Quantum computing offers the potential for super-polynomial speedups over any known classical algorithm for a broad class of computational tasks. The need for optimal control of quantum systems lies at the heart of several emerging technologies from quantum sensing to dynamical control of chemical reactions and, most significantly, quantum computing.
We developed numerical methods for the optimal control problem for realizing logical gates in closed quantum systems, where the evolution of the state vector is governed by the time-dependent Schrödinger equation. The number of parameters in the control functions is made independent of the number of time steps by expanding them in terms of B-spline basis functions, with and without carrier waves. We used an interior point, gradient-based technique from the Interior Point Optimizer package to minimize the gate infidelity, subject to amplitude constraints on the control functions. The symplectic Stromer-Verlet scheme is used to integrate a real-valued formulation of Schrödinger's equation in time, and the gradient of the gate infidelity is obtained by solving the corresponding adjoint equation. This allows all components of the gradient to be calculated at the cost of solving three Schrödinger systems, independently of the number of parameters in the control functions. We verified the method is correct and applied to Hamiltonians that model the dynamics of coupled super-conducting qubits.
Our project leveraged and advanced Lawrence Livermore National Laboratory's core competencies in high-performance computing, simulation, and data science. Further development of this technology will allow Livermore researchers to significantly accelerate the realization of practical high performance quantum computing technologies and help position the lab as a world leader in the emerging fields of quantum sensing, control, and scientific quantum computing, all central to the DOE and NNSA mission space.
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