Universal quantum dynamics from two 2-local Hamiltonians

TL;DR

This paper demonstrates that switching between two specific 2-local Hamiltonians, one involving nearest-neighbor interactions and the other single-qubit interactions, can generate universal quantum dynamics on n qubits, though the scheme is currently inefficient.

Contribution

It shows that two simple 2-local Hamiltonians are sufficient for universal quantum control, highlighting a new approach to quantum universality.

Findings

Universal dynamics achieved by switching between two 2-local Hamiltonians.

Construction of a scheme for arbitrary quantum gate generation.

Open problem: improving efficiency of the switching scheme.

Abstract

In this paper, we show that the ability to switch globally between two 2-local Hamiltonians on n qubits is sufficient for achieving universal unitary dynamics on those n qubits. Of the two Hamiltonians used in the construction, one is comprised of nearest-neighbour two-qubit interactions on a one-dimensional chain, the other is comprised of single-qubit interactions. We describe a scheme for choosing the switching times in order to generate arbitrary one- and two-qubit gates on the n qubits. However the switching scheme is inefficient, and we leave as an open problem the question of whether the universality of the Hamiltonians can be exploited in an efficient way.