Numerical Gate Synthesis for Quantum Heuristics on Bosonic Quantum Processors

TL;DR

This paper explores numerical gate synthesis for quantum heuristics on bosonic quantum processors, demonstrating high-fidelity control of qudit operations using optimal control techniques, with potential applications in quantum algorithms and cQED systems.

Contribution

It introduces a method for numerically synthesizing quantum gates on bosonic modes, achieving high fidelity and enabling practical implementations in quantum algorithms.

Findings

High-fidelity (>0.99) single-qudit and two-qutrit gates achieved

Numerical pulse engineering effective for closed systems

Potential extension to noisy, multi-mode systems

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.