Quantum memory optimisation using finite-horizon, decoherence time and discounted mean-square performance criteria

TL;DR

The paper develops quantum memory optimisation by analyzing mean-square deviation functionals in both Heisenberg and Schrödinger pictures for open quantum stochastic systems. It extends memory-decoherence-time maximisation beyond short horizons to finite-horizon and discounted criteria, establishing relationships between $\Delta(t)$ and the decoherence time $\tau(\epsilon)$ and providing p-parametrised, differentiable formulations. It delivers computable, closed-form expressions for discounted memory performance in both the OQHO (via ALEs) and Schrödinger-picture frameworks, and outlines extensions to finite-level systems. The approach offers a practical pathway to design and assess quantum memories under stochastic environmental interactions, with potential numerical methods such as homotopy to solve the discounted problems and applicability to a broader class of quantum devices.

Abstract

This paper is concerned with open quantum memory systems for approximately retaining quantum information, such as initial dynamic variables or quantum states to be stored over a bounded time interval. In the Heisenberg picture of quantum dynamics, the deviation of the system variables from their initial values lends itself to closed-form computation in terms of tractable moment dynamics for open quantum harmonic oscillators and finite-level quantum systems governed by linear or quasi-linear Hudson-Parthasarathy quantum stochastic differential equations, respectively. This tractability is used in a recently proposed optimality criterion for varying the system parameters so as to maximise the memory decoherence time when the mean-square deviation achieves a given critical threshold. The memory decoherence time maximisation approach is extended beyond the previously considered low-threshold asymptotic approximation and to Schrödinger type mean-square deviation functionals for the reduced system state governed by the Lindblad master equation. We link this approach with the minimisation of the mean-square deviation functionals at a finite time horizon and with their discounted version which quantifies the averaged performance of the quantum system as a temporary memory under a Poisson flow of storage requests.

Figures (1)

• Figure 1: An illustration of the local inverse of the function $\Delta$ in a neighbourhood of $T:=\tau(\epsilon_0)$ with a regular fidelity level $\epsilon_0$ in the sense of (\ref{['Deldotpos']}).