All-Microwave Leakage Reduction Units for Quantum Error Correction with Superconducting Transmon Qubits.

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.

High-Fidelity Controlled-Z Gate with Maximal Intermediate Leakage Operating at the Speed Limit in a Superconducting Quantum Processor.

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.

Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements.

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.

Fast, High-Fidelity Conditional-Phase Gate Exploiting Leakage Interference in Weakly Anharmonic Superconducting Qubits.

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.

Evolution of Nanowire Transmon Qubits and Their Coherence in a Magnetic Field.

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.

Experimentally simulating the dynamics of quantum light and matter at deep-strong coupling.

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.

Direct Oral Anticoagulants Vs. Enoxaparin for Prevention of Venous Thromboembolism Following Orthopedic Surgery: A Dose-Response Meta-analysis.

We carried out a dose-response model-based meta-analysis to assess venous thromboembolism (VTE) and bleeding with factor Xa (FXa) inhibitors (apixaban, edoxaban, rivaroxaban) and a thrombin inhibitor (dabigatran) compared with European (EU) (40 mg q.d.) and North American (NA) (30 mg Q12H) dose regimens of a low molecular weight heparin (enoxaparin) following orthopedic surgery. Statistically significant differences in both VTE and bleeding outcomes were found between the NA and EU doses of enoxaparin, with odds ratios (95% confidence interval) for the NA vs. EU dose of 0.73 (0.71-0.76) and 1.20 (1.14-1.29) for total VTE and major bleeding, respectively. At approved doses, estimated odds ratios vs. both doses of enoxaparin for the three FXa inhibitors (range: 0.35-0.75 for VTE; 0.76-1.09 for bleeding) compared with those for dabigatran (range: 0.66-1.21 for VTE; 1.10-1.38 for bleeding) suggested generally greater efficacy and less bleeding for the FXa inhibitors.

Realization of Microwave Quantum Circuits Using Hybrid Superconducting-Semiconducting Nanowire Josephson Elements.

We report the realization of quantum microwave circuits using hybrid superconductor-semiconductor Josephson elements comprised of InAs nanowires contacted by NbTiN. Capacitively shunted single elements behave as transmon circuits with electrically tunable transition frequencies. Two-element circuits also exhibit transmonlike behavior near zero applied flux but behave as flux qubits at half the flux quantum, where nonsinusoidal current-phase relations in the elements produce a double-well Josephson potential. These hybrid Josephson elements are promising for applications requiring microwave superconducting circuits operating in a magnetic field.

Detecting bit-flip errors in a logical qubit using stabilizer measurements.

Quantum data are susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction to actively protect against both. In the smallest error correction codes, the information in one logical qubit is encoded in a two-dimensional subspace of a larger Hilbert space of multiple physical qubits. For each code, a set of non-demolition multi-qubit measurements, termed stabilizers, can discretize and signal physical qubit errors without collapsing the encoded information. Here using a five-qubit superconducting processor, we realize the two parity measurements comprising the stabilizers of the three-qubit repetition code protecting one logical qubit from physical bit-flip errors. While increased physical qubit coherence times and shorter quantum error correction blocks are required to actively safeguard the quantum information, this demonstration is a critical step towards larger codes based on multiple parity measurements.

Digital quantum Rabi and Dicke models in superconducting circuits.

We propose the analog-digital quantum simulation of the quantum Rabi and Dicke models using circuit quantum electrodynamics (QED). We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps. Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes. Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.

Entanglement genesis by ancilla-based parity measurement in 2D circuit QED.

We present an indirect two-qubit parity meter in planar circuit quantum electrodynamics, realized by discrete interaction with an ancilla and a subsequent projective ancilla measurement with a dedicated, dispersively coupled resonator. Quantum process tomography and successful entanglement by measurement demonstrate that the meter is intrinsically quantum nondemolition. Separate interaction and measurement steps allow the execution of subsequent data-qubit operations in parallel with ancilla measurement, offering time savings over continuous schemes.

Deterministic entanglement of superconducting qubits by parity measurement and feedback.

The stochastic evolution of quantum systems during measurement is arguably the most enigmatic feature of quantum mechanics. Measuring a quantum system typically steers it towards a classical state, destroying the coherence of an initial quantum superposition and the entanglement with other quantum systems. Remarkably, the measurement of a shared property between non-interacting quantum systems can generate entanglement, starting from an uncorrelated state. Of special interest in quantum computing is the parity measurement, which projects the state of multiple qubits (quantum bits) to a state with an even or odd number of excited qubits. A parity meter must discern the two qubit-excitation parities with high fidelity while preserving coherence between same-parity states. Despite numerous proposals for atomic, semiconducting and superconducting qubits, realizing a parity meter that creates entanglement for both even and odd measurement results has remained an outstanding challenge. Here we perform a time-resolved, continuous parity measurement of two superconducting qubits using the cavity in a three-dimensional circuit quantum electrodynamics architecture and phase-sensitive parametric amplification. Using postselection, we produce entanglement by parity measurement reaching 88 per cent fidelity to the closest Bell state. Incorporating the parity meter in a feedback-control loop, we transform the entanglement generation from probabilistic to fully deterministic, achieving 66 per cent fidelity to a target Bell state on demand. These realizations of a parity meter and a feedback-enabled deterministic measurement protocol provide key ingredients for active quantum error correction in the solid state.

