General, efficient, and robust Hamiltonian engineering

TL;DR

This paper presents a fast, robust method for engineering local many-body Hamiltonians in quantum systems using optimized pulse sequences, demonstrated by high-fidelity simulations on large qubit lattices.

Contribution

It introduces an efficient linear programming approach combined with robust composite pulses for Hamiltonian engineering, improving speed and error resilience over previous methods.

Findings

Able to engineer Hamiltonians on 196 qubits in 60 seconds

Achieved >99.9% fidelity in Heisenberg from Ising Hamiltonians

Demonstrated robustness against pulse and control errors

Abstract

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 $\pi$ or $\pi/2$ 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.