Pulse family optimization for parametrized quantum gates using spectral clustering

TL;DR

This paper introduces a spectral clustering method to organize high-fidelity quantum gate pulses into families, enabling more reliable interpolation and improved gate performance in parametrized quantum circuits.

Contribution

The work presents a novel spectral clustering approach to categorize optimized pulses into families, ensuring interpolations stay within high-fidelity solution groups.

Findings

Spectral clustering effectively groups pulses into families.

Interpolating within the same pulse family yields higher fidelities.

Application to Rydberg and Cat qubits demonstrates practical benefits.

Abstract

Parametrized gate circuits are used in plentiful applications in the current NISQ era of quantum computing. These parametrized gates are chiefly implemented using analytically found pulse protocols, often yielding suboptimal gate times, and consequently, fidelities. Alternatively, gate optimization algorithms are designed to construct high fidelity pulses for individual, fixed points in continuous parameter space. Gates for intermediate parameters can subsequently be found by some form of interpolation between previously constructed pulses. Nevertheless, it is not guaranteed (as with analytic protocols) that the pulses found by the optimization algorithms belong to the same \textit{family} of solutions and thus show resemblance. Interpolation between two pulses of differing solution families often leads to high infidelities, as the pulse strays away from the minimum in the parameter/fidelity landscape. In this work, we introduce a \textit{spectral clustering} method to sort high-fidelity, optimized pulses in families, and interpolating solely between pulses of the same family. Accordingly, interpolations will always approach maximal fidelity. Furthermore, as more than one pulse family is constructed, the parameter space can be partitioned according to which family prevails fidelity-wise. This work provides a meticulous demonstration of our constitutive continuous gate family construction by applying it to a universal gate set for Rydberg and Cat qubits under noise.