Quantum fermions from classical bits

A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically on bit configurations. The genuinely probabilistic character of quantum physics is realized by probabilistic initial conditions. In turn, the probabilistic automaton is equivalent to the classical statistical system of a generalized Ising model. For a description of the probabilistic information at any given time quantum concepts as wave functions and non-commuting operators for observables emerge naturally. Quantum mechanics can be understood as a particular case of classical statistics. This offers prospects to realize aspects of quantum computing in the form of probabilistic classical computing. This article is part of the theme issue ‘Quantum technologies in particle physics’.

Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium Oxides

Cerium oxides (ceria) are materials that exhibit weak, room-temperature ferromagnetism without d-electrons. The latter are usually responsible for magnetism in a variety of other oxide compounds, but the underlying mechanism for such a magnetic response in ceria without the d-electrons (d0-magnetism) is still under debate. A possible explanation is Zener double-exchange, where itinerant electrons polarize the localized spins via Hund-coupling as they hop from site to site. Here, we report magnetization and spin-spin correlation results using various values of the Hund-coupling in a one-orbital double-exchange model with Ising spins. In the real material with formula CeO2−x, the oxygen-deficient sites are denoted by x. These sites are related to the density of tetravalent cerium spins (the Ising spin background in our model), which we denoted as and set at N=0.50 in our simulations. Our results at this value of localized spin concentration show ferromagnetic tendencies at low carrier densities (n=0.25). However, ferromagnetism is lost at intermediate carrier concentrations (n=0.50) due to charge localization at high temperatures, as evident from density of states calculations and Monte Carlo snapshots. To our knowledge, our study based on a realistic Zener-type double exchange mechanism is a first in the study of magnetism in cerium oxides. Our results are also consistent with previous studies using similar Hamiltonians in the context of diluted magnetic semiconductors, where Heisenberg spins were used.

Neural Network for Prediction of Curie Temperature of Two-Dimensional Ising Model

The authors describe a method for determining the critical point of a second-order phase transitions using a convolutional neural network based on the Ising model on a square lattice. Data for training were obtained using Metropolis algorithm for different temperatures. The neural network was trained on the data corresponding to the low-temperature phase, that is a ferromagnetic one and high-temperature phase, that is a paramagnetic one, respectively. After training, the neural network analyzed input data from the entire temperature range: from 0.1 to 5.0 (in dimensionless units) and determined (the Curie temperature T_c). The accuracy of the obtained results was estimated relative to the Onsager solution for a flat lattice of Ising spins.

(Four) Dual Plaquette 3D Ising Models

A characteristic feature of the 3 d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3 d plaquette Ising and the X-Cube model is similar to that between the 2 d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2 d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3 d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3 d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin–Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.

Machine-Learning Quantum States in the NISQ Era

We review the development of generative modeling techniques in machine learning for the purpose of reconstructing real, noisy, many-qubit quantum states. Motivated by its interpretability and utility, we discuss in detail the theory of the restricted Boltzmann machine. We demonstrate its practical use for state reconstruction, starting from a classical thermal distribution of Ising spins, then moving systematically through increasingly complex pure and mixed quantum states. We review recent techniques in reconstruction of a cold atom wavefunction, intended for use on experimental noisy intermediate-scale quantum (NISQ) devices. Finally, we discuss the outlook for future experimental state reconstruction using machine learning in the NISQ era and beyond.