We analyze the newly proposed quantum feedback loop for a solid-state qubit, based on monitoring the quadrature components of the current from a weakly coupled detector, which continuously measures the qubit. Similar to the earlier proposal of the "Bayesian" feedback, the feedback loop is used to maintain the coherent (Rabi)oscillations in a qubit for an arbitrarily long time; however, this is done in a significantly simpler way, which requires much smaller bandwidth of the control circuitry. The price for simplicity is a less-than-ideal operation: the fidelity is limited to about 95%. The feedback loop operation can be experimentally verified by appearance of a positive in-phase component of the detector current relative to an external oscillating signal used for synchronization. The quadrature-based quantum feedback seems to be within the reach of the present-day technology.
We discuss the operation of the one-qubit quantum feedback loop,
which may be used for
initialization of a qubit in a solid-state quantum computer.
The continuous monitoring of a quantum state, which makes
the feedback possible, is done by means of a weak continuous measurement
and processing of the obtained information via quantum Bayesian
The properly designed quantum feedback
loop can keep the desired phase of a single-qubit quantum
coherent oscillations for infinitely long time, even in presence
of a dephasing environment. Various nonidealities reduce the
fidelity of the feedback synchronization. We report our
study of the effects of finite available bandwidth and time delay
on the one-qubit quantum feedback performance, and also discuss
the effect of environment-induced dephasing.
The quantum evolution of an individual solid-state qubit during the process of its continuous measurement can be described by the recently developed Bayesian formalism. In contrast to the conventional ensemble-averaged formalism, it takes into account the measurement record (in a way similar to the standard Bayesian analysis) and therefore is able to consider individual realizations of the measurement process. The formalism provides testable experimental predictions and can be used for the analysis of a quantum feedback control of solid-state qubits. The Bayesian formalism can be also applied to the continuous measurement of entangled qubits; in particular, it shows how to create a fully entangled pair of qubits without their direct interaction, just by measuring them with an equally coupled detector.