Information storage capacity of discrete spin systems

Details Information storage capacity of discrete spin systems Information storage capacity of discrete spin systems

2011-11-14

arxiv.org/abs/1111.3275v2

Computer Science

Information Theory

30 pages, 15 figures

Scientific paper

What is the limit of information storage capacity of discrete spin systems? To answer this question, we study classical error-correcting codes which can be physically realized as the energy ground space of gapped local Hamiltonians. For discrete spin systems on a D-dimensional lattice governed by local frustration-free Hamiltonians, the following bound is known to hold; $kd^{1/D}\leq O(n)$ where k is the number of encodable logical bits, d is the code distance, and n is the total number of spins in the system. Yet, previously found codes were far below this bound and it remained open whether there exists an error-correcting code which saturates the bound or not. Here, we give a construction of local spin systems which saturate the bound asymptotically with $k \sim O(L^{D-1})$ and $d \sim O(L^{D-\epsilon})$ for an arbitrary small $\epsilon> 0$ where L is the linear length of the system. Our model borrows an idea from a fractal geometry arising in Sierpinski triangle.

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