Numerical Gate Synthesis for Quantum Heuristics on Multi-Mode Bosonic Systems

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms [1]. 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 the quantum optimal control approaches described in [2,3], we showcase universal control of single-qudit operations up to 8 states, and two-qutrit operations, mapped respectively on 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 QAOA qudit algorithms [4]. The results show that high fidelity (> 0.99) is achievable with sufficient computational effort on HPC for all cases under study, and extension 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 cQED systems.

[1] PRX Quantum 2, 010101 (2021).

[2] arXiv:2001.01013

[3] arXiv:2106.14310

[4] Algorithms 12.2 (2019): 34.