Speed limits of two-qubit gates with qudits

TL;DR

This paper investigates the fundamental speed limits of two-qubit gates by expanding the computational space to qudits, providing theoretical bounds, experimental protocols, and control algorithms to optimize gate speed in realistic settings.

Contribution

It introduces the concept of using qudits to surpass traditional speed limits of two-qubit gates and presents practical protocols and algorithms to achieve these limits.

Findings

Identified a theoretical speed limit for two-qubit gates using qudits.

Proposed an experimentally feasible protocol with superconducting transmons.

Developed a machine learning based control algorithm achieving near-limit speeds.

Abstract

The speed of elementary quantum gates ultimately sets the limit on the speed at which quantum circuits can operate. For a fixed physical interaction strength between two qubits, the speed of any two-qubit gate is limited even with arbitrarily fast single-qubit gates. In this work, we explore the possibilities of speeding up two-qubit gates beyond such a limit by expanding our computational space outside the qubit subspace, which is experimentally relevant for qubits encoded in multi-level atoms or anharmonic oscillators. We identify an optimal theoretical bound for the speed limit of a two-qubit gate achieved using two qudits with a bounded interaction strength and arbitrarily fast single-qudit gates. In addition, we find an experimentally feasible protocol using two parametrically coupled superconducting transmons that achieves this theoretical speed limit in a non-trivial way. We also consider practical scenarios with limited single-qudit drive strengths and off-resonant transitions. For such scenarios, we develop an open-source, machine learning assisted, quantum optimal control algorithm that can achieve a speedup close to the theoretical limit with near-perfect gate fidelity. This work opens up a new avenue to speed up two-qubit gates when the physical interaction strength between qubits cannot be easily increased while extra states outside the qubit subspace can be well controlled.