We investigate die-level and wafer-scale uniformity of Dolan-bridge and bridgeless Manhattan-style Josephson junctions, using multiple substrates with and without through-silicon vias (TSVs). Dolan junctions fabricated on planar substrates have the highest yield and lowest room-temperature conductance spread, equivalent to ∼ 100 M H z in transmon frequency. In TSV-integrated substrates, Dolan junctions suffer most in both yield and disorder, making Manhattan junctions preferable. Manhattan junctions show pronounced conductance decrease from wafer center to edge, which we qualitatively capture using a geometric model of spatially-dependent resist shadowing during junction electrode evaporation. Analysis of actual junction overlap areas using scanning electron micrographs supports the model, and further points to a remnant spatial dependence possibly due to contact resistance.

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Artificial neural networks are becoming an integral part of digital solutions to complex problems. However, employing neural networks on quantum processors faces challenges related to the implementation of non-linear functions using quantum circuits. In this paper, we use repeat-until-success circuits enabled by real-time control-flow feedback to realize quantum neurons with non-linear activation functions. These neurons constitute elementary building blocks that can be arranged in a variety of layouts to carry out deep learning tasks quantum coherently. As an example, we construct a minimal feedforward quantum neural network capable of learning all 2-to-1-bit Boolean functions by optimization of network activation parameters within the supervised-learning paradigm. This model is shown to perform non-linear classification and effectively learns from multiple copies of a single training state consisting of the maximal superposition of all inputs.

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Simple tuneup of fast two-qubit gates is essential for the scaling of quantum processors. We introduce the sudden variant (SNZ) of the net zero scheme realizing controlled-Z (CZ) gates by flux control of transmon frequency. SNZ CZ gates realized in a multitransmon processor operate at the speed limit of transverse coupling between computational and noncomputational states by maximizing intermediate leakage. Beyond speed, the key advantage of SNZ is tuneup simplicity, owing to the regular structure of conditional phase and leakage as a function of two control parameters. SNZ is compatible with scalable schemes for quantum error correction and adaptable to generalized conditional-phase gates useful in intermediate-scale applications.

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The preparation of thermal equilibrium states is important for the simulation of condensed matter and cosmology systems using a quantum computer. We present a method to prepare such mixed states with unitary operators and demonstrate this technique experimentally using a gate-based quantum processor. Our method targets the generation of thermofield double states using a hybrid quantum-classical variational approach motivated by quantum-approximate optimization algorithms, without prior calculation of optimal variational parameters by numerical simulation. The fidelity of generated states to the thermal-equilibrium state smoothly varies from 99 to 75% between infinite and near-zero simulated temperature, in quantitative agreement with numerical simulations of the noisy quantum processor with error parameters drawn from experiment.

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Future fault-tolerant quantum computers will require storing and processing quantum data in logical qubits. Here we realize a suite of logical operations on a distance-2 surface code qubit built from seven physical qubits and stabilized using repeated error-detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.

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Protecting quantum information from errors is essential for large-scale quantum computation. Quantum error correction (QEC) encodes information in entangled states of many qubits and performs parity measurements to identify errors without destroying the encoded information. However, traditional QEC cannot handle leakage from the qubit computational space. Leakage affects leading experimental platforms, based on trapped ions and superconducting circuits, which use effective qubits within many-level physical systems. We investigate how two-transmon entangled states evolve under repeated parity measurements and demonstrate the use of hidden Markov models to detect leakage using only the record of parity measurement outcomes required for QEC. We show the stabilization of Bell states over up to 26 parity measurements by mitigating leakage using postselection and correcting qubit errors using Pauli-frame transformations. Our leakage identification method is computationally efficient and thus compatible with real-time leakage tracking and correction in larger quantum processors.

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Superconducting coplanar-waveguide resonators that can operate in strong magnetic fields are important tools for a variety of high-frequency superconducting devices. Magnetic fields degrade resonator performance by creating Abrikosov vortices that cause resistive losses and frequency fluctuations or suppress the superconductivity entirely. To mitigate these effects, we investigate lithographically defined artificial defects in resonators fabricated from Nb-Ti-N superconducting films. We show that by controlling the vortex dynamics, the quality factor of resonators in perpendicular magnetic fields can be greatly enhanced. Coupled with the restriction of the device geometry to enhance the superconductors critical field, we demonstrate stable resonances that retain quality factors ≃105 at the single-photon power level in perpendicular magnetic fields up to B⊥ ≃20mT and parallel magnetic fields up to B⥠≃6T. We demonstrate the effectiveness of this technique for hybrid systems by integrating an In-Sb nanowire into a field-resilient superconducting resonator and use it to perform fast charge readout of a gate-defined double quantum dot at B=1T.

