Quantum entanglement is a key resource for quantum technologies, yet its efficient and high-fidelity generation remains a challenge due to the complexity of quantum dynamics. This paper presents a quantum optimal control framework to maximize bipartite entanglement within a fixed time horizon, under bounded control inputs. By leveraging Pontryagin’s Minimum Principle, we derive a set of necessary conditions that guide the design of time-dependent control fields to steer a two-qubit system toward maximally entangled Bell states. The entanglement is quantified using concurrence, and the control objective is formulated as maximizing this measure at the terminal time. Our approach is validated through numerical simulations of Liouville–von Neumann dynamics. The results demonstrate the effectiveness of switching-based control strategies in achieving robust entanglement, offering insights into practical implementations of quantum control for entanglement generation in quantum networks.Quantum entanglement is a key resource for quantum technologies, yet its efficient and high-fidelity generation remains a challenge due to the complexity of quantum dynamics. This paper presents a quantum optimal control framework to maximize bipartite entanglement within a fixed time horizon, under bounded control inputs. By leveraging Pontryagin’s Minimum Principle, we derive a set of necessary conditions that guide the design of time-dependent control fields to steer a two-qubit system toward maximally entangled Bell states. The entanglement is quantified using concurrence, and the control objective is formulated as maximizing this measure at the terminal time. Our approach is validated through numerical simulations of Liouville–von Neumann dynamics. The results demonstrate the effectiveness of switching-based control strategies in achieving robust entanglement, offering insights into practical implementations of quantum control for entanglement generation in quantum networks.

International Conference on Control, Decision and Information Technologies (CoDIT)Jul 15, 20250 citations

Optimizing Maximally Entangled State Generation Via Pontryagin's Principle

Nahid Binandeh Dehaghani, A. Pedro Aguiar, Rafał Wiśniewski

We propose an optimal control strategy to generate maximally entangled states in bipartite quantum systems. Leveraging the Pontryagin's Principle, we derive time-dependent control fields that maximize the entanglement measure, specifically concurrence, within minimal time while adhering to input constraints. Our formulation addresses the Liouville-von Neumann dynamics of the reduced density matrix under unitary evolution. The strategy is numerically validated through simulations, demonstrating its ability to drive the system from an initial perturbed separable state to a maximally entangled target state. The results showcase the effectiveness of switching control fields in optimizing entanglement, with potential applications in quantum technologies, including communication, computation, and sensing.We propose an optimal control strategy to generate maximally entangled states in bipartite quantum systems. Leveraging the Pontryagin's Principle, we derive time-dependent control fields that maximize the entanglement measure, specifically concurrence, within minimal time while adhering to input constraints. Our formulation addresses the Liouville-von Neumann dynamics of the reduced density matrix under unitary evolution. The strategy is numerically validated through simulations, demonstrating its ability to drive the system from an initial perturbed separable state to a maximally entangled target state. The results showcase the effectiveness of switching control fields in optimizing entanglement, with potential applications in quantum technologies, including communication, computation, and sensing.

arXiv:2403.16321IEEE International Conference on Quantum Control, Computing and Learning (qCCL)Jun 25, 20250 citations

Optimal generation of entanglement under local control

Raffaele Romano, Alessio Del Fabbro

We study the optimal generation of entanglement between two qubits subject to local unitary control. With only the assumptions of linear control and unitary dynamics, by means of a numerical protocol based on the variational approach (Pontryagin minimum principle), we evaluate the optimal control strategy leading to the maximal achievable entanglement. Unlike previous analyses of the entanglement generation process, our model considers an arbitrary interaction time, and it is possible to account for the energy cost associated with the controls. We can arbitrarily choose the relative weight between a large entanglement and a small energy cost.We study the optimal generation of entanglement between two qubits subject to local unitary control. With only the assumptions of linear control and unitary dynamics, by means of a numerical protocol based on the variational approach (Pontryagin minimum principle), we evaluate the optimal control strategy leading to the maximal achievable entanglement. Unlike previous analyses of the entanglement generation process, our model considers an arbitrary interaction time, and it is possible to account for the energy cost associated with the controls. We can arbitrarily choose the relative weight between a large entanglement and a small energy cost.

arXiv:0707.1634Physical Review AOct 2, 20071 citation

Fast generation of entanglement between coupled spins using optimization and deep learning methods

