Control and readout of a superconducting qubit using a photonic link.

Delivering on the revolutionary promise of a universal quantum computer will require processors with millions of quantum bits (qubits)1-3. In superconducting quantum processors4, each qubit is individually addressed with microwave signal lines that connect room-temperature electronics to the cryogenic environment of the quantum circuit. The complexity and heat load associated with the multiple coaxial lines per qubit limits the maximum possible size of a processor to a few thousand qubits5. Here we introduce a photonic link using an optical fibre to guide modulated laser light from room temperature to a cryogenic photodetector6, capable of delivering shot-noise-limited microwave signals directly at millikelvin temperatures. By demonstrating high-fidelity control and readout of a superconducting qubit, we show that this photonic link can meet the stringent requirements of superconducting quantum information processing7. Leveraging the low thermal conductivity and large intrinsic bandwidth of optical fibre enables the efficient and massively multiplexed delivery of coherent microwave control pulses, providing a path towards a million-qubit universal quantum computer.

Efficient Qubit Measurement with a Nonreciprocal Microwave Amplifier.

The act of observing a quantum object fundamentally perturbs its state, resulting in a random walk toward an eigenstate of the measurement operator. Ideally, the measurement is responsible for all dephasing of the quantum state. In practice, imperfections in the measurement apparatus limit or corrupt the flow of information required for quantum feedback protocols, an effect quantified by the measurement efficiency. Here, we demonstrate the efficient measurement of a superconducting qubit using a nonreciprocal parametric amplifier to directly monitor the microwave field of a readout cavity. By mitigating the losses between the cavity and the amplifier, we achieve a measurement efficiency of (72±4)%. The directionality of the amplifier protects the readout cavity and qubit from excess backaction caused by amplified vacuum fluctuations. In addition to providing tools for further improving the fidelity of strong projective measurement, this work creates a test bed for the experimental study of ideal weak measurements, and it opens the way toward quantum feedback protocols based on weak measurement such as state stabilization or error correction.

Ultrastrong Parametric Coupling between a Superconducting Cavity and a Mechanical Resonator.

We present a new optomechanical device where the motion of a micromechanical membrane couples to a microwave resonance of a three-dimensional superconducting cavity. With this architecture, we realize ultrastrong parametric coupling, where the coupling not only exceeds the dissipation in the system but also rivals the mechanical frequency itself. In this regime, the optomechanical interaction induces a frequency splitting between the hybridized normal modes that reaches 88% of the bare mechanical frequency, limited by the fundamental parametric instability. The coupling also exceeds the mechanical thermal decoherence rate, enabling new applications in ultrafast quantum state transfer and entanglement generation.

Mechanically Mediated Microwave Frequency Conversion in the Quantum Regime.

We report the observation of efficient and low-noise frequency conversion between two microwave modes, mediated by the motion of a mechanical resonator subjected to radiation pressure. We achieve coherent conversion of more than 10^{12} photons/s with a 95% efficiency and a 14 kHz bandwidth. With less than 10^{-1} photons·s^{-1}·Hz^{-1} of added noise, this optomechanical frequency converter is suitable for quantum state transduction. We show the ability to operate this converter as a tunable beam splitter, with direct applications for photon routing and communication through complex quantum networks.

Tunable resonant and nonresonant interactions between a phase qubit and LC resonator.

We use a flux-biased radio frequency superconducting quantum interference device (rf SQUID) with an embedded flux-biased direct current SQUID to generate strong resonant and nonresonant tunable interactions between a phase qubit and a lumped-element resonator. The rf SQUID creates a tunable magnetic susceptibility between the qubit and resonator providing resonant coupling strengths from zero to near the ultrastrong coupling regime. By modulating the magnetic susceptibility, nonresonant parametric coupling achieves rates >100 MHz. Nonlinearity of the magnetic susceptibility also leads to parametric coupling at the subharmonics of the qubit-resonator detuning.

Low-noise cryogenic microwave amplifier characterization with a calibrated noise source.

Parametric amplifiers have become a workhorse in superconducting quantum computing; however, research and development of these devices has been hampered by inconsistent and, sometimes, misleading noise performance characterization methodologies. The concepts behind noise characterization are deceptively simple, and there are many places where one can make mistakes, either in measurement or in interpretation and analysis. In this article, we cover the basics of noise performance characterization and the special problems it presents in parametric amplifiers with limited power handling capability. We illustrate the issues with three specific examples: a high-electron mobility transistor amplifier, a Josephson traveling-wave parametric amplifier, and a Josephson parametric amplifier. We emphasize the use of a 50-Ω shot noise tunnel junction (SNTJ) as a broadband noise source, demonstrating its utility for cryogenic amplifier amplifications. These practical examples highlight the role of loss as well as the additional parametric amplifier "idler" input mode.

