Efficient Hamiltonian programming in qubit arrays with nearest-neighbour couplings

Abstract

A powerful control method in experimental quantum computing is the use of spin echoes, employed to select a desired term in the system’s internal Hamiltonian, while refocusing others. Here, we address a more general problem, describing a method to not only turn on and off particular interactions but also to rescale their strengths so that we can generate any desired effective internal Hamiltonian. We propose an algorithm based on linear programming for achieving time-optimal rescaling solutions in fully coupled systems of tens of qubits, which can be modified to obtain near-time-optimal solutions for rescaling systems with hundreds of qubits. Further, we propose an analytic method based on graph colouring to address the rescaling problem in systems with any number of qubits, however, with only nearest/next-nearest neighbour couplings. [1] Rescaling interactions for quantum control, G. Bhole, T. Tsunoda, P. J. Leek, and J. A. Jones, Phys. Rev. Appl. 13, 034002 (2020). [2] Efficient Hamiltonian programming in qubit arrays with nearest-neighbour couplings, T. Tsunoda, G. Bhole, S. A. Jones, J. A. Jones, and P. J. Leek, Phys. Rev. A 102 032405 (2020).