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Encoding universal computation in the ground states of Ising lattices
1Center for Quantum Technologies, National University of Singapore, Singapore.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study shows how Ising Hamiltonians can perform universal computation using ground states. This offers a new method for encoding computation in Ising lattices, simplifying demonstrations of NP-completeness.
Area of Science:
- Condensed Matter Physics
- Quantum Information Science
- Computational Complexity Theory
Background:
- Ising Hamiltonians are fundamental in statistical mechanics and condensed matter physics.
- Understanding ground states is crucial for predicting material properties and computational capabilities.
- Previous work explored emergent properties in infinite Ising lattices.
Purpose of the Study:
- To characterize ground states synthesizable by classical two-body Ising Hamiltonians.
- To demonstrate a novel method for encoding universal computation within these ground states.
- To provide a simpler proof for the NP-completeness of finding ground states in finite Ising spin glass models.
Main Methods:
- Characterization of ground states for two-body Ising Hamiltonians.
- Construction of simple, planar Ising blocks for simulating logic gates.
- Encoding of Boolean functions using Ising lattice ground states.
Main Results:
- Identified the set of ground states synthesizable by classical two-body Ising Hamiltonians.
- Developed Ising planar blocks capable of simulating universal logic gates.
- Established a new method for encoding universal computation in Ising ground states.
- Provided a simplified demonstration of the NP-completeness of the Ising spin glass ground state problem.
Conclusions:
- Classical two-body Ising Hamiltonians can encode universal computation through their ground states.
- This work offers a more accessible demonstration of the computational complexity of Ising spin glass models.
- The findings connect to previous research on emergent properties in infinite lattices.
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