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arXiv:1104.2337 · Physical Review A

Optimizing entangling quantum gates for physical systems

M. M. Müller, Daniel M. Reich, Michael Murphy, Haidong Yuan, Jiří Vala, K. Birgitta Whaley, Tommaso Calarco, Christiane P. Koch

Published Oct 10, 2011• 80 citations
arXivHTMLPDF

Abstract

Optimal control theory is a versatile tool that presents a route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric theory for local equivalence classes of two-qubit operations to derive an optimization algorithm that determines the best entangling two-qubit gate for a given physical setting. We demonstrate the power of this approach for trapped polar molecules and neutral atoms.

DOI
10.1103/physreva.84.042315

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Optimal control theory is a versatile tool that presents a route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric theory for local equivalence classes of two-qubit operations to derive an optimization algorithm that determines the best entangling two-qubit gate for a given physical setting. We demonstrate the power of this approach for trapped polar molecules and neutral atoms.
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally entangled state out of some initial product state. The functional depends on easily computable local invariants and unequivocally determines whether a gate is a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.
The difficulty of an optimization task in quantum information science depends on the proper mathematical expression of the physical target. Here we demonstrate the power of optimization functionals targeting an arbitrary perfect two-qubit entangler, which allow generation of a maximally entangled state from some initial product state. We show for two quantum information platforms of current interest, i.e., nitrogen vacancy centers in diamond and superconducting Josephson junctions, that an arbitrary perfect entangler can be reached faster and with higher fidelity than both specific two-qubit gates and local equivalence classes of two-qubit gates. Our results are obtained using two independent optimization approaches, underscoring the critical role of the optimization target.
We use a novel optimization procedure that includes the temporal and spatial parameters of the pulses acting on arrays of trapped neutral atoms to prepare entangling gates in N-qubit systems. The spatiotemporal control allows treating a denser array of atoms, where each pulse acts on a subset of the qubits, potentially allowing to speed up the gate operation by two orders of magnitude by boosting the dipole-blockade between the Rydberg states. Studying the rate of success of the algorithm under different constraints, we evaluate the impact of the proximity of the atoms and, indirectly, the role of the geometry of the arrays in three and four-qubit systems, as well as the minimal energy requirements and how this energy is used among the different qubits. Finally, we characterize and classify all optimal protocols according to the mechanism of the gate using a quantum pathway analysis.
Arrays of identical neutral atoms trapped in optical tweezers are a promising candidate for use in quantum computing. These platforms are highly scalable to large numbers of qubits and neutral atoms boost several attractive features as long coherence times and the possibility to be entangled via strong dipole-dipole interactions by driving them to highly excited Rydberg states. \nThe Thesis work is developed inside the framework of the QRydDemo project, whose aim in the next few years is to realize a neutral atom quantum processor with several hundred qubits. The smallest building blocks for the quantum computer are one and two-qubit gates: to entangle two atoms in the quantum register, a controlled-phase (CZ) gate will be implemented by shining fine-tuned laser pulses onto them. In this work, after giving a theoretical description of the Hamiltonian of two neutral atoms in the quantum register, a numerical simulation of this system is exploited to reproduce the behavior of the two-qubit CZ gate. Realistic effects are taken into account as finite temperature, imperfect Rydberg blockade, or decay out of the Rydberg state. A protocol with constant pulses is analyzed and its optimal parameters are found through classical optimizers. Then, time-dependent pulses are introduced and the optimal pulses are found through the optimal control algorithm dCRAB in an open-loop optimization. For the experimental realization of the gate, this analysis is of pivotal importance to know in which aspect more effort has to be put to maximize the experimental precision of the operation and thus improving the performance of the whole device \n