All-optical coherent network computer for simulating spin glass systems

Boris E. Vugmeister, HERSCHEL A. RABITZ

L. A. Fernández, Víctor Martín-Mayor

The statics-dynamics correspondence in spin glasses relate nonequilibrium results on large samples (the experimental realm) with equilibrium quantities computed on small systems (the typical arena for theoretical computations). Here we employ statics-dynamics equivalence to study the Ising spin-glass critical behavior in three dimensions. By means of Monte Carlo simulation, we follow the growth of the coherence length (the size of the glassy domains), on lattices too large to be thermalized. Thanks to the large coherence lengths we reach, we are able to obtain accurate results in excellent agreement with the best available equilibrium computations. To do so, we need to clarify the several physical meanings of the dynamic exponent close to the critical temperature.

Kendall Preston

L. A. Fernández, Víctor Martín-Mayor

The statics-dynamics correspondence in spin glasses relate non-equilibrium results on large samples (the experimental realm) with equilibrium quantities computed on small systems (the typical arena for theoretical computations). Here we employ statics-dynamics equivalence to study the Ising spin-glass critical behavior in three dimensions. By means of Monte Carlo simulation, we follow the growth of the coherence length (the size of the glassy domains), on lattices too large to be thermalized. Thanks to the large coherence lengths we reach, we are able to obtain accurate results in excellent agreement with the best available equilibrium computations. To do so, we need to clarify the several physical meanings of the dynamic exponent close to the critical temperature.

Anonymous

Richard Barney

Spin glasses are, in essence, simply systems of magnetic moments with disordered interactions. Despite this basic premise, spin glasses have become relevant in a wide variety of fields, including condensed matter physics, complexity and optimization theory, error correction, quantum computing, machine learning, and even neuroscience. The pervasiveness of spin glasses stems from the fact that they are paradigmatic examples of how global complexity emerges from disordered interactions between a large number of basic constituents. The inclusion of quantum effects in spin glasses creates an even richer picture, due to the interplay between the energy barriers arising from disorder and quantum fluctuations which allow for tunneling. This thesis initially focuses on quantum glasses and how their initial states explore their Hilbert spaces. Two complementary approaches are used. One is comparison of the spectral statistics, particularly the spectral form factor, with the spectral statistics of random matrix ensembles, a hallmark of quantum chaotic behavior. The other approach uses the Thouless-Anderson-Palmer mean-field equations to determine the number of local minima which appear in the free energy landscape. This thesis then applies methods from spin glass theory to the field of machine learning. Neural networks, like spin glasses, are systems in which remarkable behavior emerges from interactions between basic constituents. By studying the phase diagrams of spin models analogous to snapshots of neural networks throughout their training process, insight is gained into the mechanisms of learning. Finally, this thesis investigates how quantum effects can lead to advantages in machine learning. It is shown, through classical simulation and experiments on both trapped-ion and superconducting quantum computing hardware, that a natural quantization of a classical neural network can demonstrate superior generalization performance due to the injection of quantum uncertainty.