We present two pulse schemes for actively depleting measurement photons from a readout resonator in the nonlinear dispersive regime of circuit QED. One method uses digital feedbackconditioned 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 shorten the photon depletion time by more than six inverse resonator linewidths compared to passive 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 microsecond cycle time.
A critical ingredient for realizing large-scale quantum information processors will be the ability to make economical use of qubit control hardware. We demonstrate an extensible strategyfor reusing control hardware on same-frequency transmon qubits in a circuit QED chip with surface-code-compatible connectivity. A vector switch matrix enables selective broadcasting of input pulses to multiple transmons with individual tailoring of pulse quadratures for each, as required to minimize the effects of leakage on weakly anharmonic qubits. Using randomized benchmarking, we compare multiple broadcasting strategies that each pass the surface-code error threshold for single-qubit gates. In particular, we introduce a selective-broadcasting control strategy using five pulse primitives, which allows independent, simultaneous Clifford gates on arbitrary numbers of qubits.
This chapter covers the development of feedback control of superconducting qubits using projective measurement and a discrete set of conditional actions, here referred to as digitalfeedback. We begin with an overview of the applications of digital feedback in quantum computing. We then introduce an implementation of high-fidelity projective measurement of superconducting qubits. This development lays the ground for closed-loop control based on the binary measurement result. A first application of digital feedback control is fast and deterministic qubit reset, allowing the repeated initialization of a qubit more than an order of magnitude faster than its relaxation rate. A second application employs feedback in a multi-qubit setting to convert the generation of entanglement by parity measurement from probabilistic to deterministic, targeting an entangled state with the desired parity every time.
We report the realization of quantum microwave circuits using hybrid superconductor-semiconductor Josephson elements comprised of InAs nanowires contacted by NbTiN. Capacitively-shuntedsingle elements behave as transmon qubits with electrically tunable transition frequencies. Two-element circuits also exhibit transmon-like behavior near zero applied flux, but behave as flux qubits at half the flux quantum, where non-sinusoidal 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 magnetic field.
We present microwave-frequency NbTiN resonators on silicon, systematically achieving internal quality factors above 1 M in the quantum regime. We use two techniques to reduce lossesassociated with two-level systems: an additional substrate surface treatment prior to NbTiN deposition to optimize the metal-substrate interface, and deep reactive-ion etching of the substrate to displace the substrate-vacuum interfaces away from high electric fields. The temperature and power dependence of resonator behavior indicate that two-level systems still contribute significantly to energy dissipation, suggesting that more interface optimization could further improve performance.
Quantum data is 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(QEC) to actively protect against both. In the smallest QEC 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. Experimental demonstrations of QEC to date, using nuclear magnetic resonance, trapped ions, photons, superconducting qubits, and NV centers in diamond, have circumvented stabilizers at the cost of decoding at the end of a QEC cycle. This decoding leaves the quantum information vulnerable to physical qubit errors until re-encoding, violating a basic requirement for fault tolerance. 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. We construct these stabilizers as parallelized indirect measurements using ancillary qubits, and evidence their non-demolition character by generating three-qubit entanglement from superposition states. We demonstrate stabilizer-based quantum error detection (QED) by subjecting a logical qubit to coherent and incoherent bit-flip errors on its constituent physical qubits. While increased physical qubit coherence times and shorter QED blocks are required to actively safeguard quantum information, this demonstration is a critical step toward larger codes based on multiple parity measurements.
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 thosewhich 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.
A challenge for scaling up quantum processors using frequency-crowded, weakly anharmonic qubits is to drive individual qubits without causing leakage into non-computational levels ofthe others, while also minimizing the number of control lines. To address this, we implement single-qubit Wah-Wah control in a circuit QED processor with a single feedline for all transmon qubits, operating at the maximum gate speed achievable given the frequency crowding. Randomized benchmarking and quantum process tomography confirm alternating qubit control with ≤1 average error per computational step and decoherence-limited idling of one qubit while driving another with a Wah-Wah pulse train.
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 measurementwith a dedicated, dispersively coupled resonator. Quantum process tomography and successful entanglement by measurement demonstrate that the meter is intrinsically quantum non-demolition. Separate interaction and measurement steps allow commencing subsequent data qubit operations in parallel with ancilla measurement, offering time savings over continuous schemes.
We demonstrate the active suppression of transmon qubit dephasing induced by dispersive measurement, using parametric amplification and analog feedback. By real-time processing of thehomodyne record, the feedback controller reverts the stochastic quantum phase kick imparted by the measurement on the qubit. The feedback operation matches a model of quantum trajectories with measurement efficiency η~≈0.5, consistent with the result obtained by postselection. We overcome the bandwidth limitations of the amplification chain by numerically optimizing the signal processing in the feedback loop and provide a theoretical model explaining the optimization result.