Quantum computers use the principles of quantum mechanics to store and manipulate information encoded in the quantized levels of physical systems. A goal of quantum computers is to accurately solve problems that are intractable for classical computers, such as simulating molecular dynamics and prime factorization of large integers. However, the failure probability is too high for quantum computers to solve useful problems. Fortunately, quantum error correction (QEC) provides a way to perform robust computations in the presence of errors by distributing information across multiple physical systems. Bosonic quantum error-correcting codes offer a hardware-efficient avenue for QEC where information is encoded in the continuous phase-space of a single harmonic oscillator. The linear harmonic oscillator realised as the microwave modes of a superconducting resonator is controlled via a nonlinear superconducting control qubit. Experiments on bosonic QEC are limited by bit flip errors in the control qubit, leading to low logical lifetimes of the storage resonator. Our idea is to replace the transmon with a heavy fluxonium qubit that has intrinsic protection against bit-flips. With this architecture in mind, we investigate the performance of a universal gateset comprising of Echoed Conditional Displacement gates and single qubit rotations. Wenumerically solve the Schrödinger equation for a closed resonator- fluxonium device and use a combination of quantum and semiclassical approaches to simulate the system exactly. We adopt a pulse-level implementation of quantum gates where we realize target gates by applying tailored drives on the resonator. We develop a resonator frame-tracking technique that allows us to simulate the dynamics of the driven resonator exactly with less than five fock levels while retaining all the physics of the problem. This technique allowed us to accurately simulate the device up to a few 10000s of photons, matching experimental results, that otherwise would not be possible even using high-performance computers due to excessive memory and simulation time required.
Quantum computers use the principles of quantum mechanics to store and manipulate information encoded in the quantized levels of physical systems. A goal of quantum computers is to accurately solve problems that are intractable for classical computers, such as simulating molecular dynamics and prime factorization of large integers. However, the failure probability is too high for quantum computers to solve useful problems. Fortunately, quantum error correction (QEC) provides a way to perform robust computations in the presence of errors by distributing information across multiple physical systems. Bosonic quantum error-correcting codes offer a hardware-efficient avenue for QEC where information is encoded in the continuous phase-space of a single harmonic oscillator. The linear harmonic oscillator realised as the microwave modes of a superconducting resonator is controlled via a nonlinear superconducting control qubit. Experiments on bosonic QEC are limited by bit flip errors in the control qubit, leading to low logical lifetimes of the storage resonator. Our idea is to replace the transmon with a heavy fluxonium qubit that has intrinsic protection against bit-flips. With this architecture in mind, we investigate the performance of a universal gateset comprising of Echoed Conditional Displacement gates and single qubit rotations. Wenumerically solve the Schrödinger equation for a closed resonator- fluxonium device and use a combination of quantum and semiclassical approaches to simulate the system exactly. We adopt a pulse-level implementation of quantum gates where we realize target gates by applying tailored drives on the resonator. We develop a resonator frame-tracking technique that allows us to simulate the dynamics of the driven resonator exactly with less than five fock levels while retaining all the physics of the problem. This technique allowed us to accurately simulate the device up to a few 10000s of photons, matching experimental results, that otherwise would not be possible even using high-performance computers due to excessive memory and simulation time required.
Echoed Conditional Displacement (ECD) gates constitute a fundamental building block for quantum control of harmonic oscillator modes. However, bit-flips of the auxiliary qubit remain a dominant error mechanism for this kind of bosonic control. In this work, we present a numerical case study of a bit-flip protected fluxonium operating as the control qubit and numerically implement ECD gates in a single-mode resonator-fluxonium device, demonstrating that fidelities exceeding 99.9% are possible. We systematically investigate the resonator dynamics using a combination of semiclassical trajectories and master equation simulations, numerically revealing asymptotic saturation of the dispersive shift in the strongly driven regime of the resonator. We develop an efficient technique to numerically simulate the strongly driven regime of the resonator using a semiclassical formulation that maps the full perturbation series in the dispersive expansion as order-by-order frequency shifts. This provides a compact polynomial description of the resonator which is intuitive and remains valid throughout the dispersive regime. Furthermore, we propose an improved ECD sequence that accounts for the effects of photon loss and spurious nonlinear terms on resonator trajectories.
Bosonic quantum error correction (QEC) offers a hardware-efficient route to fault-tolerant quantum computing. To date, however, superconducting circuit implementations of bosonic codes have utilized centimeter-scale 3D microwave cavities controlled by fixed-frequency transmon qubits, with logical lifetimes limited by transmon bit-flip errors. Here, we realize bosonic QEC in a fully planar architecture by pairing a heavy fluxonium, whose 451±70μs bit-flip lifetime exceeds that of any control qubit in previous demonstrations, with an on-chip Archimedean spiral resonator several orders of magnitude smaller in mode volume than prior 3D cavities. We prepare finite-energy Gottesman-Kitaev-Preskill (GKP) states and stabilize them using measurement-free error correction with rapid fluxonium reset, extending the logical lifetime by a factor of 1.59±0.05. These results provide the first demonstration of resonator control using a weakly coupled fluxonium and, with it, the first realization of standalone bosonic QEC in a fully planar superconducting circuit architecture.