Performance of a Kinetic Inductance Traveling-Wave Parametric Amplifier at 4 Kelvin: Toward an Alternative to Semiconductor Amplifiers.

Most microwave readout architectures in quantum computing or sensing rely on a semiconductor amplifier at 4 K, typically a high-electron mobility transistor (HEMT). Despite its remarkable noise performance, a conventional HEMT dissipates several milliwatts of power, posing a practical challenge to scale up the number of qubits or sensors addressed in these architectures. As an alternative, we present an amplification chain consisting of a kinetic inductance traveling-wave parametric amplifier (KITWPA) placed at 4 K, followed by a HEMT placed at 70 K, and demonstrate a chain-added noise TΣ=6.3±0.5K between 3.5 and 5.5 GHz. While, in principle, any parametric amplifier can be quantum limited even at 4 K, in practice we find the performance of the KITWPA to be limited by the temperature of its inputs and by an excess of noise Tex=1.9K. The dissipation of the rf pump of the KITWPA constitutes the main power load at 4 K and is about 1% that of a HEMT. These combined noise and power dissipation values pave the way for the use of the KITWPA as a replacement for semiconductor amplifiers.

Trade off-free entanglement stabilization in a superconducting qutrit-qubit system.

Quantum reservoir engineering is a powerful framework for autonomous quantum state preparation and error correction. However, traditional approaches to reservoir engineering are hindered by unavoidable coherent leakage out of the target state, which imposes an inherent trade off between achievable steady-state state fidelity and stabilization rate. In this work we demonstrate a protocol that achieves trade off-free Bell state stabilization in a qutrit-qubit system realized on a circuit-QED platform. We accomplish this by creating a purely dissipative channel for population transfer into the target state, mediated by strong parametric interactions coupling the second-excited state of a superconducting transmon and the engineered bath resonator. Our scheme achieves a state preparation fidelity of 84% with a stabilization time constant of 339 ns, leading to a 54 ns error-time product in a solid-state quantum information platform.

Dispersive photon blockade in a superconducting circuit.

Mediated photon-photon interactions are realized in a superconducting coplanar waveguide cavity coupled to a superconducting charge qubit. These nonresonant interactions blockade the transmission of photons through the cavity. This so-called dispersive photon blockade is characterized by measuring the total transmitted power while varying the energy spectrum of the photons incident on the cavity. A staircase with four distinct steps is observed and can be understood in an analogy with electron transport and the Coulomb blockade in quantum dots. This work differs from previous efforts in that the cavity-qubit excitations retain a photonic nature rather than a hybridization of qubit and photon and provides the needed tolerance to disorder for future condensed matter experiments.

Modeling Bloch oscillations in nanoscale Josephson junctions.

Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging energy comparable to the Josephson coupling energy are explored within the context of a model previously considered by Geigenmüller and Schön that includes Zener tunneling and treats quasiparticle tunneling as an explicit shot-noise process. The dynamics of the junction quasicharge are investigated numerically using both Monte Carlo and ensemble approaches to calculate voltage-current characteristics in the presence of microwaves. We examine in detail the origin of harmonic and subharmonic Bloch steps at dc biases I = (n/m)2ef induced by microwaves of frequency f and consider the optimum parameters for the observation of harmonic (m = 1) steps. We also demonstrate that the GS model allows a detailed semiquantitative fit to experimental voltage-current characteristics previously obtained at the Chalmers University of Technology, confirming and strengthening the interpretation of the observed microwave-induced steps in terms of Bloch oscillations.

Nonreciprocal Microwave Signal Processing with a Field-Programmable Josephson Amplifier.

We report on the design and implementation of a field-programmable Josephson amplifier (FPJA)-a compact and lossless superconducting circuit that can be programmed in situ by a set of microwave drives to perform reciprocal and nonreciprocal frequency conversion and amplification. In this work, we demonstrate four modes of operation: frequency conversion (transmission of -0.5 dB, reflection of -30 dB), circulation (transmission of -0.5 dB, reflection of -30 dB, isolation of 30 dB), phase-preserving amplification (gain > 20 dB, one photon of added noise) and directional phase-preserving amplification (reflection of -10 dB, forward gain of 18 dB, reverse isolation of 8 dB, one photon of added noise). The system exhibits quantitative agreement with the theoretical prediction. Based on a gradiometric superconducting quantum-interference device with Nb/Al-AlOx/Nb Josephson junctions, the FPJA is first-order insensitive to flux noise and can be operated without magnetic shielding at low temperature. Owing to its flexible design and compatibility with existing superconducting fabrication techniques, the FPJA offers a straightforward route toward on-chip integration with superconducting quantum circuits such as qubits and microwave optomechanical systems.

Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object.

By coupling a macroscopic mechanical oscillator to two microwave cavities, we simultaneously prepare and monitor a nonclassical steady state of mechanical motion. In each cavity, correlated radiation pressure forces induced by two coherent drives engineer the coupling between the quadratures of light and motion. We, first, demonstrate the ability to perform a continuous quantum nondemolition measurement of a single mechanical quadrature at a rate that exceeds the mechanical decoherence rate, while avoiding measurement backaction by more than 13 dB. Second, we apply this measurement technique to independently verify the preparation of a squeezed state in the mechanical oscillator, resolving quadrature fluctuations 20% below the quantum noise.

Energy decay in superconducting Josephson-junction qubits from nonequilibrium quasiparticle excitations.

We calculate the energy decay rate of Josephson qubits and superconducting resonators from nonequilibrium quasiparticles. The decay rates from experiments are shown to be consistent with predictions based on a prior measurement of the quasiparticle density n(qp) = 10/microm(3), which suggests that nonequilibrium quasiparticles are an important decoherence source for Josephson qubits. Calculations of the energy-decay and diffusion of quasiparticles also indicate that prior engineered gap and trap structures, which reduce the density of quasiparticles, should be redesigned to improve their efficacy. This model also explains a striking feature in Josephson qubits and resonators-a small reduction in decay rate with increasing temperature.

Phase-locking transition in a chirped superconducting Josephson resonator.

We observe a sharp threshold for dynamic phase locking in a high-Q transmission line resonator embedded with a Josephson tunnel junction, and driven with a purely ac, chirped microwave signal. When the drive amplitude is below a critical value, which depends on the chirp rate and is sensitive to the junction critical current I0, the resonator is only excited near its linear resonance frequency. For a larger amplitude, the resonator phase locks to the chirped drive and its amplitude grows until a deterministic maximum is reached. Near threshold, the oscillator evolves smoothly in one of two diverging trajectories, providing a way to discriminate small changes in I0 with a nonswitching detector, with potential applications in quantum state measurement.

Narrow-band microwave radiation from a biased single-Cooper-pair transistor.

We show that a single-Cooper-pair transistor (SCPT) electrometer emits narrow-band microwave radiation when biased in its subgap region. Photoexcitation of quasiparticle tunneling in a nearby SCPT is used to spectroscopically detect this radiation in a configuration that closely mimics a qubit-electrometer integrated circuit. We identify emission lines due to Josephson radiation and radiative transport processes in the electrometer and argue that a dissipative superconducting electrometer can severely disrupt the system it attempts to measure.

Poisson transition rates from time-domain measurements with a finite bandwidth.

In time-domain measurements of a Poisson two-level system, the observed transition rates are always smaller than those of the actual system, a general consequence of a finite measurement bandwidth in an experiment. This underestimation of the rates is significant even when the measurement and detection apparatus are 10 times faster than the process under study. We derive here a quantitative form for this correction, using a straightforward state transition model that includes the detection apparatus, and provide a method for determining a system's actual transition rates from bandwidth-limited measurements. We support our results with computer simulations and experimental data from time-domain measurements of quasiparticle tunneling in a single-Cooper-pair transistor.

Rabi oscillations in a large Josephson-junction qubit.

We have designed and operated a circuit based on a large-area current-biased Josephson junction whose two lowest energy quantum levels are used to implement a solid-state qubit. The circuit allows measurement of the qubit states with a fidelity of 85% while providing sufficient decoupling from external sources of relaxation and decoherence to allow coherent manipulation of the qubit state, as demonstrated by the observation of Rabi oscillations. This qubit circuit is the basis of a scalable quantum computer.

Nonequilibrium quasiparticles and 2e periodicity in single-Cooper-pair transistors.

We have fabricated single-Cooper-pair transistors in which the spatial profile of the superconducting gap energy was controlled by oxygen doping. The profile dramatically affects the switching current vs gate voltage curve of the transistor, changing its period from 1e to 2e. A model based on nonequilibrium quasiparticles in the leads explains our results, including the observation that even devices with a clean 2e period are "poisoned" by small numbers of these quasiparticles.