Effective quantum memory Hamiltonian from local two-body interactions

Abstract

In [Phys. Rev. A 88, 062313 (2013)] we proposed and studied a model for a self-correcting quantum memory in which the energetic cost for introducing a defect in the memory grows without bounds as a function of system size. This positive behavior is due to attractive long-range interactions mediated by a bosonic field to which the memory is coupled. The crucial ingredients for the implementation of such a memory are the physical realization of the bosonic field as well as local five-body interactions between the stabilizer operators of the memory and the bosonic field. Here, we show that both of these ingredients appear in a low-energy effective theory of a Hamiltonian that involves only two-body interactions between neighboring spins. In particular, we consider the low-energy, long-wavelength excitations of an ordered Heisenberg ferromagnet (magnons) as a realization of the bosonic field. Furthermore, we present perturbative gadgets for generating the required five-spin operators. Our Hamiltonian involving only local two-body interactions is thus expected to exhibit self-correcting properties as long as the noise affecting it is in the regime where the effective low-energy description remains valid.

14 pages, 3 figures

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• A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)
• Can long-range interactions stabilize quantum memory at nonzero temperature?
• Symmetry protected self correcting quantum memory in three space dimensions
• Exponential Lifetime Improvement in Topological Quantum Memories
• Self-correction in Wegner's 3D Ising lattice gauge theory
• Stable quantum memories with limited measurement
• Monte Carlo studies of modified scalable designs for quantum computation