# Efficient Hamiltonian engineering

**Authors:** Pascal Baßler, Markus Heinrich, Martin Kliesch  
**arXiv:** [2410.19903](https://arxiv.org/abs/2410.19903)  
**Date:** 2024-10-25  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2410.19903v1/

## Key points

- Authors: Pascal Baßler, Markus Heinrich, and Martin Kliesch
- Proposed scheme for engineering arbitrary many-body Hamiltonians
- Combines fixed system Hamiltonian evolution with single-qubit Pauli or Clifford gates
- Creation of target Hamiltonians limited by locality of Pauli terms in system Hamiltonian
- Efficient relaxation of linear program with polynomial classical runtime scaling with qubits number
- Method enables engineering of Hamiltonians even with partial knowledge of system's properties and eliminates unwanted Pauli terms
- Demonstrated classical efficiency in engineering an arbitrary two-body Hamiltonian on a 2D square lattice using 225 qubits in 60 seconds
- Application to model an ion trap device with Ising Hamiltonian and engineer a general Heisenberg Hamiltonian shown through numerical simulations
- Addresses key error sources in practical implementations, highlighting robustness and applicability in quantum computing research

## Summary

In their paper titled "Efficient Hamiltonian Engineering," authors Pascal Baßler, Markus Heinrich, and Martin Kliesch propose a groundbreaking scheme for engineering arbitrary many-body Hamiltonians. Their innovative approach combines the evolution of a fixed system Hamiltonian with layers of single-qubit Pauli or Clifford gates. This allows for the creation of target Hamiltonians limited only by the locality of the Pauli terms in the system Hamiltonian. The authors further develop an efficient relaxation of this linear program with a classical runtime that scales polynomially with the number of qubits, making it practical for real-world applications. Notably, their method enables the engineering of Hamiltonians even with partial knowledge of the system's properties and offers a means to eliminate unwanted Pauli terms. Demonstrating its effectiveness, the authors showcase its classical efficiency by successfully engineering an arbitrary two-body Hamiltonian on a 2D square lattice using 225 qubits in just 60 seconds. Additionally, they provide numerical simulations illustrating its application to model an ion trap device with an Ising Hamiltonian and engineer a general Heisenberg Hamiltonian. Moreover, the paper addresses key error sources in practical implementations and highlights its robustness and applicability in quantum computing research. Overall, this work presents a significant advancement in efficient Hamiltonian engineering that holds promise for various quantum computing applications.