Encoding a qubit in a high quality superconducting microwave cavity offers the opportunity to perform the first layer of error correction in a single device, but presents a challenge:how can quantum oscillators be controlled while introducing a minimal number of additional error channels? We focus on the two-qubit portion of this control problem by using a 3-wave mixing coupling element to engineer a programmable beamsplitter interaction between two bosonic modes separated by more than an octave in frequency, without introducing major additional sources of decoherence. Combining this with single-oscillator control provided by a dispersively coupled transmon provides a framework for quantum control of multiple encoded qubits. The beamsplitter interaction gbs is fast relative to the timescale of oscillator decoherence, enabling over 103 beamsplitter operations per coherence time, and approaching the typical rate of the dispersive coupling χ used for individual oscillator control. Further, the programmable coupling is engineered without adding unwanted interactions between the oscillators, as evidenced by the high on-off ratio of the operations, which can exceed 105. We then introduce a new protocol to realize a hybrid controlled-SWAP operation in the regime gbs≈χ, in which a transmon provides the control bit for the SWAP of two bosonic modes. Finally, we use this gate in a SWAP test to project a pair of bosonic qubits into a Bell state with measurement-corrected fidelity of 95.5%±0.2%.
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.
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.
Superconducting qubits are a leading platform for scalable quantum computing and quantum error correction. One feature of this platform is the ability to perform projective measurementsorders of magnitude more quickly than qubit decoherence times. Such measurements are enabled by the use of quantum-limited parametric amplifiers in conjunction with ferrite circulators – magnetic devices which provide isolation from noise and decoherence due to amplifier backaction. Because these non-reciprocal elements have limited performance and are not easily integrated on-chip, it has been a longstanding goal to replace them with a scalable alternative. Here, we demonstrate a solution to this problem by using a superconducting switch to control the coupling between a qubit and amplifier. Doing so, we measure a transmon qubit using a single, chip-scale device to provide both parametric amplification and isolation from the bulk of amplifier backaction. This measurement is also fast, high fidelity, and has 70% efficiency, comparable to the best that has been reported in any superconducting qubit measurement. As such, this work constitutes a high-quality platform for the scalable measurement of superconducting qubits.
We present a design for a superconducting, on-chip circulator composed of dynamically modulated transfer switches and delays. Design goals are set for the multiplexed readout of superconductingqubits. Simulations of the device show that it allows for low-loss circulation (insertion loss < 0.35 dB and isolation >20 dB) over an instantaneous bandwidth of 2.3 GHz. As the device is estimated to be linear for input powers up to -65 dBm, this design improves on the bandwidth and power-handling of previous superconducting circulators by over a factor of 50, making it ideal for integration with broadband quantum limited amplifiers.
We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency. Non-reciprocity is created with a combination of frequencyconversion and delay, and requires neither permanent magnets nor microwave control tones, allowing on-chip integration with other superconducting circuits without expensive control hardware. Isolation in the device exceeds 20 dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at select operation frequencies. Furthermore, the device is linear with respect to input power for signal powers up to hundreds of fW (≈103 circulating photons), and the direction of circulation can be dynamically reconfigured. We demonstrate its operation at a selection of frequencies between 4 and 6 GHz.
We introduce a method for breaking Lorentz reciprocity based upon the non-commutation of frequency conversion and delay. The method requires no magnetic materials or resonant physics,allowing for the design of scalable and broadband non-reciprocal circuits. With this approach, two types of gyrators — universal building blocks for linear, non-reciprocal circuits — are constructed. Using one of these gyrators, we create a circulator with > 15 dB of isolation across the 5 — 9 GHz band. Our designs may be readily extended to any platform with suitable frequency conversion elements, including semiconducting devices for telecommunication or an on-chip superconducting implementation for quantum information processing.