# Hamiltonian engineering of general two-body spin-1/2 interactions

## TL;DR

This paper introduces a method for engineering general two-body spin-1/2 interactions using symmetry-based pulse sequences, enhancing quantum simulation and sensing capabilities.

## Contribution

It identifies all interchangeable interaction terms in a general two-body spin-1/2 Hamiltonian and derives novel pulse sequences based on icosahedral symmetry for optimal manipulation.

## Key findings

- Pulse sequences outperform Clifford rotations in creating Zeeman terms
- Linear programming determines exact pulses for desired interactions
- Proposed experimental approaches enable practical implementation

## Abstract

Spin Hamiltonian engineering in solid-state systems plays a key role in a variety of applications ranging from quantum information processing and quantum simulations to novel studies of many-body physics. By analyzing the irreducible form of a general two-body spin-1/2 Hamiltonian, we identify all interchangeable interaction terms using rotation pulses. Based on this identification, we derive novel pulse sequences, defined by an icosahedral symmetry group, providing the most general achievable manipulation of interaction terms. We demonstrate that, compared to conventional Clifford rotations, these sequences offer advantages for creating Zeeman terms essential for magnetic sensing, and could be utilized to generate new interaction forms. The exact series of pulses required to generate desired interaction terms can be determined from a linear programming algorithm. For realizing the sequences, we propose two experimental approaches, involving pulse product de-composition, and off-resonant driving. Resulting engineered Hamiltonians could contribute to the understanding of many-body physics, and result in the creation of novel quantum simulators and the generation of highly-entangled states, thereby opening avenues in quantum sensing and information processing.