Generation of high-fidelity quantum control methods for multi-level systems

TL;DR

This paper introduces a novel technique leveraging SU(2) symmetry to develop high-fidelity, robust quantum control methods for multi-level systems, demonstrated experimentally with trapped ions achieving very low infidelity.

Contribution

It presents a new approach for designing multi-level quantum controls based on SU(2) symmetry, extending control methods beyond two-level systems.

Findings

Achieved average infidelity around 10^{-4} in experiments

Developed new adiabatic and composite control methods

Demonstrated applicability to quantum computing protocols

Abstract

In recent decades there has been a rapid development of methods to experimentally control individual quantum systems. A broad range of quantum control methods has been developed for two-level systems, however the complexity of multi-level quantum systems make the development of analogous control methods extremely challenging. Here, we exploit the equivalence between multi-level systems with SU(2) symmetry and spin-1/2 systems to develop a technique for generating new robust, high-fidelity, multi-level control methods. As a demonstration of this technique, we develop new adiabatic and composite multi-level quantum control methods and experimentally realise these methods using an $^{171}$Yb$^+$ ion system. We measure the average infidelity of the process in both cases to be around $10^{-4}$, demonstrating that this technique can be used to develop high-fidelity multi-level quantum control methods and can, for example, be applied to a wide range of quantum computing protocols including implementations below the fault-tolerant threshold in trapped ions.