Engineering Precise and Robust Effective Hamiltonians

TL;DR

This paper introduces a comprehensive framework for designing effective Hamiltonians that improve the precision and robustness of quantum control, crucial for quantum technologies like simulation, sensing, and computing.

Contribution

It provides a general method to engineer target zeroth-order Hamiltonians with minimized higher-order effects and enhanced robustness against errors.

Findings

Framework enables robust state transfer and Hamiltonian characterization.

Includes methods to extend robustness to stochastic fluctuations.

Examples demonstrate improved precision and control robustness.

Abstract

Engineering effective Hamiltonians is essential for advancing quantum technologies including quantum simulation, sensing, and computing. This paper presents a general framework for effective Hamiltonian engineering, enabling robust, precise, and efficient quantum control strategies. To achieve efficiency, we focus on creating target zeroth-order effective Hamiltonians while minimizing higher-order contributions and enhancing robustness against systematic errors. The control design identifies the minimal subspace of the toggling-frame Hamiltonian and the full set of achievable, zeroth-order, effective Hamiltonians. The framework also enables robust state transfer, characterization of achievable density matrices, and extension to stochastic parameter fluctuations via a cumulant expansion. Examples are included to illustrate the process flow and resultant precision and robustness.