Bosonic codes in superconducting resonators are a hardware-efficient avenue for quantum error correction and benefit from the inherent bias toward relaxation errors provided by long-lived cavities compared to typical superconducting qubits. The required coupling to an ancillary control qubit, however, can negate these benefits by inducing highly detrimental effects such as excess decoherence and undesired nonlinearities. This is exemplified by the typically employed transmon qubit that imposes limits on cavity operations due to its finite lifetime as well as the inevitably induced self-Kerr nonlinearity. An important question is thus whether a cavity-qubit coupling can be realized that offers readout and control capabilities without spoiling the cavity. Here, motivated by its long lifetime and design flexibility of its Hamiltonian, we experimentally investigate the fluxonium as a control qubit for superconducting cavities. We couple a fluxonium qubit to a superconducting resonator in the strong-dispersive regime and use it to measure the coherence and flux-tunable inherited nonlinearities of the resonator. We then demonstrate quantum control of the oscillator by preparing and characterizing resonator Fock states and their superpositions, with fidelities limited by resonator decay in our planar prototype device. Finally, we show that the fluxonium can realize cavity-couplings that eliminate undesirable cavity nonlinearities and reach regimes of suppressed self-Kerr that are inaccessible to transmon-based devices. Our results thus demonstrate the potential of the fluxonium as a high-performance bosonic control qubit for superconducting cavities that can outperform existing transmon-based architectures.
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum electrodynamics (cQED) architecture. There, the low energy states of a nonlinear electronic oscillator are isolated and addressed as a qubit. These qubits are capacitively coupled to the modes of a microwave-frequency transmission line resonator which serves as a quantum communication bus. Microwave electrical pulses are applied to the resonator to manipulate or measure the qubit state. State control is calibrated using diagnostic sequences that expose systematic errors. Hybridization of the resonator with the qubit gives it a nonlinear response when driven strongly, useful for amplifying the measurement signal to enhance accuracy. Qubits coupled to the same bus may coherently interact with one another via the exchange of virtual photons. A two-qubit conditional phase gate mediated by this interaction can deterministically entangle its targets, and is used to generate two-qubit Bell states and three-qubit GHZ states. These three-qubit states are of particular interest because they redundantly encode quantum information. They are the basis of the quantum repetition code prototypical of more sophisticated schemes required for quantum computation. Using a three-qubit Toffoli gate, this code is demonstrated to autonomously correct either bit- or phase-flip errors. Despite observing the expected behavior, the overall fidelity is low because of decoherence. A superior implementation of cQED replaces the transmission-line resonator with a three-dimensional box mode, increasing lifetimes by an order of magnitude. In-situ qubit frequency control is enabled with control lines, which are used to fully characterize and control the system Hamiltonian.
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 processors rely on controllable quantum systems, which are prone to many kinds of errors, partly due to the environment, and therefore require quantum error correction with many physical resources to operate fault-tolerantly.To reduce physical errors hence resource overheads, bosonic encodings have emerged, taking advantage of the infinitely large Hilbert space of harmonic oscillators for intrinsic autonomous error correction.However, with such infinite systems, capturing the physics of gates and error processes becomes challenging, and classical simulations require taking into account many excited states of the Hilbert space to model their dynamics.Besides, for the quantum error correction to work, the level of noise has to be below a constant value called the accuracy threshold.Optimizing the implementation of a quantum computer based on the concatenation of such a bosonic code with a multi-qubit code is two-fold.First, one can optimize the physical systems and their dynamics which require tools to simulate their behavior accurately.Second, one can optimize the quantum error correction code to increase the threshold value hence easing the experimental requirements for the construction of a large-scale quantum computer.In this thesis, we propose and analyze analytical and numerical methods for the simulation of the repetition cat code, both at the physical level of the cat qubit and also at the logical level of the multi-qubit code, and design a performance optimization for the code.The protection against the environment induced noise is achieved via a two-photon dissipation confinement, which protects arbitrarily well the cat qubit against bit-flip errors with the average number of photons in the cat state.To simulate the dynamics of composite cat-qubit systems, we rely on the invariant operators of this dissipation and design a numerical method based on a perturbation analysis with an asymptotic expansion exploiting the formulation of the slow dynamics of reduced dimension.The repetition code implemented using cat qubits then protects against phase-flips.We propose a performance optimization of the repetition cat code architecture using fast ancilla and fast but noisy CNOT gates for parity measurements, leading to high thresholds as well as a better sub-threshold logical error suppression and demonstrate its robustness in presence of the leakage by developing a new sampling method.