Related papers: Quantum Gauged Neural Network: U(1) Gauge Theory
A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…
We consider a system of two-level quantum quasi-spins and gauge bosons put on a 3+1D lattice. As a model of neural network of the brain functions, these spins describe neurons quantum-mechanically, and the gauge bosons describes weights of…
We propose a new model of neural network. It consists of spin variables to describe the state of neurons as in the Hopfield model and new gauge variables to describe the state of synapses. The model possesses local gauge symmetry and…
Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave…
We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable Si = \pm1 on the i-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable Jij = \pm1…
Quantum link models are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. Quantum link models not only reproduce the standard features of Wilson's lattice gauge…
The phase transition of the two-dimensional $U(1)$ quantum link model on the triangular lattice is investigated by employing a supervised neural network (NN) consisting of only one input layer, one hidden layer of two neurons, and one…
In the present paper we shall study (2+1) dimensional Z_N gauge theories on a lattice. It is shown that the gauge theories have two phases, one is a Higgs phase and the other is a confinement phase. We investigate low-energy excitation…
At its core, Quantum Mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases. Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely…
Quantum machine learning with parametrised quantum circuits has attracted significant attention over the past years as an early application for the era of noisy quantum processors. However, the possibility of achieving concrete advantages…
It is shown that quantum nucleardynamics (QND) as an SU(2)_N \times U(1)_Z gauge theory, which is generated from quantum chromodynamics (QCD) as an SU(3)_C gauge theory through dynamical spontaneous symmetry breaking, successfully describes…
Quantum link models provide an extension of Wilson's lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson's parallel transporters,…
Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body…
Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last…
Lattice gauge theories (LGTs) form an intriguing class of theories highly relevant to both high-energy particle physics and low-energy condensed matter physics with the rapid development of engineered quantum devices providing new tools to…
We study the three-dimensional random Z(2) lattice gauge theory with Higgs field, which has the link Higgs coupling $c_1 SUS$ and the plaquette gauge coupling $c_2 UUUU$. The randomness is introduced by replacing $c_1 \to -c_1$ for each…
It is illustrated that quantum nucleardynamics (QND) as an SU(2)_N x U(1)_Z gauge theory, which is generated from quantum chromodynamics (QCD) as an SU(3)_C gauge theory through dynamical spontaneous symmetry breaking, successfully…
Lattice gauge theories are a fascinating and rich class of theories relating to the most fundamental models of particle physics, and as experimental control on the quantum level increases there is a growing interest in non-equilibrium…
Quantum computers promise improving machine learning. We investigated the performance of new quantum neural network designs. Quantum neural networks currently employed rely on a feature map to encode the input into a quantum state. This…
Artificial intelligence (AI) has drawn significant inspiration from neuroscience to develop artificial neural network (ANN) models. However, these models remain constrained by the Von Neumann architecture and struggle to capture the…