Numerical Gate Synthesis for Quantum Heuristics on Bosonic Quantum Processors

Abstract

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity ($>$ 0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.

11 pages, 4 figures. To appear

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• Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
• Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping
• Neural network accelerator for quantum control
• Dynamics of qudit gates and effects of spectator modes on optimal control pulses
• Performance evaluation of variational quantum eigensolver and quantum dynamics algorithms on the advection-diffusion equation