Partial-measurement backaction and nonclassical weak values in a superconducting circuit.

We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit backaction is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a nonclassical weak value and the violation of a Leggett-Garg inequality.

An adaptive-design dose-ranging study of PD 0348292, an oral factor Xa inhibitor, for thromboprophylaxis after total knee replacement surgery.

BACKGROUND: PD 0348292 is an oral, selective, direct and reversible factor Xa inhibitor. This was an adaptive dose-ranging study evaluating a 100-fold PD 0348292 dose range in subjects undergoing total knee replacement (TKR). OBJECTIVE: To assess the efficacy and safety of a dose range of PD 0348292 relative to enoxaparin for the prevention of venous thromboembolism (VTE). METHODS: Extensive dose-response modeling and trial simulations were used to select the PD 0348292 dose range for the Phase 2 study. Subjects were randomized to a blinded PD 0348292 dose (0.1 mg qd to 10 mg qd) or open-label enoxaparin (30 mg bid) for 6-14 days after TKR surgery. Efficacy was assessed by mandatory bilateral venography. Results were analyzed using a dose-response modeling approach. RESULTS: Observed VTE frequency ranged from 1.4-37.1% across PD 0348292 doses and was 18.1% for enoxaparin. The PD 0348292 dose-response relationship for VTE was statistically significant (P < 0.0001). The dose of PD 0348292 equivalent to enoxaparin 30 mg bid for VTE prevention was estimated to be 1.16 mg (95% CI = 0.56 mg, 2.41 mg) qd. Total bleeding ranged from 4.9% to 13.8% across PD 0348292 doses and was 6.3% with enoxaparin. The dose-response relationship for total bleeding was not statistically significant (P = 0.2464). Overall, PD 0348292 and enoxaparin were well tolerated. CONCLUSION: Characterization of the dose-response relationship for VTE and bleeding using an adaptive Phase 2 study design provided a strong quantitative basis for Phase 3 dose selection.

Millisecond charge-parity fluctuations and induced decoherence in a superconducting transmon qubit.

The tunnelling of quasiparticles across Josephson junctions in superconducting quantum circuits is an intrinsic decoherence mechanism for qubit degrees of freedom. Understanding the limits imposed by quasiparticle tunnelling on qubit relaxation and dephasing is of theoretical and experimental interest, particularly as improved understanding of extrinsic mechanisms has allowed crossing the 100 microsecond mark in transmon-type charge qubits. Here, by integrating recent developments in high-fidelity qubit readout and feedback control in circuit quantum electrodynamics, we transform a state-of-the-art transmon into its own real-time charge-parity detector. We directly measure the tunnelling of quasiparticles across the single junction and isolate the contribution of this tunnelling to qubit relaxation and dephasing, without reliance on theory. The millisecond timescales measured demonstrate that quasiparticle tunnelling does not presently bottleneck transmon qubit coherence, leaving room for yet another order of magnitude increase.

Probing dynamics of an electron-spin ensemble via a superconducting resonator.

We study spin relaxation and diffusion in an electron-spin ensemble of nitrogen impurities in diamond at low temperature (0.25-1.2 K) and polarizing magnetic field (80-300 mT). Measurements exploit field-controlled coupling of the ensemble to two modes of a transmission-line resonator. The observed temperature-independent spin relaxation time indicates that spin outdiffusion across the mode volume dominates over spin-lattice relaxation. Depolarization of one hyperfine-split subensemble by pumping of another indicates fast cross relaxation, with implications for the use of subensembles as independent quantum memories.

Measurements of quasiparticle tunneling dynamics in a band-gap-engineered transmon qubit.

We have engineered the band gap profile of transmon qubits by combining oxygen-doped Al for tunnel junction electrodes and clean Al as quasiparticle traps to investigate energy relaxation due to quasiparticle tunneling. The relaxation time T1 of the qubits is shown to be insensitive to this band gap engineering. Operating at relatively low-E(J)/E(C) makes the transmon transition frequency distinctly dependent on the charge parity, allowing us to detect the quasiparticles tunneling across the qubit junction. Quasiparticle kinetics have been studied by monitoring the frequency switching due to even-odd parity change in real time. It shows the switching time is faster than 10 µs, indicating quasiparticle-induced relaxation has to be reduced to achieve T1 much longer than 100 µs.

Initialization by measurement of a superconducting quantum bit circuit.

We demonstrate initialization by joint measurement of two transmon qubits in 3D circuit quantum electrodynamics. Homodyne detection of cavity transmission is enhanced by Josephson parametric amplification to discriminate the two-qubit ground state from single-qubit excitations nondestructively and with 98.1% fidelity. Measurement and postselection of a steady-state mixture with 4.7% residual excitation per qubit achieve 98.8% fidelity to the ground state, thus outperforming passive initialization.