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arXiv:2506.20730 · Physical Review A

Engineering precise and robust effective Hamiltonians

Jiahui Chen, David G. Cory

Published Mar 5, 2026• 2 citations
arXivHTMLPDF

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 and characterization of achievable density matrices, and extends to stochastic fluctuations via a cumulant expansion. Examples are included to illustrate the process flow and resultant precision and robustness.

DOI
10.1103/j65l-f8lf

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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 and characterization of achievable density matrices, and extends to stochastic fluctuations via a cumulant expansion. Examples are included to illustrate the process flow and resultant precision and robustness.
Advancing quantum technologies requires precise and robust coherent control of quantum systems. Robust higher-order Hamiltonian engineering is essential for high-precision control and for accessing effective dynamics absent at zeroth order. Here, we introduce a systematic methodology for achieving the precision, robustness, and complexity required for quantum control through the engineering of higher-order processes and effective Hamiltonians. We identify the minimal subspace of achievable effective Hamiltonian at each order and provide universal cost functions for achieving desired targets. Examples include robust sequences for decoupling, three-body interactions and detuning/interaction correlations.
Abstract In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilizes perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system. Here, we provide a general framework for computing arbitrary time-dependent perturbation theory terms, as well as their gradients with respect to control variations, enabling the use of gradient methods for optimizing these terms. In particular, we show that effective Hamiltonian engineering is an instance of a bilinear control problem—the same general problem class as that of standard unitary design—and hence the same optimization algorithms apply. We demonstrate this method in various examples, including decoupling, recoupling, and robustness to control errors and stochastic errors. We also present a control engineering example that was used in experiment, demonstrating the practical feasibility of this approach.
We introduce a framework for designing Hamiltonian engineering pulse sequences that systematically accounts for the effects of higher-order contributions to the Floquet-Magnus expansion. Our techniques result in simple, intuitive decoupling rules, despite the higher-order contributions naively involving complicated, nonlocal-in-time commutators. We illustrate how these rules can be used to efficiently design improved Hamiltonian engineering pulse sequences for a wide variety of tasks such as dynamical decoupling, quantum sensing, and quantum simulation.
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase in the number of parameters with system size and experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit πππ or π/2π/2π/2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and using robust composite pulses, we make our schemes robust against errors, including finite pulse time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian engineering problem on a laptop for arbitrary two-local Hamiltonians on a 2D square lattice with 196196196 qubits in only 606060 seconds. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians using imperfect single-qubit pulses for smaller system sizes and achieve a fidelity exceeding 99.9%99.9\%99.9%, which is orders of magnitude better than non-robust implementations.
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase of parameters in the system size and due to experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit π or π / 2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and by using robust composite pulses, we make our schemes robust against errors, including finite-pulse-time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian-engineering problem on a laptop for arbitrary two-local Hamiltonians on a two-dimensional square lattice with 196 qubits in only 60 s. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians with imperfect single-qubit pulses for smaller system sizes, and achieve a fidelity larger than 99.9%, which is orders of magnitude better than nonrobust implementations.
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase of parameters in the system size and due to experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit π or π/2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and by using robust composite pulses, we make our schemes robust against errors, including finite-pulse-time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian-engineering problem on a laptop for arbitrary two-local Hamiltonians on a two-dimensional square lattice with 196 qubits in only 60 s. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians with imperfect single-qubit pulses for smaller system sizes, and achieve a fidelity larger than 99.9%, which is orders of magnitude better than nonrobust implementations.