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  • Open Access

General, Efficient, and Robust Hamiltonian Engineering

P. Baßler1,2,*, M. Heinrich1,3,†, and M. Kliesch2,‡

  • *Contact author: bassler@hhu.de
  • †Contact author: markus.heinrich@uni-koeln.de
  • ‡Contact author: martin.kliesch@tuhh.de
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PRX Quantum 6, 040346 – Published 26 November, 2025

DOI: https://doi.org/10.1103/9yxv-tdqr

Abstract

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.

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Popular Summary

A central challenge in quantum science is the precise control of quantum dynamics. Every quantum device comes with its own built-in interactions its “native Hamiltonian”—but scientists often need to change these interactions to mimic entirely different physical systems or to perform complex computations. Doing this accurately and efficiently, especially on large and noisy quantum devices, is notoriously difficult.

In this work, we introduce a general and practical framework that allows researchers to reprogram the natural interacting dynamics of a given quantum system using only simple, local operations. Our method applies carefully chosen sequences of single-qubit pulses to redirect the evolution of the system toward a desired Hamiltonian. We cast this task as a linear-optimization problem that can be solved quickly, even for systems with hundreds of qubits. The result is an engineered quantum evolution that is fast, precise, and tolerant to experimental imperfections such as control errors or finite-duration pulses.

Because our approach works efficiently for essentially any type of local interactions, it unifies and extends many existing Hamiltonian-engineering techniques. It turns the challenge of designing pulse sequences into a straightforward, programmable task. This capability could enable faster and more reliable quantum simulations, help realize complex models in quantum chemistry, and enhance gate-based computation on near-term devices. Looking ahead, we envision this framework as a cornerstone for flexible, digital-analog quantum platforms that can be “reprogrammed” on demand to explore new realms of quantum dynamics.

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PRX Quantum 6, 040346– Published 26 November, 2025
  • Received 2 May 2025
  • Accepted 15 October 2025
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