Optimality of qubit purification protocols in the presence of imperfections

Abstract

Quantum control is an essential tool for the operation of quantum technologies such as quantum computers, simulators, and sensors. Although there are sophisticated theoretical tools for developing quantum control protocols, formulating optimal protocols while incorporating experimental conditions remains a challenge. In this paper, motivated by recent advances in realization of real-time feedback control in circuit quantum electrodynamics systems, we study the effect of experimental imperfections on the optimality of qubit purification protocols. Specifically, we find that the optimal control solutions in the presence of detector inefficiency and non-negligible decoherence can be significantly different from the known solutions to idealized dynamical models. In addition, we present a simplified form of the verification theorem to examine the global optimality of a control protocol.

Deterministic generation of remote entanglement with active quantum feedback

“…The ASLO feedback strategies developed here possess interesting relationships to the locally optimal strategies for single qubit purification by measurement and feedback [14]. In particular, the semiclassical protocol bears some resemblance to the locally optimal strategy for qubit purification in the small η limit, while the quantum protocol at unit measurement efficiency also bears a striking resemblance to the corresponding optimal feedback for qubit purification in Ref.…”

“…Like this quantum protocol for pure states, the single qubit state evolution under optimal feedback is also deterministic, and has been shown to be globally optimal for η = 1 [9,12,14]. These parallels lead us to speculate that the protocol given by Eqn.…”

Efficient quantum filtering for quantum feedback control

“…Other work has generalized these results for different optimization conditions [16], N-level systems [17], practical implementation of the controls [18], shared entangled states [19], imperfections [20], inefficient detection [21], and mixed protocols [21,22]. In particular, Li et al demonstrated that when the efficiency of the detector is lower than 50%, there is no predicted speed up in purification rate [21]. This result is significant for the recent quantum trajectory experiments in superconducting microwave systems because the estimated detection efficiency is given as 40% in [6].…”

“…The two measurement records are local and we restrict ourselves to local controls, for simplicity and to demonstrate that feedback control provides some advantages even without explicit control over the entangling interaction itself [26][27][28]. In the one-qubit case, the approach to quantum rapid purification has centered on the use of Bloch rotations to rotate the conditioned qubit state towards the plane orthogonal to the measurement axis [14], or towards the measurement axis [15], or some combination of the two [21,22]. These approaches have the advantage of being relatively robust and insensitive to small errors in these rotations [18].…”

“…Subsequent studies on rapid purification showed that the proposed protocol was optimal, in that it maximized the average rate of purification, but it did not minimize the time taken to reach a given level of purity [15]. Other work has generalized these results for different optimization conditions [16], N-level systems [17], practical implementation of the controls [18], shared entangled states [19], imperfections [20], inefficient detection [21], and mixed protocols [21,22]. In particular, Li et al demonstrated that when the efficiency of the detector is lower than 50%, there is no predicted speed up in purification rate [21].…”