Bosonic modes have wide applications in various quantum technologies, such as optical photons for quantum communication, magnons in spin ensembles for quantum information storage andmechanical modes for reversible microwave-to-optical quantum transduction. There is emerging interest in utilizing bosonic modes for quantum information processing, with circuit quantum electrodynamics (circuit QED) as one of the leading architectures. Quantum information can be encoded into subspaces of a bosonic superconducting cavity mode with long coherence time. However, standard Gaussian operations (e.g., beam splitting and two-mode squeezing) are insufficient for universal quantum computing. The major challenge is to introduce additional nonlinear control beyond Gaussian operations without adding significant bosonic loss or decoherence. Here we review recent advances in universal control of a single bosonic code with superconducting circuits, including unitary control, quantum feedback control, driven-dissipative control and holonomic dissipative control. Entangling different bosonic modes with various approaches is also discussed.
Single-photon detectors are ubiquitous and integral components of photonic quantum cryptography, communication, and computation. Many applications, however, require not only detectingthe presence of any photons, but distinguishing the number present with a single shot. Here, we implement a single-shot, high-fidelity photon number-resolving detector of up to 15 microwave photons in a cavity-qubit circuit QED platform. This detector functions by measuring a series of generalized parity operators which make up the bits in the binary decomposition of the photon number. Our protocol consists of successive, independent measurements of each bit by entangling the ancilla with the cavity, then reading out and resetting the ancilla. Photon loss and ancilla readout errors can flip one or more bits, causing nontrivial errors in the outcome, but these errors have a traceable form which can be captured in a simple hidden Markov model. Relying on the independence of each bit measurement, we mitigate biases in the measurement result, showing good agreement with the predictions of the model. The mitigation improves the average total variation distance error of Fock states from 13.5% to 1.3%. We also show that the mitigation is efficiently scalable to an M-mode system provided that the errors are independent and sufficiently small. Our work motivates the development of new algorithms that utilize single-shot, high-fidelity PNR detectors.
Low-loss cavities are important in building high-coherence superconducting quantum computers. Generating high quality joints between parts is crucial to the realization of a scalablequantum computer using the circuit quantum electrodynamics (cQED) framework. In this paper, we adapt the technique of indium bump bonding to the cQED architecture to realize high quality superconducting microwave joints between chips. We use this technique to fabricate compact superconducting cavities in the multilayer microwave integrated quantum circuits (MMIQC) architecture and achieve single photon quality factor over 300 million or single-photon lifetimes approaching 5 ms. To quantify the performance of the resulting seam, we fabricate microwave stripline resonators in multiple sections connected by different numbers of bonds, resulting in a wide range of seam admittances. The measured quality factors combined with the designed seam admittances allow us to bound the conductance of the seam at gseam≥2×1010/(Ωm). Such a conductance should enable construction of micromachined superconducting cavities with quality factor of at least a billion. These results demonstrate the capability to construct very high quality microwave structures within the MMIQC architecture.
Ancilla systems are often indispensable to universal control of a nearly isolated quantum system. However, ancilla systems are typically more vulnerable to environmental noise, whichlimits the performance of such ancilla-assisted quantum control. To address this challenge of ancilla-induced decoherence, we propose a general framework that integrates quantum control and quantum error correction, so that we can achieve robust quantum gates resilient to ancilla noise. We introduce the path independence criterion for fault-tolerant quantum gates against ancilla errors. As an example, a path-independent gate is provided for superconducting circuits with a hardware-efficient design.
The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. A controllable bosonic machine is naturally suited for simulatingsystems with underlying bosonic structure, exploiting both quantum interference and an intrinsically large Hilbert space. Here, we experimentally realize a bosonic superconducting processor that combines arbitrary state preparation, a complete set of Gaussian operations, plus an essential non-Gaussian resource – a novel single-shot photon number resolving measurement scheme – all in one device. We utilize these controls to simulate the bosonic problem of molecular vibronic spectra, extracting the corresponding Franck-Condon factors for photoelectron processes in H2O, O3, NO2, and SO2. Our results demonstrate the versatile capabilities of the circuit QED platform, which can be extended to include non-Gaussian operations for simulating an even wider class of bosonic systems.
