General, efficient, and robust Hamiltonian engineering

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 $π$ 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 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 $196$ qubits in only $60$ 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 $99.9%$, which is orders of magnitude better than non-robust implementations.

💡 Research Summary

The fundamental challenge in quantum simulation and quantum information processing lies in the precise implementation of a target Hamiltonian to drive the desired time evolution of a quantum system. As quantum many-body systems scale, the complexity of controlling these systems grows exponentially due to the massive number of parameters and the presence of experimental imperfections, such as control errors and finite pulse durations. This paper presents a groundbreaking framework for “General, efficient, and robust Hamiltonian engineering” that addresses these challenges simultaneously.

The proposed method utilizes an “always-on” native system Hamiltonian, which is a common characteristic of many quantum hardware platforms. Instead of attempting to control every interaction individually, the scheme applies a sequence of single-qubit $\pi$ or $\pi/2$ pulses to manipulate the existing interactions. The core innovation lies in the use of Linear Programming (LP) to solve the optimization problem. By formulating the Hamiltonian engineering task as an LP problem, the researchers can minimize the total evolution time while achieving the target Hamiltonian. This approach demonstrates extraordinary computational efficiency; for instance, the authors successfully computed the optimal pulse sequences for a 2D square lattice containing 196 qubits on a standard laptop in just 60 seconds. This represents a significant leap in scalability, moving away from the exponential complexity typically associated with many-body control.

Furthermore, the paper introduces a robust layer to the engineering process. Leveraging Average Hamiltonian Theory (AHT) and the implementation of robust composite pulses, the scheme is designed to be resilient against various experimental errors, including finite pulse width effects and control inaccuracies. The effectiveness of this robust design is validated through numerical simulations. Specifically, when simulating the transformation from an Ising Hamiltonian to a Heisenberg Hamiltonian under imperfect pulse conditions, the proposed method achieved a fidelity exceeding 99.9%. This performance is orders of magnitude superior to conventional non-robust implementations. Ultimately, this work provides a scalable and highly accurate methodology for controlling complex quantum many-body systems, paving the way for more advanced quantum simulators and large-scale quantum computing architectures.