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.

Gapped two-body Hamiltonian for continuous-variable quantum computation / L. Aolita, A.J. Roncaglia, A. Ferraro, A. Acin. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 106:9(2011), pp. 090501.1-090501.4. [10.1103/PhysRevLett.106.090501]

Gapped two-body Hamiltonian for continuous-variable quantum computation

A. Ferraro;
2011

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.
Settore FIS/03 - Fisica della Materia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/889654
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