Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates

Abstract

Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for essentially any quantum control problem. So far this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here, using differential geometry, we reformulate the quantum brachistochrone curves as geodesics on the unitary group. With this identification we are able to obtain a numerical method that efficiently solves the brachistochrone problem. We apply it to two examples demonstrating its power.

5 pages, 8 pages of supplemental material, 1 figure, 3 tables

References in corpus (5)

• Quantum Computation as Geometry
• Singular extremals for the time-optimal control of dissipative spin 1/2 particles
• Quantum Adiabatic Brachistochrone
• Optimal control for fast and high-fidelity quantum gates in coupled superconducting flux qubits
• Time-Optimal Generation of Cluster States

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• Robust nonadiabatic geometric quantum computation by dynamical correction
• Quantum Zermelo problem for general energy resource bounds
• Time Optimal Quantum Control of Spinor States
• Accelerating the computation of quantum brachistochrone
• Optimal-speed unitary quantum time evolutions and propagation of light with maximal degree of coherence