Time-Optimal Generation of Cluster States

Abstract

The definition of a cluster state naturally suggests an implementation scheme: find a physical system with an Ising coupling topology identical to that of the target state, and evolve freely for a time of 1/2J. Using the tools of optimal control theory, we address the question of whether or not this implementation is time-optimal. We present some examples where it is not and provide an explanation in terms of geodesics on the Bloch-sphere.

Published version

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• Experimental time-optimal universal control of spin qubits in solids
• Broadband 180 degree universal rotation pulses for NMR spectroscopy designed by optimal control
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• Preparing Greenberger-Horne-Zeilinger and $W$ states on a long-range Ising spin model by global controls
• Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
• Multiple-spin coherence transfer in linear Ising spin chains and beyond: numerically-optimized pulses and experiments
• Fast Quantum Communication in Linear Networks
• Generation of complete graph states in a spin-$1/2$ Heisenberg chain with a globally optimized magnetic field