Single-step controlled-NOT logic from any exchange interaction

TL;DR

This paper presents a unified, analytical method for implementing high-fidelity, single-step CNOT gates using exchange interactions in coupled qubits, applicable to various physical systems including superconducting qubits.

Contribution

It introduces a self-contained approach to analyze unitary evolution under exchange Hamiltonians, enabling direct CNOT gate implementation with minimal leakage, tailored for different physical platforms.

Findings

Analytical solution for anisotropic exchange with tracking controls.

Any exchange interaction can generate high-fidelity CNOTs with individual qubit control.

Identified efficient CNOT implementations for superconducting qubits.

Abstract

A self-contained approach to studying the unitary evolution of coupled qubits is introduced, capable of addressing a variety of physical systems described by exchange Hamiltonians containing Rabi terms. The method automatically determines both the Weyl chamber steering trajectory and the accompanying local rotations. Particular attention is paid to the case of anisotropic exchange with tracking controls, which is solved analytically. It is shown that, if computational subspace is well isolated, any exchange interaction can always generate high-fidelity, single-step controlled-NOT (CNOT) logic, provided that both qubits can be individually manipulated. The results are then applied to superconducting qubit architectures, for which several CNOT gate implementations are identified. The paper concludes with consideration of two CNOT gate designs having high efficiency and operating with no significant leakage to higher-lying non-computational states.