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Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by applying the recently proposed symmetry verification technique to the experimental estimation of the ground-state energy and ground state of the hydrogen molecule. A finely adjustable exchange interaction between two qubits in a circuit QED processor efficiently prepares variational ansatz states in the single-excitation subspace respecting the parity symmetry of the qubit-mapped Hamiltonian. Symmetry verification improves the energy and state estimates by mitigating the effects of qubit relaxation and residual qubit excitation, which violate the symmetry. A full-density-matrix simulation matching the experiment dissects the contribution of these mechanisms from other calibrated error sources. Enforcing positivity of the measured density matrix via scalable convex optimization correlates the energy and state estimate improvements when using symmetry verification, with interesting implications for determining system properties beyond the ground-state energy.

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Conditional-phase (cz) gates in transmons can be realized by flux pulsing computational states towards resonance with noncomputational ones. We present a 40 ns cz gate based on a bipolar flux pulse suppressing leakage (0.1%) by interference and approaching the speed limit set by exchange coupling. This pulse harnesses a built-in echo to enhance fidelity (99.1%) and is robust to long-timescale distortion in the flux-control line, ensuring repeatability. Numerical simulations matching experiment show that fidelity is limited by high-frequency dephasing and leakage by short-timescale distortion.

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We present an experimental study of flux- and gate-tunable nanowire transmons with state-of-the-art relaxation time allowing quantitative extraction of flux and charge noise coupling to the Josephson energy. We evidence coherence sweet spots for charge, tuned by voltage on a proximal side gate, where first order sensitivity to switching two-level systems and background 1/f noise is minimized. Next, we investigate the evolution of a nanowire transmon in a parallel magnetic field up to 70 mT, the upper bound set by the closing of the induced gap. Several features observed in the field dependence of qubit energy relaxation and dephasing times are not fully understood. Using nanowires with a thinner, partially covering Al shell will enable operation of these circuits up to 0.5 T, a regime relevant for topological quantum computation and other applications.

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While the on-chip processing power in circuit QED devices is growing rapidly, an open challenge is to establish high-fidelity quantum links between qubits on different chips. Here, we show entanglement between transmon qubits on different cQED chips with 49% concurrence and 73% Bell-state fidelity. We engineer a half-parity measurement by successively reflecting a coherent microwave field off two nearly identical transmon-resonator systems. By ensuring the measured output field does not distinguish |01) from |10), unentangled superposition states are probabilistically projected onto entangled states in the odd-parity subspace. We use in situ tunability and an additional weakly coupled driving field on the second resonator to overcome imperfect matching due to fabrication variations. To demonstrate the flexibility of this approach, we also produce an even-parity entangled state of similar quality, by engineering the matching of outputs for the |00) and |11) states. The protocol is characterized over a range of measurement strengths using quantum state tomography showing good agreement with a comprehensive theoretical model.

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We present and demonstrate a general three-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of the non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephson traveling-wave parametric amplifier and to quantify different noise contributions in the readout amplification chain.

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Analog quantum simulations offer rich opportunities for exploring complex quantum systems and phenomena through the use of specially engineered, well-controlled quantum systems. A critical element, increasing the scope and flexibility of such experimental platforms, is the ability to access and tune in situ different interaction regimes. Here, we present a superconducting circuit building block of two highly coherent transmons featuring in situ tuneable photon hopping and nonlinear cross-Kerr couplings. The interactions are mediated via a nonlinear coupler, consisting of a large capacitor in parallel with a tuneable superconducting quantum interference device (SQUID). We demonstrate the working principle by experimentally characterising the system in the single-excitation and two-excitation manifolds, and derive a full theoretical model that accurately describes our measurements. Both qubits have high coherence properties, with typical relaxation times in the range of 15 to 40 μs at all bias points of the coupler. Our device could be used as a scalable building block in analog quantum simulators of extended Bose-Hubbard and Heisenberg XXZ models, and may also have applications in quantum computing such as realising fast two-qubit gates and perfect state transfer protocols.@en

We present a tuneup protocol for qubit gates with tenfold speedup over traditional methods reliant on qubit initialization by energy relaxation. This speedup is achieved by constructing a cost function for Nelder-Mead optimization from real-time correlation of nondemolition measurements interleaving gate operations without pause. Applying the protocol on a transmon qubit achieves 0.999 average Clifford fidelity in one minute, as independently verified using randomized benchmarking and gate-set tomography. The adjustable sensitivity of the cost function allows the detection of fractional changes in the gate error with a nearly constant signal-to-noise ratio. The restless concept demonstrated can be readily extended to the tuneup of two-qubit gates and measurement operations.

