A critical challenge in developing scalable error-corrected quantum systems is the accumulation of errors while performing operations and measurements. One promising approach is todesign a system where errors can be detected and converted into erasures. A recent proposal aims to do this using a dual-rail encoding with superconducting cavities. In this work, we implement such a dual-rail cavity qubit and use it to demonstrate a projective logical measurement with erasure detection. We measure logical state preparation and measurement errors at the 0.01%-level and detect over 99% of cavity decay events as erasures. We use the precision of this new measurement protocol to distinguish different types of errors in this system, finding that while decay errors occur with probability ∼0.2% per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 170 times less frequently. These findings represent the first confirmation of the expected error hierarchy necessary to concatenate dual-rail erasure qubits into a highly efficient erasure code.
Fast, high-fidelity operations between microwave resonators are an important tool for bosonic quantum computation and simulation with superconducting circuits. An attractive approachfor implementing these operations is to couple these resonators via a nonlinear converter and actuate parametric processes with RF drives. It can be challenging to make these processes simultaneously fast and high fidelity, since this requires introducing strong drives without activating parasitic processes or introducing additional decoherence channels. We show that in addition to a careful management of drive frequencies and the spectrum of environmental noise, leveraging the inbuilt symmetries of the converter Hamiltonian can suppress unwanted nonlinear interactions, preventing converter-induced decoherence. We demonstrate these principles using a differentially-driven DC-SQUID as our converter, coupled to two high-Q microwave cavities. Using this architecture, we engineer a highly-coherent beamsplitter and fast (∼ 100 ns) swaps between the cavities, limited primarily by their intrinsic single-photon loss. We characterize this beamsplitter in the cavities‘ joint single-photon subspace, and show that we can detect and post-select photon loss events to achieve a beamsplitter gate fidelity exceeding 99.98%, which to our knowledge far surpasses the current state of the art.
The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computations. To this end, we introducethe circuit-QED dual-rail qubit in which our physical qubit is encoded in the single-photon subspace of two superconducting cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers completely new capabilities. Using a single transmon ancilla, we describe a universal gate set that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors due to the cavity and transmon in all of these operations can be detected and converted to erasure errors, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit delivers an optimal hierarchy of errors and rates, and is expected to be well below the relevant QEC thresholds with today’s devices.
Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates betweenencoded qubits are needed. To that end, we present a family of error-detectable two-qubit gates for a variety of bosonic encodings. From a new geometric framework based on a „Bloch sphere“ of bosonic operators, we construct ZZL(θ) and eSWAP(θ) gates for the binomial, 4-legged cat, dual-rail and several other bosonic codes. The gate Hamiltonian is simple to engineer, requiring only a programmable beamsplitter between two bosonic qubits and an ancilla dispersively coupled to one qubit. This Hamiltonian can be realized in circuit QED hardware with ancilla transmons and microwave cavities. The proposed theoretical framework was developed for circuit QED but is generalizable to any platform that can effectively generate this Hamiltonian. Crucially, one can also detect first-order errors in the ancilla and the bosonic qubits during the gates. We show that this allows one to reach error-detected gate fidelities at the 10−4 level with today’s hardware, limited only by second-order hardware errors.
Many proposals to scale quantum technology rely on modular or distributed designs where individual quantum processors, called nodes, are linked together to form one large multinodequantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, a limiting factor of these machines will be internode gates, which may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require a range of techniques, including improvements in entanglement generation, the use of entanglement distillation, and optimized software and compilers, and it remains unclear how improvements to these components interact to affect overall system performance, what performance from each is required, or even how to quantify the performance of each. In this paper, we employ a `co-design‘ inspired approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. In the case of superconducting MNQCs with microwave-to-optical links, we uncover a tradeoff between entanglement generation and distillation that threatens to degrade performance. We show how to navigate this tradeoff, lay out how compilers should optimize between local and internode gates, and discuss when noisy quantum links have an advantage over purely classical links. Using these results, we introduce a roadmap for the realization of early MNQCs which illustrates potential improvements to the hardware and software of MNQCs and outlines criteria for evaluating the landscape, from progress in entanglement generation and quantum memory to dedicated algorithms such as distributed quantum phase estimation. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.
Acoustic spontaneous emission into bulk dielectrics can be a strong source of decoherence in quantum devices, especially when a qubit is in the presence of piezoelectric materials.We study the dynamics of a qubit coupled to an acoustic resonator by a piezoelectric film. By varying the surface topography of the resonator from rough to polished to shaped, we explore the crossover from fast decay of an excited qubit to quantum-coherent coupling between the qubit and an isolated phonon mode. Our experimental approach may be used for precision measurements of crystalline vibrations, the design of quantum memories, and the study of electro-mechanical contributions to dielectric loss.
