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.
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.
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.
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.
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.
Modular quantum computing architectures require fast and efficient distribution of quantum information through propagating signals. Here we report rapid, on-demand quantum state transferbetween two remote superconducting cavity quantum memories through traveling microwave photons. We demonstrate a quantum communication channel by deterministic transfer of quantum bits with 76% fidelity. Heralding on errors induced by experimental imperfection can improve this to 87% with a success probability of 0.87. By partial transfer of a microwave photon, we generate remote entanglement at a rate that exceeds photon loss in either memory by more than a factor of three. We further show the transfer of quantum error correction code words that will allow deterministic mitigation of photon loss. These results pave the way for scaling superconducting quantum devices through modular quantum networks.
Entangling gates between qubits are a crucial component for performing algorithms in quantum computers. However, any quantum algorithm will ultimately have to operate on error-protectedlogical qubits, which are effective qubits encoded in a high-dimensional Hilbert space. A common approach is to encode logical qubits in collective states of multiple two-level systems, but algorithms operating on multiple logical qubits are highly complex and have not yet been demonstrated. Here, we experimentally realize a controlled NOT (CNOT) gate between two multiphoton qubits in two microwave cavities. In this approach, we encode a qubit in the large Hilbert space of a single cavity mode, rather than in multiple two-level systems. We couple two such encoded qubits together through a transmon, which is driven with an RF pump to apply the CNOT gate within 190 ns. This is two orders of magnitude shorter than the decoherence time of any part of the system, enabling high-fidelity operations comparable to state-of-the-art gates between two-level systems. These results are an important step towards universal algorithms on error-corrected logical qubits.
Encoding quantum states in complex multiphoton fields can overcome loss during signal transmission in a quantum network. Transmitting quantum information encoded in this way requiresthat locally stored states can be converted to propagating fields. Here we experimentally show the controlled conversion of multiphoton quantum states, like „Schr\“odinger cat“ states, from a microwave cavity quantum memory into propagating modes. By parametric conversion using the nonlinearity of a single Josephson junction, we can release the cavity state in ~500 ns, about 3 orders of magnitude faster than its intrinsic lifetime. This `catapult‘ faithfully converts arbitrary cavity fields to traveling signals with an estimated efficiency of > 90%, enabling on-demand generation of complex itinerant quantum states. Importantly, the release process can be controlled precisely on fast time scales, allowing us to generate entanglement between the cavity and the traveling mode by partial conversion. Our system can serve as the backbone of a microwave quantum network, paving the way towards error-correctable distribution of quantum information and the transfer of highly non-classical states to hybrid quantum systems.