Experimental characterization of the Toffoli gate via channel spectrum benchmarking

TL;DR

This paper extends channel spectrum benchmarking to better characterize noisy quantum gates like the Toffoli gate, providing more reliable fidelity estimates and demonstrating advantages of qutrit-based implementations on a trapped-ion processor.

Contribution

We introduce an extended CSB model with a fidelity estimate interval, improving noise robustness and accuracy in quantum gate characterization.

Findings

FEI remains narrow and reliable in fidelity estimation

Qutrit-based Toffoli implementation outperforms qubit-based one

Protocol validated on a trapped-ion quantum processor

Abstract

Channel spectrum benchmarking (CSB) provides a robust framework for characterizing quantum gate fidelities while remaining insensitive to state preparation and measurement (SPAM) errors. Yet, current CSB implementations encounter fundamental challenges when reconstructing noisy eigenvalues, particularly in the presence of spectral degeneracies and off-diagonal noise components in the target gate's eigenbasis. These issues become especially pronounced in the strong noise regime for gates with fidelities around $90\%$. To address these limitations, we introduce an extended CSB model together with a fidelity estimate interval (FEI) -- an interval-valued estimate of the target gate fidelity. Numerical simulation demonstrates that FEI remains sufficiently narrow, with its midpoint reliably approximating the true fidelity. We further validate the protocol on a trapped-ion quantum processor by benchmarking two implementations of the three-qubit Toffoli gate. The results reveal a clear advantage of the qutrit-based implementation over its qubit-based counterpart.