Gapped Two-Body Hamiltonian for continuous-variable quantum computation

TL;DR

This paper introduces a family of quadratic, short-range, frustration-free Hamiltonians with a constant energy gap, whose ground states are Gaussian graph states serving as universal resources for continuous-variable quantum computation.

Contribution

It presents a new class of gapped, two-body Hamiltonians for continuous-variable quantum computing, enabling adiabatic state preparation beyond optical methods.

Findings

Ground states are Gaussian graph states used for universal quantum computation.

Hamiltonians are quadratic, short-range, frustration-free, with a constant energy gap.

Correlation properties follow an area law, simplifying thermal state analysis.

Abstract

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv) possess a constant energy gap proportional to the squared inverse of the squeezing. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation in the limit of infinite squeezing. These Hamiltonians constitute the basic ingredient for the adiabatic preparation of graph states and thus open new venues for the physical realization of continuous-variable quantum computing beyond the standard optical approaches. We characterize the correlations in these systems at thermal equilibrium. In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law.