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Quantum Feedback Cooling without State Filtering

Lorenzo Franceschetti, Francesco Ticozzi

Abstract

We introduce a state-based feedback law that stabilizes quantum states or subspaces associated with extremal values of a continuously monitored observable - a problem motivated by quantum cooling tasks. We then propose an output-based approximation that uses simple filtering of the measurement record to emulate the required feedback signal, thereby avoiding full real-time quantum state estimation, a key bottleneck for implementing and scaling filtering-based feedback control. The performance of the resulting strategy is demonstrated numerically on two test-bed models for feedback cooling.

Quantum Feedback Cooling without State Filtering

Abstract

We introduce a state-based feedback law that stabilizes quantum states or subspaces associated with extremal values of a continuously monitored observable - a problem motivated by quantum cooling tasks. We then propose an output-based approximation that uses simple filtering of the measurement record to emulate the required feedback signal, thereby avoiding full real-time quantum state estimation, a key bottleneck for implementing and scaling filtering-based feedback control. The performance of the resulting strategy is demonstrated numerically on two test-bed models for feedback cooling.
Paper Structure (7 sections, 7 theorems, 21 equations, 2 figures)

This paper contains 7 sections, 7 theorems, 21 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Model and Assumptions
  3. A Switching Control law for Cooling
  4. Implementation without state filtering
  5. Simulations
  6. Outlook
  7. Supporting lemmas

Key Result

Theorem 3.1

Under assumptions $(A_1), (A_2)$ and $(A_3^c)$, consider the controlled system (model:ctrl), with $H_0, L, F_0 \in \mathfrak h(\mathcal{H})$. Let $V(\rho) = Tr[L\rho] - \lambda_1$ and $\delta = \lambda_2 - \lambda_1$. Let $\gamma \in (0, \delta)$ and define $f(x)$ as follows: Assume that $F_0$ is such that, when $f(x) = 1$, the associated average equation has $\rho_{mix} = \frac{1}{N}\mathds{1}$

Figures (2)

  • Figure 1: Average $F(\rho_t)$ trajectories for the qutrit system using different control strategies.
  • Figure 2: Average $F(\rho_t)$ trajectories for the antiferromagnetic Heisenberg triangle using different control strategies.

Theorems & Definitions (13)

  • Theorem 3.1
  • Lemma 1
  • proof
  • proof : Proof of Theorem (\ref{['convthm']})
  • Remark
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • ...and 3 more