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Superconducting electronic devices have reemerged as contenders for both classical and quantum computing due to their fast operation speeds, low dissipation, and long coherence times. An ultimate demonstration of coherence is lasing. We use one of the fundamental aspects of superconductivity, the ac Josephson effect, to demonstrate a laser made from a Josephson junction strongly coupled to a multimode superconducting cavity. A dc voltage bias applied across the junction provides a source of microwave photons, and the circuit's nonlinearity allows for efficient down-conversion of higher-order Josephson frequencies to the cavity's fundamental mode. The simple fabrication and operation allows for easy integration with a range of quantum devices, allowing for efficient on-chip generation of coherent microwave photons at low temperatures.

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With the introduction of superconducting circuits into the field of quantum optics, many experimental demonstrations of the quantum physics of an artificial atom coupled to a single-mode light field have been realized. Engineering such quantum systems offers the opportunity to explore extreme regimes of light-matter interaction that are inaccessible with natural systems. For instance the coupling strength g can be increased until it is comparable with the atomic or mode frequency ω_a,m and the atom can be coupled to multiple modes which has always challenged our understanding of light-matter interaction. Here, we experimentally realize a transmon qubit in the ultra-strong coupling regime, reaching coupling ratios of g/ω_m = 0.19 and we measure multi-mode interactions through a hybridization of the qubit up to the fifth mode of the resonator. This is enabled by a qubit with 88% of its capacitance formed by a vacuum-gap capacitance with the center conductor of a coplanar waveguide resonator. In addition to potential applications in quantum information technologies due to its small size, this architecture offers the potential to further explore the regime of multi-mode ultra-strong coupling.

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The quantum Rabi model describing the fundamental interaction between light and matter is a cornerstone of quantum physics. It predicts exotic phenomena like quantum phase transitions and ground-state entanglement in ultrastrong and deep-strong coupling regimes, where coupling strengths are comparable to or larger than subsystem energies. Demonstrating dynamics remains an outstanding challenge, the few experiments reaching these regimes being limited to spectroscopy. Here, we employ a circuit quantum electrodynamics chip with moderate coupling between a resonator and transmon qubit to realise accurate digital quantum simulation of deep-strong coupling dynamics. We advance the state of the art in solid-state digital quantum simulation by using up to 90 second-order Trotter steps and probing both subsystems in a combined Hilbert space dimension of 80, demonstrating characteristic Schrödinger-cat-like entanglement and large photon build-up. Our approach will enable exploration of extreme coupling regimes and quantum phase transitions, and demonstrates a clear first step towards larger complexities such as in the Dicke model.

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We present a scalable scheme for executing the error-correction cycle of a monolithic surface-code fabric composed of fast-flux-tunable transmon qubits with nearest-neighbor coupling. An eight-qubit unit cell forms the basis for repeating both the quantum hardware and coherent control, enabling spatial multiplexing. This control uses three fixed frequencies for all single-qubit gates and a unique frequency-detuning pattern for each qubit in the cell. By pipelining the interaction and readout steps of ancilla-based X- and Z-type stabilizer measurements, we can engineer detuning patterns that avoid all second-order transmon-transmon interactions except those exploited in controlled-phase gates, regardless of fabric size. Our scheme is applicable to defect-based and planar logical qubits, including lattice surgery.

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Quantum computing holds the promise of exponential speedup compared to classical computing for select algorithms and applications. Relatively small numbers of logical quantum bits or qubits could outperform the largest of supercomputers. Quantum dots in Si-based heterostructures and superconducting Josephson junctions are just two of the many approaches to construct the qubit. These, in particular, bear similarities to the transistors and interconnects used in advanced semiconductor manufacturing. While initial results on few-qubit systems are promising, advanced process control is expected to improve the qubit uniformity, coherence time, and gate fidelity needed for larger systems. This can be realized through the systematic characterization of film growth, interface control, and patterning.

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We present two pulse schemes to actively deplete measurement photons from a readout resonator in the nonlinear dispersive regime of circuit QED. One method uses digital feedback conditioned on the measurement outcome, while the other is unconditional. In the absence of analytic forms and symmetries to exploit in this nonlinear regime, the depletion pulses are numerically optimized using the Powell method. We speed up photon depletion by more than six inverse resonator linewidths, saving approximately 1650 ns compared to depletion by waiting. We quantify the benefit by emulating an ancilla qubit performing repeated quantum-parity checks in a repetition code. Fast depletion increases the mean number of cycles to a spurious error detection event from order 1 to 75 at a 1-μs cycle time.

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