Dimitris Koutromanos, Dionisis Stefanatos, Emmanuel Paspalakis

Coupled spins form composite quantum systems which play an important role in many quantum technology applications, with an essential task often being the efficient generation of entanglement between two constituent qubits. The simplest such system is a pair of spins- $1/2$ coupled with Ising interaction, and in previous works various quantum control methods such as adiabatic processes, shortcuts to adiabaticity and optimal control have been employed to quickly generate there one of the maximally entangled Bell states. In this study, we use machine learning and optimization methods to produce maximally entangled states in minimum time, with the Rabi frequency and the detuning used as bounded control functions. We do not target a specific maximally entangled state, like the preceding studies, but rather find the controls which maximize the concurrence, leading thus automatically the system to the closest such state in shorter time. By increasing the bounds of the control functions we observe that the corresponding optimally selected maximally entangled state also changes and the necessary time to reach it is reduced. The present work demonstrates also that machine learning and optimization offer efficient and flexible techniques for the fast generation of entanglement in coupled spin systems, and we plan to extent it to systems involving more spins, for example spin chains.Coupled spins form composite quantum systems which play an important role in many quantum technology applications, with an essential task often being the efficient generation of entanglement between two constituent qubits. The simplest such system is a pair of spins- $1/2$ coupled with Ising interaction, and in previous works various quantum control methods such as adiabatic processes, shortcuts to adiabaticity and optimal control have been employed to quickly generate there one of the maximally entangled Bell states. In this study, we use machine learning and optimization methods to produce maximally entangled states in minimum time, with the Rabi frequency and the detuning used as bounded control functions. We do not target a specific maximally entangled state, like the preceding studies, but rather find the controls which maximize the concurrence, leading thus automatically the system to the closest such state in shorter time. By increasing the bounds of the control functions we observe that the corresponding optimally selected maximally entangled state also changes and the necessary time to reach it is reduced. The present work demonstrates also that machine learning and optimization offer efficient and flexible techniques for the fast generation of entanglement in coupled spin systems, and we plan to extent it to systems involving more spins, for example spin chains.

arXiv:2412.17489EPJ Quantum TechnologyDec 1, 20249 citations

Optimal Control of Bipartite Quantum Systems

Emanuel Malvetti, Léo Van Damme

Closed bipartite quantum systems subject to fast local unitary control are studied using quantum optimal control theory and a method of reduced control systems based on the Schmidt decomposition. Particular focus is given to the time-optimal generation of maximally entangled states and product states, as well as to the problem of stabilizing quantum states with a certain amount of entanglement. Explicit analytical solutions are given for general systems consisting of two qubits (as well as for bosonic and fermionic analogues) and also for a class of systems consisting of two coupled qutrits which is studied using the Pontryagin Maximum Principle.Closed bipartite quantum systems subject to fast local unitary control are studied using quantum optimal control theory and a method of reduced control systems based on the Schmidt decomposition. Particular focus is given to the time-optimal generation of maximally entangled states and product states, as well as to the problem of stabilizing quantum states with a certain amount of entanglement. Explicit analytical solutions are given for general systems consisting of two qubits (as well as for bosonic and fermionic analogues) and also for a class of systems consisting of two coupled qutrits which is studied using the Pontryagin Maximum Principle.

arXiv:2405.20034May 30, 20240 citations

Topological Entanglement Network Optimization Based on Quantum Coherence Time

Jincheng Zhang

This paper explores a novel approach to optimizing topological entanglement networks by leveraging precise control over quantum coherence time. The core concept involves utilizing a feedback control system to monitor and dynamically adjust coherence times within the network, guided by the underlying topological structure. This adaptive control mechanism aims to maximize information transmission efficiency and enhance the network's resilience to noise and errors. We present a theoretical framework detailing the optimization process, incorporating mathematical models to describe coherence time dynamics and network connectivity. The proposed strategy offers a pathway towards realizing more robust and efficient quantum entanglement networks, crucial for applications in quantum communication, computation, and sensing. The key elements of this work include a detailed mathematical description of coherence time control, a topological network optimization algorithm, and an analysis of the resulting performance improvements.This paper explores a novel approach to optimizing topological entanglement networks by leveraging precise control over quantum coherence time. The core concept involves utilizing a feedback control system to monitor and dynamically adjust coherence times within the network, guided by the underlying topological structure. This adaptive control mechanism aims to maximize information transmission efficiency and enhance the network's resilience to noise and errors. We present a theoretical framework detailing the optimization process, incorporating mathematical models to describe coherence time dynamics and network connectivity. The proposed strategy offers a pathway towards realizing more robust and efficient quantum entanglement networks, crucial for applications in quantum communication, computation, and sensing. The key elements of this work include a detailed mathematical description of coherence time control, a topological network optimization algorithm, and an analysis of the resulting performance improvements.

Aug 31, 20260 citations

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coupled with Ising interaction, and in previous works various quantum control methods such as adiabatic processes, shortcuts to adiabaticity and optimal control have been employed to quickly generate there one of the maximally entangled Bell states. In this study, we use machine learning and optimization methods to produce maximally entangled states in minimum time, with the Rabi frequency and the detuning used as bounded control functions. We do not target a specific maximally entangled state, like the preceding studies, but rather find the controls which maximize the concurrence, leading thus automatically the system to the closest such state in shorter time. By increasing the bounds of the control functions we observe that the corresponding optimally selected maximally entangled state also changes and the necessary time to reach it is reduced. The present work demonstrates also that machine learning and optimization offer efficient and flexible techniques for the fast generation of entanglement in coupled spin systems, and we plan to extent it to systems involving more spins, for example spin chains.