Steven Weber

Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback

The act of measurement bridges the quantum and classical worlds by projecting a superposition of possible states into a single, albeit probabilistic, outcome. The time-scale of this “instantaneous” process can be stretched using weak measurements so that it takes the form of a gradual random walk towards a final state. Remarkably, the interim measurement record is sufficient to continuously track and steer the quantum state using feedback. Here, we report the first implementation of quantum feedback control in a solid state system, in our case a superconducting quantum bit (qubit) coupled to a microwave cavity. Probing the state of the cavity with less than one photon on average, implements a weak measurement of the qubit state. These photons are then directed to a high-bandwidth quantum-noise-limited amplifier, which enables realtime monitoring of the state of the cavity—and hence that of the qubit—with high fidelity. We demonstrate quantum feedback control by inhibiting the decay of Rabi oscillations, allowing them to persist indefinitely. This new ability permits active suppression of decoherence and defines a path for continuous quantum error correction. Other novel avenues include quantum state stabilization, entanglement generation using measurement, state purification, and adaptive measurements.The act of measurement bridges the quantum and classical worlds by projecting a superposition of possible states into a single (probabilistic) outcome. The timescale of this ‘instantaneous’ process can be stretched using weak measurements, such that it takes the form of a gradual random walk towards a final state. Remarkably, the interim measurement record is sufficient to continuously track and steer the quantum state using feedback. Here we implement quantum feedback control in a solid-state system, namely a superconducting quantum bit (qubit) coupled to a microwave cavity. A weak measurement of the qubit is implemented by probing the cavity with microwave photons, maintaining its average occupation at less than one photon. These photons are then directed to a high-bandwidth, quantum-noise-limited amplifier, which allows real-time monitoring of the state of the cavity (and, hence, that of the qubit) with high fidelity. We demonstrate quantum feedback control by inhibiting the decay of Rabi oscillations, allowing them to persist indefinitely. Such an ability permits the active suppression of decoherence and enables a method of quantum error correction based on weak continuous measurements. Other applications include quantum state stabilization, entanglement generation using measurement, state purification and adaptive measurements.

Observing single quantum trajectories of a superconducting quantum bit

The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum state with the inherent fluctuations of the environment. If these fluctuations are not measured, the environment can be viewed as a source of noise, causing random evolution of the quantum system from an initially pure state into a statistical mixture—a process known as decoherence. However, by accurately measuring the environment in real time, the quantum system can be maintained in a pure state and its time evolution described by a ‘quantum trajectory’ determined by the measurement outcome. Here we use weak measurements to monitor a microwave cavity containing a superconducting quantum bit (qubit), and track the individual quantum trajectories of the system. In this set-up, the environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. Using a near-quantum-limited parametric amplifier, we selectively measure either the phase or the amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We perform quantum state tomography at discrete times along the trajectory to verify that we have faithfully tracked the state of the quantum system as it diffuses on the surface of the Bloch sphere. Our results demonstrate that decoherence can be mitigated by environmental monitoring, and validate the foundation of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new means of implementing ‘quantum steering’—the harnessing of action at a distance to manipulate quantum states through measurement.

The flux qubit revisited to enhance coherence and reproducibility.

The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad-frequency tunability, strong anharmonicity, high reproducibility and relaxation times in excess of 40 μs at its flux-insensitive point. Qubit relaxation times T1 across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise and 1/f-flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal-photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T2≈85 μs, approximately the 2T1 limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T2 in contemporary qubits based on transverse qubit–resonator interaction.

Organizing International Politics: Sovereignty and Open Systems

Changes in the meaning of sovereignty are at the center of intersecting discussions between comparative and international politics. This article uses open-system perspectives from organization theory to move beyond arguments over the erosion or resilience of sovereignty, toward more substantive questions about the nature of the boundaries of political actors, and to frame the possibility that changes in world politics are constituting new actors whose relationships would follow logics different from those ascribed to sovereign states.

Single crystal silicon capacitors with low microwave loss in the single photon regime

We have fabricated superconducting microwave resonators in a lumped element geometry using single crystal silicon dielectric parallel plate capacitors with C>2 pF. Aluminum devices with resonant frequencies between 4.0 and 6.5 GHz exhibited an average internal quality factor Qi of 2×105 in the single photon excitation regime at T=20 mK. Attributing the observed loss solely to the capacitive element, our measurements place an upper bound on the loss tangent of the silicon dielectric layer of tan δi=5×10−6. This level of loss is an order of magnitude lower than is currently observed in structures incorporating amorphous dielectric materials, thus making single crystal silicon capacitors an attractive, robust route for realizing long-lived quantum circuits.

Measurement-induced qubit state mixing in circuit QED from up-converted dephasing noise.

We observe measurement-induced qubit state mixing in a transmon qubit dispersively coupled to a planar readout cavity. Our results indicate that dephasing noise at the qubit-readout detuning frequency is up-converted by readout photons to cause spurious qubit state transitions, thus limiting the nondemolition character of the readout. Furthermore, we use the qubit transition rate as a tool to extract an equivalent flux noise spectral density at f~1 GHz and find agreement with values extrapolated from a 1/f(α) fit to the measured flux noise spectral density below 1 Hz.

Quantum Zeno effect in the strong measurement regime of circuit quantum electrodynamics

We observe the quantum Zeno effect -- where the act of measurement slows the rate of quantum state transitions -- in a superconducting qubit using linear circuit quantum electrodynamics readout and a near-quantum-limited following amplifier. Under simultaneous strong measurement and qubit drive, the qubit undergoes a series of quantum jumps between states. These jumps are visible in the experimental measurement record and are analyzed using maximum likelihood estimation to determine qubit transition rates. The observed rates agree with both analytical predictions and numerical simulations. The analysis methods are suitable for processing general noisy random telegraph signals.

Coherent Coupled Qubits for Quantum Annealing

Quantum annealing is an optimization technique which potentially leverages quantum tunneling to enhance computational performance. Existing quantum annealers use superconducting flux qubits with short coherence times, limited primarily by the use of large persistent currents

1/f noise of Josephson-junction-embedded microwave resonators at single photon energies and millikelvin temperatures

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Visualizing ambivalence: showing what mixed feelings look like

. Here, we examine an alternative approach, using qubits with smaller