Related papers: Advantages in Choosing Real Generators for SU(N)
Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically…
We introduce generative adversarial models in which the discriminator is replaced by a calibrated (non-differentiable) classifier repeatedly enhanced by domain relevant features. The role of the classifier is to prove that the actual and…
In the presented note we aim at exploring the possibility of abandoning complex numbers in the representation of quantum states and operations. We demonstrate a simplified version of quantum mechanics in which the states are represented…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
We construct new invariants and give several theorems which determine in general (i) the number of physically meaningful phases in quark mass matrices and (ii) which elements of these matrices can be rendered real by rephasings. We…
We discuss the current state of the art of Quantum Random Number Generators (QRNG) and their possible applications in the search for quantum advantages. To this aim, we first discuss a possible way of benchmarking QRNG by applying them to…
A description of the quantum superalgebra U_q[sl(n+1|m)] via creation and annihilation generators (CAGs) is given. A statement that the Fock representations of the CAGs provide microscopic realizations of exclusion statistics is formulated.
The Glauber-Sudarshan P-representation is well-known within quantum optics, and is widely applied to problems involving photon statistics. Less familiar, perhaps, is its fermionic counterpart. We present a derivation of both the bosonic and…
A composite non-abelian model $SU(N) \times SU(N)$ is proposed as possible extension of the Yang-Mills symmetry. We obtain the corresponding gauge symmetry of the model and the most general lagrangian invariant by $SU(N) \times SU(N)$. The…
We discuss the group theory relevant to the ground-state baryons in large N_c QCD. For very large representation, the group generators become classical variables. We find the form of the classical generators for the completely symmetric N…
Quantum computers are expected to give major speed-ups for the simulation of quantum systems. In this work, we present quantum gates that simulate the colour part of the interactions of quarks and gluons in perturbative quantum…
The Kalman canonical form for quantum linear systems was derived in \cite{ZGPG18}. The purpose of this paper is to present an alternative derivation by means of a Gramian matrix approach. Controllability and observability Gramian matrices…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
We construct realistic equity option market simulators based on generative adversarial networks (GANs). We consider recurrent and temporal convolutional architectures, and assess the impact of state compression. Option market simulators are…
In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N)…
Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…
The choice of generator in the Similarity Renormalization Group (SRG) flow equation determines the evolution pattern of the Hamiltonian. The kinetic energy has been used in the generator for most prior applications to nuclear interactions,…
Conventional random number generators provide the speed but not necessarily the high quality output streams needed for large-scale stochastic simulations. Cryptographically-based generators, on the other hand, provide superior quality…
Hilbert space representations of quantum SU(2) by multiplication operators on a local chart are constructed, where the local chart is given by tensor products of square integrable functions on a quantum disc and on the classical unit…
The vector fields of the quantum Lie algebra are described for the quantum groups $GL_q(N), SL_q(N)$ and $SO_q(N)$ as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their…