Gapped Two-Body Hamiltonian for continuous-variable quantum computation

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.

4 pages, one figure. New version: typos corrected, one reference added. To appear in PRL

References in corpus (10)

• Multi-party entanglement in graph states
• Observation of strong coupling between a micromechanical resonator and an optical cavity field
• Universal Quantum Computation with Continuous-Variable Cluster States
• Quantum Many-Body Phenomena in Coupled Cavity Arrays
• A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
• Thermal bound entanglement in macroscopic systems and area laws
• Open-system dynamics of graph-state entanglement
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• Optimal purification of thermal graph states

Cited by in corpus (2)

• Graphical calculus for Gaussian pure states
• Thermal States as Universal Resources for Quantum Computation with Always-on Interactions