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arXiv:0910.4908 · Physical Review Letters

Optimal Dynamical Control of Many-Body Entanglement

Felix Platzer, Florian Mintert, Andreas Buchleitner

Published Jul 7, 2010• 49 citations
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Abstract

We construct time-dependent optimal control pulses based on a multipartite entanglement measure as the target functional. The control Hamiltonian is given purely algebraically and drives a composite quantum system rapidly into a highly entangled state that is robust against decoherence.
DOI
10.1103/physrevlett.105.020501

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We construct optimal time-local control pulses based on a multipartite entanglement measure as target functional. The underlying control Hamiltonians are derived in a purely algebraic fashion, and the resulting pulses drive a composite quantum system rapidly into that highly entangled state which can be created most efficiently for a given interaction mechanism, and which bears entanglement that is robust against decoherence. Moreover, it is shown that the control scheme is insensitive to experimental imperfections in first order.
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We propose a universal approach based on Hamiltonian inverse engineering to realize a set of parameterized two-qubit gates. This method possesses unique advantages to simultaneous control of transitions among four energy levels, providing a simpler and effective way to construct composite two-qubit gates with fewer operations than traditional methods. Applied to silicon double quantum dots (DQDs), one can realize a one-step fSim gate and a B gate with only one pulse switch. Of note, the method can be further integrated with various optimization theories to enhance gate performance. Based on quantum optimal control theory, we develop a high-fidelity fSim gate scheme with experimentally feasible pulse shapes, featuring an average gate time of 50 ns and a theoretical fidelity of 99.95% in the presence of decoherence and approximation error. By incorporating geometric quantum gate principles, we propose a combined geometric and dynamic fSim gate scheme. Numerical simulations demonstrate that this hybrid scheme exhibits stronger robustness against systematic errors compared to the purely dynamic approach. Our method is generalizable to arbitrary two-qubit physical systems, offering a feasible pathway for rapidly and robustly constructing composite two-qubit gates.
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.
A rapid incoherent control scheme for driving a simple qubit system from an initial mixed state to an arbitrary target pure state is proposed. This scheme consists of two main steps: rapid purification of the initial mixed state and time optimal transition from the conditional state to the target state. The first step rapidly purifies the initial mixed state into an almost-pure state of the simple qubit system through continuous measurements and feedback control by the protocol proposed in Jacobs 2003 Physical Review A 67 030301(R). The second step finds a set of suitable time optimal controls to drive the simple qubit system from the conditional state to the target state. The switching time between the first step and the second step is determined by the expected purity and the resultant state is an almost-pure state with a high fidelity with the target state. This rapid incoherent control scheme provides an alternative quantum engineering strategy for the rapid preparation of arbitrary pure states of a simple qubit system.