Qubit measurements are central to quantum information processing. In the field of superconducting qubits, standard readout techniques are not only limited by the signal-to-noise ratio,but also by state relaxation during the measurement. In this work, we demonstrate that the limitation due to relaxation can be suppressed by using the many-level Hilbert space of superconducting circuits: in a multilevel encoding, the measurement is only corrupted when multiple errors occur. Employing this technique, we show that we can directly resolve transmon gate errors at the level of one part in 103. Extending this idea, we apply the same principles to the measurement of a logical qubit encoded in a bosonic mode and detected with a transmon ancilla, implementing a proposal by Hann et al. [Phys. Rev. A \textbf{98} 022305 (2018)]. Qubit state assignments are made based on a sequence of repeated readouts, further reducing the overall infidelity. This approach is quite general and several encodings are studied; the codewords are more distinguishable when the distance between them is increased with respect to photon loss. The tradeoff between multiple readouts and state relaxation is explored and shown to be consistent with the photon-loss model. We report a logical assignment infidelity of 5.8×10−5 for a Fock-based encoding and 4.2×10−3 for a QEC code (the S=2,N=1 binomial code). Our results will not only improve the fidelity of quantum information applications, but also enable more precise characterization of process or gate errors.
To solve classically hard problems, quantum computers need to be resilient to the influence of noise and decoherence. In such a fault-tolerant quantum computer, noise-induced errorsmust be detected and corrected in real-time to prevent them from propagating between components. This requirement is especially pertinent while applying quantum gates, when the interaction between components can cause errors to quickly spread throughout the system. However, the large overhead involved in most fault-tolerant architectures makes implementing these systems a daunting task, which motivates the search for hardware-efficient alternatives. Here, we present a gate enacted by a multilevel ancilla transmon on a cavity-encoded logical qubit that is fault-tolerant with respect to decoherence in both the ancilla and the encoded qubit. We maintain the purity of the encoded qubit in the presence of ancilla errors by detecting those errors in real-time, and applying the appropriate corrections. We show a reduction of the logical gate error by a factor of two in the presence of naturally occurring decoherence, and demonstrate resilience against ancilla bit-flips and phase-flips by observing a sixfold suppression of the gate error with increased energy relaxation, and a fourfold suppression with increased dephasing noise. The results demonstrate that bosonic logical qubits can be controlled by error-prone ancilla qubits without inheriting the ancilla’s inferior performance. As such, error-corrected ancilla-enabled gates are an important step towards fully fault-tolerant processing of bosonic qubits.
Hybrid quantum systems in which acoustic resonators couple to superconducting qubits are promising quantum information platforms. High quality factors and small mode volumes make acousticmodes ideal quantum memories, while the qubit-phonon coupling enables the initialization and manipulation of quantum states. We present a scheme for quantum computing with multimode quantum acoustic systems, and based on this scheme, propose a hardware-efficient implementation of a quantum random access memory (qRAM). Quantum information is stored in high-Q phonon modes, and couplings between modes are engineered by applying off-resonant drives to a transmon qubit. In comparison to existing proposals that involve directly exciting the qubit, this scheme can offer a substantial improvement in gate fidelity for long-lived acoustic modes. We show how these engineered phonon-phonon couplings can be used to access data in superposition according to the state of designated address modes–implementing a qRAM on a single chip.
The realization of robust universal quantum computation with any platform ultimately requires both the coherent storage of quantum information and (at least) one entangling operationbetween individual elements. The use of continuous-variable bosonic modes as the quantum element is a promising route to preserve the coherence of quantum information against naturally-occurring errors. However, operations between bosonic modes can be challenging. In analogy to the exchange interaction between discrete-variable spin systems, the exponential-SWAP unitary [UE(θc)] can coherently transfer the states between two bosonic modes, regardless of the chosen encoding, realizing a deterministic entangling operation for certain θc. Here, we develop an efficient circuit to implement UE(θc) and realize the operation in a three-dimensional circuit QED architecture. We demonstrate high-quality deterministic entanglement between two cavity modes with several different encodings. Our results provide a crucial primitive necessary for universal quantum computation using bosonic modes.
High-fidelity qubit measurements play a crucial role in quantum computation, communication, and metrology. In recent experiments, it has been shown that readout fidelity may be improvedby performing repeated quantum non-demolition (QND) readouts of a qubit’s state through an ancilla. For a qubit encoded in a two-level system, the fidelity of such schemes is limited by the fact that a single error can destroy the information in the qubit. On the other hand, if a bosonic system is used, this fundamental limit could be overcome by utilizing higher levels such that a single error still leaves states distinguishable. In this work, we present a robust readout scheme, applicable to bosonic systems dispersively coupled to an ancilla, which leverages both repeated QND readouts and higher-level encodings to asymptotically suppress the effects of qubit/cavity relaxation and individual measurement infidelity. We calculate the measurement fidelity in terms of general experimental parameters, provide an information-theoretic description of the scheme, and describe its application to several encodings, including cat and binomial codes.