16 research outputs found
Action principle for continuous quantum measurement
We present a stochastic path integral formalism for continuous quantum
measurement that enables the analysis of rare events using action methods. By
doubling the quantum state space to a canonical phase space, we can write the
joint probability density function of measurement outcomes and quantum state
trajectories as a phase space path integral. Extremizing this action produces
the most-likely paths with boundary conditions defined by preselected and
postselected states as solutions to a set of ordinary differential equations.
As an application, we analyze continuous qubit measurement in detail and
examine the structure of a quantum jump in the Zeno measurement regime.Comment: Published version. 8 pages, 3 figures, movies available at
http://youtu.be/OQ3PwkSKEUw and http://youtu.be/sTlV2amQtj
Mapping the optimal route between two quantum states
A central feature of quantum mechanics is that a measurement is intrinsically
probabilistic. As a result, continuously monitoring a quantum system will
randomly perturb its natural unitary evolution. The ability to control a
quantum system in the presence of these fluctuations is of increasing
importance in quantum information processing and finds application in fields
ranging from nuclear magnetic resonance to chemical synthesis. A detailed
understanding of this stochastic evolution is essential for the development of
optimized control methods. Here we reconstruct the individual quantum
trajectories of a superconducting circuit that evolves in competition between
continuous weak measurement and driven unitary evolution. By tracking
individual trajectories that evolve between an arbitrary choice of initial and
final states we can deduce the most probable path through quantum state space.
These pre- and post-selected quantum trajectories also reveal the optimal
detector signal in the form of a smooth time-continuous function that connects
the desired boundary conditions. Our investigation reveals the rich interplay
between measurement dynamics, typically associated with wave function collapse,
and unitary evolution of the quantum state as described by the Schrodinger
equation. These results and the underlying theory, based on a principle of
least action, reveal the optimal route from initial to final states, and may
enable new quantum control methods for state steering and information
processing.Comment: 12 pages, 9 figure
Linear Feedback Stabilization for a Continuously Monitored Qubit
In quantum mechanics, standard or strong measurement approaches generally result in the collapse of an ensemble of wavefunctions into a stochastic mixture of eigenstates. On the other hand, continuous or weak measurements have the propensity to dynamically control the evolution of quantum states over time, guiding the trajectory of the state into non-trivial superpositions and maintaining state purity. This kind of measurement-induced state steering is of great theoretical and experimental interest for the harnessing of quantum bits or qubits , which are the fundamental unit of the emerging quantum computer. We explore continuous measurement-based quantum state stabilization through linear feedback control for a single quantum bit. By applying a time-varying Rabi drive that includes a linear feedback term, we show that the fixed points of the continuous measurement may be relocated. Analytical derivations of It么 Stochastic Master Equations being ideal models, we employ them to derive the projected ensemble average while utilizing numerical simulations to characterize the stability of the set of possible fixed points, as well as their modified collapse time-scales. We include the effects of realistic experimental non-idealities, such as environmental energy relaxation, dephasing, time-delay, and inefficient measurement. Ultimately, we discuss potential experimental implementations from collaborating universities
Rapid estimation of drifting parameters in continuously measured quantum systems
We investigate the determination of a Hamiltonian parameter in a quantum
system undergoing continuous measurement. We demonstrate a computationally
rapid yet statistically optimal method to estimate an unknown and possibly
time-dependent parameter, where we maximize the likelihood of the observed
stochastic readout. By dealing directly with the raw measurement record rather
than the quantum state trajectories, the estimation can be performed while the
data is being acquired, permitting continuous tracking of the parameter during
slow drifts in real time. Furthermore, we incorporate realistic nonidealities,
such as decoherence processes and measurement inefficiency. As an example, we
focus on estimating the value of the Rabi frequency of a continuously measured
qubit, and compare maximum likelihood estimation to a simpler fast Fourier
transform. Using this example, we discuss how the quality of the estimation
depends on both the strength and duration of the measurement; we also discuss
the trade-off between the accuracy of the estimate and the sensitivity to drift
as the estimation duration is varied.Comment: 11 pages, 6 figure