# Questions tagged [spin-glasses]

For questions related to spin glasses which are disordered materials that admit particularly simple mathematical models such as the Ising model with random couplings.

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### Does the D-Wave hardware show any advantage for academic use-cases, for example in condensed matter physics?

The D-Wave team put out a few papers (like this one and this one) in the last few years describing how their methods can find ground states of certain spin-glass Hamiltonians faster than classical ...
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### Mapping a generic 2-local spin graph to one with a maximum amount of neighbours

I remember having heard once that generic spin-graphs e.g. Ising, or at least 2-local ones, can always be mapped to one another one (which will typically be larger), where every spin has at most $n$ ...
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### How to show mathematically the equivalency between Ising Model and QUBO?

It is said that the Ising Model using spin variables $s ∈ \{−1, 1\}$ $$H(s)=\sum_{i}h_is_i+\sum_{i<j}J_{ij}s_is_j,$$ and a Quadratic Unconstrained Binary Optimization (QUBO) problem with binary ...
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### Are spin-glass problems NP (-complete)?

It is well known that finding ground states for spin-glass systems (Ising, XY...) is NP-hard (at least as hard as the hardest NP-problems) so that they can be efficiently used to solve other NP ...
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Let's say, that we have an optimization problem in the form: $$\min_x f(x) \\ g_i(x) \leq 0, i = 1, ..., m \\ h_j(x) = 0, j = 1, ..., p,$$ where $f(x)$ is an objective function, $g_i(x)$ are ...