Quantum approximate optimization is computationally universal

TL;DR

This paper demonstrates that the quantum approximate optimization algorithm (QAOA) can be used to perform universal quantum computation by programming the durations of Hamiltonian applications, using simple Hamiltonians on a linear qubit array.

Contribution

It shows that QAOA's alternating Hamiltonian procedure can be adapted for universal quantum computation with simple, physically realizable Hamiltonians.

Findings

QAOA can implement universal quantum computation.

Simple Hamiltonians suffice for universal dynamics.

The approach broadens the applicability of QAOA in quantum computing.

Abstract

The quantum approximate optimization algorithm (QAOA) applies two Hamiltonians to a quantum system in alternation. The original goal of the algorithm was to drive the system close to the ground state of one of the Hamiltonians. This paper shows that the same alternating procedure can be used to perform universal quantum computation: the times for which the Hamiltonians are applied can be programmed to give a computationally universal dynamics. The Hamiltonians required can be as simple as homogeneous sums of single-qubit Pauli X's and two-local ZZ Hamiltonians on a one-dimensional line of qubits.