Non-perturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins

TL;DR

This paper introduces an algebraic method to exactly convert k-body interactions into 2-body Hamiltonians using ancillary qubits, enabling embedding of problem instances into Ising spin systems without perturbation theory.

Contribution

The authors present a non-perturbative algebraic approach for converting k-body interactions into 2-body Hamiltonians with ancillary qubits, applicable when all terms share the same basis.

Findings

Exact k-body to 2-body interaction conversion demonstrated

Embedding problem instances into Ising ground states achieved

Method avoids perturbation theory and large spectral gaps

Abstract

An algebraic method has been developed which allows one to engineer several energy levels including the low-energy subspace of interacting spin systems. By introducing ancillary qubits, this approach allows k-body interactions to be captured exactly using 2-body Hamiltonians. Our method works when all terms in the Hamiltonian share the same basis and has no dependence on perturbation theory or the associated large spectral gap. Our methods allow problem instance solutions to be embedded into the ground energy state of Ising spin systems. Adiabatic evolution might then be used to place a computational system into it's ground state.