Entangling problem Hamiltonian for adiabatic quantum computation

TL;DR

This paper introduces a novel approach to constructing problem Hamiltonians in adiabatic quantum computation that entangles excited states while keeping the ground state separable, potentially enhancing computational performance.

Contribution

It demonstrates how to design non-diagonal, entangling problem Hamiltonians that preserve the solution in the ground state, offering a new perspective for improving adiabatic quantum algorithms.

Findings

Entangling excited states can improve adiabatic quantum computation.

Constructed Hamiltonians maintain a product ground state.

Potential performance benefits in quantum algorithms.

Abstract

Adiabatic quantum computation starts from embedding a computational problem into a Hamiltonian whose ground state encodes the solution to the problem. This problem Hamiltonian, $H_{\rm p}$, is normally chosen to be diagonal in the computational basis, that is a product basis for qubits. We point out that $H_{\rm p}$ can be chosen to be non-diagonal in the computational basis. To be more precise, we show how to construct $H_{\rm p}$ in such a way that all its excited states are entangled with respect to the qubit tensor product structure, while the ground state is still of the product form and encodes the solution to the problem. We discuss how such entangling problem Hamiltonians can improve the performance of the adiabatic quantum computation.