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 qudit quantum approximate optimization (QAOA) algorithms. The results show that high fidelity (> 0.99) is achievable with sufficient computational effort on HPC for most 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.

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…For example, gradient optimization of analytic controls (GOAT) is a new algorithm that allows to target high fidelities while designing pulses that conform to hardwarespecific constraints [401]. B-splines can be used for pulse parametrization in gradientbased optimization [271,450,463]. A binary relaxed gradient in which the pulse is either on or off has been introduced [593] for generating unitary gate transformations.…”

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…For example, gradient optimization of analytic controls (GOAT) is a new algorithm that allows to target high fidelities while designing pulses that conform to hardware-specific constraints [398]. B-splines can be used for pulse parametrization in gradient-based optimization [266,446,459]. A binary relaxed gradient in which the pulse is either on or off has been introduced [587] for generating unitary gate transformations.…”

Dynamics of qudit gates and effects of spectator modes on optimal control pulses

“…Gates can be designed in modules (1-and 2-qudit gates), such as in Ref. [16] for bosonic modes. To be able to use synthesized gates in the entire space by preserving their fidelity, one needs to check if the modules function across the entire space.…”