Exponential stabilization of quantum systems under continuous non-demolition measurements

Abstract

We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a Quantum Non-Demolition (QND) measurement operator. In open-loop, the system converges to a random eigenstate of the measurement operator. The role of the feedback is to prepare a prescribed QND eigenstate with unit probability. To achieve this we introduce the use of Brownian motion to drive the unitary control actions; the feedback loop just adapts the amplitude of this Brownian noise input as a function of the system state. Essentially, it "shakes" the system away from undesired eigenstates by applying strong noise there, while relying on the open-loop dynamics to progressively reach the target. We prove exponential convergence towards the target eigenstate using standard stochastic Lyapunov methods. The feedback scheme and its stability analysis suggest the use of an approximate filter which only tracks the populations of the eigenstates of the measurement operator. Such reduced filters should play an increasing role towards advanced quantum technologies. * This work has been supported by the ANR project HAMROQS

Experimental Assessment of Entropy Production in a Continuously Measured Mechanical Resonator

“…Remarkably, they showcase the intricate interplay between fundamental energy-exchange processes and information in setting up (and sustain) the dynamical and steady-state features of a process. Such influences can be further explored by assessing whether the control of informational terms to entropy production stemming from suitable measurement strategy could be used as an effective tool for quantum state engineering [49]. Another interesting direction would address composite systems endowed with initial quantum correlations and the experimental study of their effects, in conjunction with continuous monitoring, on the thermodynamics of the systems.…”

Exponential stabilization of spin-1/2 systems based on switching state feedback

“…Thus, the suitable controllers need to be applied to make sure that the system state converges to the target eigenstate instead of arbitrary eigenstate. For this goal, static output feedback [22][23][24], state feedback [12][13][14][15][16][17][18][19][20][25][26][27][28] and noise-assisted feedback [29,30] have been proposed. In particular, the continuous state feedback in [19] achieve the exponential stabilization of eigenstate for the quantum spin- 1 2 system.…”

“…based on Theorem 3 in [29], which means that ρ f is globally exponentially stable, and the convergence rate r is not more than ηM 2 λ 2 . On the other hand, for the two-level quantum systems, ρ t can also be characterized by the Bloch sphere coordinates (x t , y t , z t ) as…”

“…based on Theorem 3 in [29], which means that ρ f is globally exponentially stable, and the convergence rate r is not more than…”

Quantum proportional-integral (PI) control

“…Recent work has extended quantum feedback control beyond proportional feedback to implementations based on estimation of the quantum state [44][45][46], implementations using stochastic noise sources [47], and to implementations using the most general form of feedback that does not include a time-delayed proportional term [48]. In the latter framework, referred to as Proportional and Quantum State Estimation (PaQS) feedback, the feedback operator can equivalently be expressed as a sum of independent deterministic and stochastic contributions.…”