Qudit-Generalization of the Qubit Echo and Its Application to a Qutrit-Based Toffoli Gate

TL;DR

This paper generalizes the qubit echo protocol to qudits, introduces basis cycling, and demonstrates improved fidelity of a qutrit-based Toffoli gate on IBM quantum computers, showing potential for qudit-based circuit optimization.

Contribution

It presents a novel basis cycling technique for qudits, extending echo protocols and enabling high-fidelity, calibration-stable qudit gates on superconducting quantum computers.

Findings

Achieved up to 93.8% CCZ gate fidelity on IBM quantum computers.

Fidelity remains stable despite resonant frequency fluctuations.

Systematic overcoming of phase error issues in qudit gate implementations.

Abstract

The fidelity of certain gates on noisy quantum computers may be improved when they are implemented using more than two levels of the involved transmons. The main impediments to achieving this potential are the dynamic gate phase errors that cannot be corrected via calibration. The standard tool for countering such phase errors in two-level qubits is the echo protocol, often referred to as the dynamical decoupling sequence, where the evolution of a qubit is punctuated by an even number of X gates. We introduce basis cycling, which is a direct generalization of the qubit echo to general qudits, and provide an analytic framework for designing gate sequences to produce desired effects using this technique. We then apply basis cycling to a Toffoli gate decomposition incorporating a qutrit and obtain CCZ gate fidelity values up to 93.8$\pm$0.1%, measured by quantum process tomography, on IBM quantum computers. The gate fidelity remains stable without recalibration even while the resonant frequency of the qutrit fluctuates, highlighting the dynamical nature of phase error cancellation through basis cycling. Our results demonstrate that one of the biggest difficulties in implementing qudit-based gate decompositions on superconducting quantum computers can be systematically overcome when certain conditions are met, and thus open a path toward fulfilling the promise of qudits as circuit optimization agents.