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.
3
questions
2
votes
1answer
65 views
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 ...
11
votes
3answers
2k views
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 ...
10
votes
1answer
497 views
Is there a general method of expressing optimization problem as a Hamiltonian?
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 ...