By applying a microwave drive to a specially designed Josephson circuit, we have realized an elementary quantum optics model, the squeezed Kerr oscillator. This model displays, as thesqueezing amplitude is increased, a cross-over from a single ground state regime to a doubly-degenerate ground state regime. In the latter case, the ground state manifold is spanned by Schrödinger-cat states, i.e. quantum superpositions of coherent states with opposite phases. For the first time, having resolved up to the tenth excited state in a spectroscopic experiment, we confirm that the proposed emergent static effective Hamiltonian correctly describes the system, despite its driven character. We also find that the lifetime of the coherent state components of the cat states increases in steps as a function of the squeezing amplitude. We interpret the staircase pattern as resulting from pairwise level kissing in the excited state spectrum. Considering the Kerr-cat qubit encoded in this ground state manifold, we achieve for the first time quantum nondemolition readout fidelities greater than 99%, and enhancement of the phase-flip lifetime by more than two orders of magnitude, while retaining universal quantum control. Our experiment illustrates the crucial role of parametric drive Hamiltonian engineering for hardware-efficient quantum computation.
Dielectric loss is known to limit state-of-the-art superconducting qubit lifetimes. Recent experiments imply upper bounds on bulk dielectric loss tangents on the order of 100 parts-per-billion,but because these inferences are drawn from fully fabricated devices with many loss channels, they do not definitively implicate or exonerate the dielectric. To resolve this ambiguity, we have devised a measurement method capable of separating and resolving bulk dielectric loss with a sensitivity at the level of 5 parts-per-billion. The method, which we call the dielectric dipper, involves the in-situ insertion of a dielectric sample into a high-quality microwave cavity mode. Smoothly varying the sample’s participation in the cavity mode enables a differential measurement of the sample’s dielectric loss tangent. The dielectric dipper can probe the low-power behavior of dielectrics at cryogenic temperatures, and does so without the need for any lithographic process, enabling controlled comparisons of substrate materials and processing techniques. We demonstrate the method with measurements of EFG sapphire, from which we infer a bulk loss tangent of 62(7)×10−9 and a substrate-air interface loss tangent of 12(2)×10−4. For a typical transmon, this bulk loss tangent would limit device quality factors to less than 20 million, suggesting that bulk loss is likely the dominant loss mechanism in the longest-lived transmons on sapphire. We also demonstrate this method on HEMEX sapphire and bound its bulk loss tangent to be less than 15(5)×10−9. As this bound is about four times smaller than the bulk loss tangent of EFG sapphire, use of HEMEX sapphire as a substrate would lift the bulk dielectric coherence limit of a typical transmon qubit to several milliseconds.
In chemical reactions, the interplay between coherent evolution and dissipation is central to determining key properties such as the rate and yield. Of particular interest are caseswhere two potential energy surfaces cross at features known as conical intersections (CIs), resulting in nonadiabatic dynamics that may promote ultrafast and highly efficient reactions when rovibrational damping is present. A prominent chemical reaction that involves a CI is the cis-trans isomerization reaction in rhodopsin, which is crucial to vision. CIs in real molecular systems are typically investigated via optical pump-probe spectroscopy, which has demanding spectral bandwidth and temporal resolution requirements, and where precise control of the environment is challenging. A complementary approach for understanding chemical reactions is to use quantum simulators that can provide access to a wider range of observables, though thus far combining strongly interacting linear (rovibrational) and nonlinear (electronic) degrees of freedom with engineered dissipation has yet to be demonstrated. Here, we create a tunable CI in a hybrid qubit-oscillator circuit QED processor and simultaneously track both a reactive wave-packet and electronic qubit in the time-domain. We identify dephasing of the electronic qubit as the mechanism that drives wave-packet branching along the reactive coordinate in our model. Furthermore, we directly observe enhanced branching when the wave-packet passes through the CI. Thus, the forces that influence a chemical reaction can be viewed as an effective measurement induced dephasing rate that depends on the position of the wave-packet relative to the CI. Our results set the groundwork for more complex simulations of chemical dynamics, offering deeper insight into the role of dissipation in determining macroscopic quantities of interest such as the quantum yield of a chemical reaction.
Efficient quantum control of an oscillator is necessary for many bosonic applications including error-corrected computation, quantum-enhanced sensing, robust quantum communication,and quantum simulation. For these applications, oscillator control is often realized through off-resonant hybridization to a qubit with dispersive shift χ where typical operation times of 2π/χ are routinely assumed. Here, we challenge this assumption by introducing and demonstrating a novel control method with typical operation times over an order of magnitude faster than 2π/χ. Using large auxiliary displacements of the oscillator to enhance gate speed, we introduce a universal gate set with built-in dynamical decoupling consisting of fast conditional displacements and qubit rotations. We demonstrate the method using a superconducting cavity weakly coupled to a transmon qubit in a regime where previously known methods would fail. Our demonstrations include preparation of a single-photon state 30 times faster than 2π/χ with 98±1(%) fidelity and preparation of squeezed vacuum with a squeezing level of 11.1 dB, the largest intracavity squeezing reported in the microwave regime. Finally, we demonstrate fast measurement-free preparation of logical states for the binomial and Gottesman-Kitaev-Preskill (GKP) code, and we identify possible fidelity limiting mechanisms including oscillator dephasing.