Observing single quantum trajectories of a superconducting qubit

  1. K. W. Murch,
  2. S. J. Weber,
  3. C. Macklin,
  4. and I. Siddiqi
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 conditioned on the measurement outcome. We employ weak measurements to monitor a microwave cavity embedding a superconducting qubit and track the individual quantum trajectories of the system. In this architecture, 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 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 foundations of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new route for implementing what Schrodinger termed „quantum steering“-harnessing action at a distance to manipulate quantum states via measurement.

Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations

  1. R. Vijay,
  2. C. Macklin,
  3. D. H. Slichter,
  4. S. J. Weber,
  5. K. W. Murch,
  6. R. Naik,
  7. A. N. Korotkov,
  8. and I. Siddiqi
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. We monitor the dynamics of a resonantly driven quantum two-level system — a superconducting quantum bit –using a near-noiseless parametric amplifier. The high-fidelity measurement output is used to actively stabilize the phase of Rabi oscillations, enabling them to persist indefinitely. This new functionality shows promise for fighting decoherence and defines a path for continuous quantum error correction.

Heralded state preparation in a superconducting qubit

  1. J. E. Johnson,
  2. C. Macklin,
  3. D. H. Slichter,
  4. R. Vijay,
  5. E. B. Weingarten,
  6. John Clarke,
  7. and I. Siddiqi
We demonstrate high-fidelity, quantum nondemolition, single-shot readout of a superconducting flux qubit in which the pointer state distributions can be resolved to below one part in
1000. In the weak excitation regime, continuous measurement permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This procedure boosts readout fidelity to 93.9% by suppressing errors due to spurious thermal population. Furthermore, heralding potentially enables a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.