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arXiv:2503.20675

Decoherence time maximization and partial isolation for open quantum harmonic oscillator memory networks

Igor G. Vladimirov, Ian R. Petersen, Guodong Shi

Published Mar 26, 2025• 0 citations
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Abstract

This paper considers a network of open quantum harmonic oscillators which interact with their neighbours through direct energy and field-mediated couplings and also with external quantum fields. The position-momentum dynamic variables of the network are governed by linear quantum stochastic differential equations associated with the nodes of a graph whose edges specify the interconnection of the component oscillators. Such systems can be employed as Heisenberg picture quantum memories with an engineered ability to approximately retain initial conditions over a bounded time interval. We use the quantum memory decoherence time defined previously in terms of a fidelity threshold on a weighted mean-square deviation for a subset (or linear combinations) of network variables from their initial values. This approach is applied to maximizing a high-fidelity asymptotic approximation of the decoherence time over the direct energy coupling parameters of the network. The resulting optimality condition is a set of linear equations for blocks of a sparse matrix associated with the edges of the direct energy coupling graph of the network. We also discuss a setting where the quantum network has a subset of dynamic variables which are affected by the external fields only indirectly, through a complementary ``shielding'' system. This holds under a rank condition on the network-field coupling matrix and can be achieved through an appropriate field-mediated coupling between the component oscillators. The partially isolated subnetwork has a longer decoherence time in the high-fidelity limit, thus providing a particularly relevant candidate for a quantum memory.

DOI
10.48550/arxiv.2503.20675

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This paper considers a network of open quantum harmonic oscillators which interact with their neighbours through direct energy and field-mediated couplings and also with external quantum fields. The position-momentum dynamic variables of the network are governed by linear quantum stochastic differential equations associated with the nodes of a graph whose edges specify the interconnection of the component oscillators. Such systems can be employed as Heisenberg picture quantum memories with an engineered ability to approximately retain initial conditions over a bounded time interval. We use the quantum memory decoherence time defined previously in terms of a fidelity threshold on a weighted mean-square deviation for a subset (or linear combinations) of network variables from their initial values. This approach is applied to maximizing a high-fidelity asymptotic approximation of the decoherence time over the direct energy coupling parameters of the network. The resulting optimality condition is a set of linear equations for blocks of a sparse matrix associated with the edges of the direct energy coupling graph of the network. We also discuss a setting where the quantum network has a subset of dynamic variables which are affected by the external fields only indirectly, through a complementary ``shielding'' system. This holds under a rank condition on the network-field coupling matrix and can be achieved through an appropriate field-mediated coupling between the component oscillators. The partially isolated subnetwork has a longer decoherence time in the high-fidelity limit, thus providing a particularly relevant candidate for a quantum memory.
This paper considers a network of open quantum harmonic oscillators which interact with their neighbours through direct energy and field-mediated couplings and also with external quantum fields. The position-momentum dynamic variables of the network are governed by linear quantum stochastic differential equations associated with the nodes of a graph whose edges specify the interconnection of the component oscillators. Such systems can be employed as quantum memories with an engineered ability to approximately retain initial conditions over a bounded time interval. We use the quantum memory decoherence time defined previously in terms of a fidelity threshold on a weighted mean-square deviation for a subset (or linear combinations) of network variables from their initial values. This approach is applied to maximizing a high-fidelity asymptotic approximation of the decoherence time over the direct energy coupling parameters of the network. The resulting optimality condition is a set of linear equations for blocks of a sparse matrix associated with the edges of the direct energy coupling graph of the network. We also discuss a setting where the quantum network has a subset of dynamic variables which are affected by the external fields only indirectly, through a complementary "shielding" system. The partially isolated subnetwork has a longer decoherence time in the high-fidelity limit, which is also amenable to optimization.
This paper is concerned with open quantum harmonic oscillators with position-momentum system variables, whose internal dynamics and interaction with the environment are governed by linear quantum stochastic differential equations. A recently proposed approach to such systems as Heisenberg picture quantum memories exploits their ability to approximately retain initial conditions over a decoherence horizon. Using the quantum memory decoherence time defined previously in terms of a fidelity threshold on a weighted mean-square deviation of the system variables from their initial values, we apply this approach to a partially isolated subsystem of the oscillator, which is not directly affected by the external fields. The partial isolation leads to an appropriate system decomposition and a qualitatively different short-horizon asymptotic behaviour of the deviation, which yields a longer decoherence time in the high-fidelity limit. The resulting approximate decoherence time maximization over the energy parameters for improving the quantum memory performance is discussed for a coherent feedback interconnection of such systems.
This paper is concerned with open quantum harmonic oscillators (OQHOs) described by linear quantum stochastic differential equations. This framework includes isolated oscillators with zero Hamiltonian, whose system variables remain unchanged (in the Heisenberg picture of quantum dynamics) over the course of time, making such systems potentially applicable as quantum memory devices. In a more realistic case of system-environment coupling, we define a memory decoherence horizon as a typical time for a mean-square deviation of the system variables from their initial values to become relatively significant as specified by a weighting matrix and a fidelity parameter. We consider the maximization of the decoherence time over the energy and coupling matrices of the OQHO as a memory system in its storage phase and obtain a condition under which the zero Hamiltonian delivers a suboptimal solution. This optimization problem is also discussed for an interconnection of OQHOs.
This paper is concerned with open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices for finite-level systems. The Hamiltonian and the operators of coupling of the system to the external bosonic fields depend linearly on the system variables. The fields are represented by quantum Wiener processes which drive the system dynamics according to a quasilinear Hudson–Parthasarathy quantum stochastic differential equation whose drift vector and dispersion matrix are affine and linear functions of the system variables. This setting includes the zero-Hamiltonian isolated system dynamics as a particular case, where the system variables are constant in time, which makes them potentially applicable as a quantum memory. In a more realistic case of nonvanishing system-field coupling, we define a memory decoherence time when a mean-square deviation of the system variables from their initial values becomes relatively significant as specified by a weighting matrix and a fidelity parameter. We consider the decoherence time maximization over the energy parameters of the system and obtain a condition under which the zero Hamiltonian provides a suboptimal solution. This optimization problem is also discussed for a direct energy coupling interconnection of such systems.
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.
This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, similar to that of the Pauli matrices, and their Heisenberg picture evolution is governed by a quasilinear quantum stochastic differential equation. The latter involves a Hamiltonian whose parameters depend affinely on a classical control signal in the form of a deterministic function of time. The memory performance is quantified by a mean-square deviation of quantum system variables of interest from their initial conditions. We relate this functional to a matrix-valued state of an auxiliary classical control-affine dynamical system. This leads to a pointwise control design where the control signal minimises the time-derivative of the mean-square deviation with an additional quadratic penalty on the control. In an alternative finite-horizon setting with a terminal-integral cost functional, we apply dynamic programming and obtain a quadratically nonlinear Hamilton-Jacobi-Bellman equation, for which a solution is outlined in the form of a recursively computed asymptotic expansion.