We experimentally optimize the frequency of flux-tunable couplers in a superconducting quantum processor to minimize the impact of spectator transmons during quantum operations (single-qubit gates, two-qubit gates, and readout) on other transmons. We adapt a popular transmonlike tunable-coupling element, achieving high-fidelity, low-leakage controlled-Z gates with unipolar, fast-adiabatic pulsing only on the coupler. We demonstrate the ability of the tunable coupler to null residual-ZZ coupling as well as exchange couplings in the one- and two-excitation manifolds. However, the nulling of these coherent interactions is not simultaneous, prompting the exploration of trade-offs. We present experiments pinpointing spectator effects on specific quantum operations. We also study the combined effect on the three types of operations using repeated quantum parity measurements.

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.

Quantum error correction allows for quantum information to be preserved using logical qubits, which are subject to lower error rates than their constituent physical qubits. The degree of error suppression depends on the choice of error correcting code and distance, the underlying physical error rate, and the accuracy of the decoder. While traditional decoders utilise a binary (hard) syndrome, recent work shows that additional (soft) information captured during qubit readout can be effectively utilised to improve decoding accuracy. In this work, we present experimental results from a distance-three surface code implemented on transmon qubits, where we perform Z-stabiliser measurements to protect the state of the logical qubit against bit-flip errors. We initialise the logical qubit in one of 16 possible computational states representing the logical zero state, and perform repeated stabiliser checks over a variable number of rounds to preserve the state over time. We compare the decoding performance for a hard minimum-weight perfect matching decoder against a soft variant where rich measurement information is incorporated, and demonstrate an improved logical fidelity. Additionally, we employ a recurrent neural network decoder with both soft and hard variants and observe improved performance when soft information is used. The general nature of soft information makes it widely applicable to different physical qubit platforms, where it can be leveraged to shorten measurement times and improve the logical fidelity in quantum error correction experiments. Pre-print available at arXiv:2403.00706.

Quantum hardware based on circuit quantum electrodynamics makes extensive use of airbridges to suppress unwanted modes of wave propagation in coplanar-waveguide transmission lines. Airbridges also provide an interconnect enabling transmission lines to cross. Traditional airbridge fabrication produces a curved profile by reflowing resist at elevated temperature prior to metallization. The elevated temperature can affect the coupling energy and even yield of pre-fabricated Josephson elements of superconducting qubits, tunable couplers, and resonators. We employ grayscale lithography to enable reflow and thereby reduce the peak temperature of our airbridge fabrication process from 200 to 150 °C and link this change to a substantial increase in the physical yield of transmon qubits with Josephson elements realized using Al-contacted InAs nanowires.

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.

Minimizing leakage from computational states is a challenge when using many-level systems like superconducting quantum circuits as qubits. We realize and extend the quantum-hardware-efficient, all-microwave leakage reduction unit (LRU) for transmons in a circuit QED architecture proposed by Battistel et al. This LRU effectively reduces leakage in the second- and third-excited transmon states with up to 99% efficacy in 220 ns, with minimum impact on the qubit subspace. As a first application in the context of quantum error correction, we show how multiple simultaneous LRUs can reduce the error detection rate and suppress leakage buildup within 1% in data and ancilla qubits over 50 cycles of a weight-2 stabilizer measurement.

We present the use of a set of airbridges to trim the frequency of microwave coplanar-waveguide (CPW) resonators post-fabrication. This method is compatible with the fabrication steps of conventional CPW airbridges and crossovers and increases device yield by allowing compensation of design and fabrication uncertainty with 100 MHz range and 10 MHz resolution. We showcase two applications in circuit QED. The first is the elimination of frequency collisions between resonators intended to readout different transmons by frequency-division multiplexing. The second is frequency matching of readout and Purcell-filter resonator pairs. Combining this matching with transmon frequency trimming by laser annealing reliably achieves fast and high-fidelity readout across 17-transmon quantum processors.

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.

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.

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.

We introduce Cryoscope, a method for sampling on-chip baseband pulses used to dynamically control qubit frequency in a quantum processor. We specifically use Cryoscope to measure the step response of the dedicated flux control lines of two-junction transmon qubits in circuit QED processors with the temporal resolution of the room-temperature arbitrary waveform generator producing the control pulses. As a first application, we iteratively improve this step response using optimized real-time digital filters to counter the linear-dynamical distortion in the control line, as needed for high-fidelity repeatable one- and two-qubit gates based on dynamical control of qubit frequency.

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.

Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this increase enables the accurate detection of the time and location of leakage. We restore the logical error rate below the memory break-even point by post-selecting out leakage, discarding less than half of the data for the given noise parameters. Leakage detection via HMMs opens the prospect for near-term QEC demonstrations, targeted leakage reduction and leakage-aware decoding and is applicable to other experimental platforms.

A widely-used quantum programming paradigm comprises of both the data flow and control flow. Existing quantum hardware cannot well support the control flow, significantly limiting the range of quantum software executable on the hardware. By analyzing the constraints in the control microarchitecture, we found that existing quantum assembly languages are either too high-level or too restricted to support comprehensive flow control on the hardware. Also, as observed with the quantum microinstruction set QuMIS [1], the quantum instruction set architecture (QISA) design may suffer from limited scalability and flexibility because of microarchitectural constraints. It is an open challenge to design a scalable and flexible QISA which provides a comprehensive abstraction of the quantum hardware. In this paper, we propose an executable QISA, called eQASM, that can be translated from quantum assembly language (QASM), supports comprehensive quantum program flow control, and is executed on a quantum control microarchitecture. With efficient timing specification, single-operationmultiple-qubit execution, and a very-long-instruction-word architecture, eQASM presents better scalability than QuMIS. The definition of eQASM focuses on the assembly level to be expressive. Quantum operations are configured at compile time instead of being defined at QISA design time. We instantiate eQASM into a 32-bit instruction set targeting a seven-qubit superconducting quantum processor. We validate our design by performing several experiments on a two-qubit quantum processor.

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.

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.

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.

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.

This article proposes a quantum microarchitecture, QuMA. Flexible programmability of a quantum processor is achieved by multilevel instructions decoding, abstracting analog control into digital control, and translating instruction execution with non-deterministic timing into event trigger with precise timing. QuMA is validated by several single-qubit experiments on a superconducting qubit.