is similar between STS and SNAIL circuits. However, STS Kerr-cat qubits exhibit enhanced resistance to higher-order photon dissipation, enabling significantly extended T α even with stronger Kerr nonlinearities (approximately 10 MHz). In contrast to SNAIL, STS Kerr-cat qubits display a T α dip under weak two-photon driving for a high Kerr coefficient. We demonstrate that this dip can be suppressed by applying drive-dependent detuning, enabling Kerr-cat qubit operation with only eight Josephson junctions (of energies 80 GHz); fewer junctions suffice for higher junction energies. We further validate the robustness of the STS design by studying the impact of strong flux driving and asymmetric Josephson junctions on T α . With the proposed design and considering a cat size of ten photons, we predict T α of the order of tens of milliseconds, even in the presence of multiphoton heating and dephasing effects. The robustness of the STS Kerr-cat qubit makes it a promising component for fault-tolerant quantum processors.