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 ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract thenatural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process faced an excessive generation of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. We answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is significantly longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of G=2.27±0.07. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.
As superconductors are cooled below their critical temperature, stray magnetic flux can become trapped in regions that remain normal. The presence of trapped flux facilitates dissipationof ac current in a superconductor, leading to losses in superconducting elements of microwave devices. In type II superconductors, dissipation is well-understood in terms of the dynamics of vortices hosting a single flux quantum. In contrast, the ac response of type I superconductors with trapped flux has not received much attention. Building on Andreev’s early work [Sov. Phys. JETP 24, 1019 (1967)], here we show theoretically that the dominant dissipation mechanism is the absorption of the ac field at the exposed surfaces of the normal regions, while the deformation of the superconducting/normal interfaces is unimportant. We use the developed theory to estimate the degradation of the quality factors in field-cooled cavities, and we satisfactorily compare these theoretical estimates to the measured field dependence of the quality factors of two aluminum cavities.
High-Q microwave cavity modes coupled to transmon ancillas provide a hardware-efficient platform for quantum computing. Due to their coupling, the cavity modes inherit finite nonlinearityfrom the transmons. In this work, we theoretically and experimentally investigate how an off-resonant drive on the transmon ancilla modifies the nonlinearities of cavity modes in qualitatively different ways, depending on the interrelation among cavity-transmon detuning, drive-transmon detuning and transmon anharmonicity. For a cavity-transmon detuning that is smaller than or comparable to the drive-transmon detuning and transmon anharmonicity, the off-resonant transmon drive can induce multiphoton resonances among cavity and transmon excitations that strongly modify cavity nonlinearities as drive parameters vary. For a large cavity-transmon detuning, the drive induces cavity-photon-number-dependent ac Stark shifts of transmon levels that translate into effective cavity nonlinearities. In the regime of a weak transmon-cavity coupling, the cavity Kerr nonlinearity relates to the third-order nonlinear susceptibility function χ(3) of the driven ancilla. This susceptibility function provides a numerically efficient way of computing the cavity Kerr particularly for systems with many cavity modes controlled by a single transmon. It also serves as a diagnostic tool for identifying undesired drive-induced multiphoton resonance processes. Lastly, we show that by judiciously choosing the drive amplitude, a single off-resonant transmon drive can be used to cancel the cavity self-Kerr nonlinearity as well as inter-cavity cross-Kerr. This provides a way of dynamically correcting the cavity Kerr nonlinearity during bosonic operations or quantum error correction protocols that rely on the cavity modes being linear.
Modular networks are a promising paradigm for increasingly complex quantum devices based on the ability to transfer qubits and generate entanglement between modules. These tasks requirea low-loss, high-speed intermodule link that enables extensible network connectivity. Satisfying these demands simultaneously remains an outstanding goal for long-range optical quantum networks as well as modular superconducting processors within a single cryostat. We demonstrate communication and entanglement in a superconducting network with a microwave-actuated beamsplitter transformation between two bosonic qubits, which are housed in separate modules and joined by a demountable coaxial bus resonator. We transfer a qubit in a multi-photon encoding and track photon loss events to improve the fidelity, making it as high as in a single-photon encoding. Furthermore, generating entanglement with two-photon interference and postselection against loss errors produces a Bell state with success probability 79% and fidelity 0.94, halving the error obtained with a single photon. These capabilities demonstrate several promising methods for faithful operations between modules, including novel possibilities for resource-efficient direct gates.
Nanofabrication techniques for superconducting qubits rely on resist-based masks patterned by electron-beam or optical lithography. We have developed an alternative nanofabricationtechnique based on free-standing silicon shadow masks fabricated from silicon-on-insulator wafers. These silicon shadow masks not only eliminate organic residues associated with resist-based lithography, but also provide a pathway to better understand and control surface-dielectric losses in superconducting qubits by decoupling mask fabrication from substrate preparation. We have successfully fabricated aluminum 3D transmon superconducting qubits with these shadow masks, and demonstrated energy relaxation times on par with state-of-the-art values.
The majority of quantum information tasks require error-corrected logical qubits whose coherence times are vastly longer than that of currently available physical qubits. Among themany quantum error correction codes, bosonic codes are particularly attractive as they make use of a single quantum harmonic oscillator to encode a correctable qubit in a hardware-efficient manner. One such encoding, based on grid states of an oscillator, has the potential to protect a logical qubit against all major physical noise processes. By stroboscopically modulating the interaction of a superconducting microwave cavity with an ancillary transmon, we have successfully prepared and permanently stabilized these grid states. The lifetimes of the three Bloch vector components of the encoded qubit are enhanced by the application of this protocol, and agree with a theoretical estimate based on the measured imperfections of the experiment.
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depends on the quantity which is measured. In a partial measurement performedby an ideal apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrate this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures is observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.
Photonic states of superconducting microwave cavities controlled by transmon ancillas provide a platform for encoding and manipulating quantum information. A key challenge in scalingup the platform is the requirement to communicate on demand the information between the cavities. It has been recently demonstrated that a tunable bilinear interaction between two cavities can be realized by coupling them to a bichromatically-driven transmon ancilla, which allows swapping and interfering the multi-photon states of the cavities [Gao et al., Phys. Rev. X 8, 021073(2018)]. Here, we explore both theoretically and experimentally the regime of relatively strong drives on the ancilla needed to achieve fast SWAP gates but which can also lead to undesired non-perturbative effects that lower the SWAP fidelity. We develop a theoretical formalism based on linear response theory that allows one to calculate the rate of ancilla-induced interaction, decay and frequency shift of the cavities in terms of a susceptibility matrix. We treat the drives non-perturbatively using Floquet theory, and find that the interference of the two drives can strongly alter the system dynamics even in the regime where the rotating wave approximation applies. We identify two major sources of infidelity due to ancilla decoherence. i) Ancilla dissipation and dephasing lead to incoherent hopping among ancilla Floquet states, which results in a sudden change of the SWAP rate thereby decohering the operations. ii) The cavities inherit finite decay from the relatively lossy ancilla through the inverse Purcell effect; the effect can be enhanced when the drive-induced AC Stark shift pushes certain ancilla transition frequencies to the vicinity of the cavity frequencies. The theoretical predictions agree quantitatively with the experimental results, paving the way for using the theory for designing and optimizing future experiments.
A quantum system driven by a weak deterministic force while under strong continuous energy measurement exhibits quantum jumps between its energy levels. This celebrated phenomenon isemblematic of the special nature of randomness in quantum physics. The times at which the jumps occur are reputed to be fundamentally unpredictable. However, certain classical phenomena, like tsunamis, while unpredictable in the long term, may possess a degree of predictability in the short term, and in some cases it may be possible to prevent a disaster by detecting an advance warning signal. Can there be, despite the indeterminism of quantum physics, a possibility to know if a quantum jump is about to occur or not? In this paper, we answer this question affirmatively by experimentally demonstrating that the completed jump from the ground to an excited state of a superconducting artificial atom can be tracked, as it follows its predictable „flight,“ by monitoring the population of an auxiliary level coupled to the ground state. Furthermore, we show that the completed jump is continuous, deterministic, and coherent. Exploiting this coherence, we catch and reverse a quantum jump mid-flight, thus preventing its completion. This real-time intervention is based on a particular lull period in the population of the auxiliary level, which serves as our advance warning signal. Our results, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory and provide new ground for the exploration of real-time intervention techniques in the control of quantum systems, such as early detection of error syndromes.