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

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 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 interaction forms unreachable by standard rotations. 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 decomposition and off-resonant driving. The resulting engineered Hamiltonians could contribute to the understanding of many-body physics, and result in the creation of quantum simulators and the generation of highly entangled states, thereby opening avenues in quantum sensing and information processing.