Related papers: Graphical Calculus for Fermionic Tensors
The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing…
We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving…
We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that…
Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The…
We introduce an exactly solvable model of interacting Majorana fermions realizing $Z_{2}$ topological order with a $Z_{2}$ fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete…
We present an iterative algorithm to count Feynman diagrams via many-body relations. The algorithm allows us to count the number of diagrams of the exact solution for the general fermionic many-body problem at each order in the interaction.…
Tensor field theory (TFT) focuses on quantum field theory aspects of random tensor models, a quantum-gravity-motivated generalisation of random matrix models. The TFT correlation functions have been shown to be classified by graphs that…
We define and compute many-body topological invariants of interacting fermionic symmetry-protected topological phases, protected by an orientation-reversing symmetry, such as time-reversal or reflection symmetry. The topological invariants…
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…
Many-body fermionic quantum calculations performed on analog quantum computers are restricted by the presence of k-local terms, which represent interactions among more than two qubits. These originate from the fermion-to-qubit mapping…
This work explores displaced fermionic Gaussian operators with nonzero linear terms. We first demonstrate equivalence between several characterizations of displaced Gaussian states. We also provide an efficient classical simulation protocol…
We continue the discussion of the fermion models on graphs that started in the first paper of the series. Here we introduce a Graphical Gauge Model (GGM) and show that : (a) it can be stated as an average/sum of a determinant defined on the…
The mathematical methods that have been used to analyze the statistical properties of boson fields, and in particular the coherence of photons in quantum optics, have their counterparts for Fermi fields. The coherent states, the…
We introduce the Spin-ZX calculus as an elevation of Penrose's diagrams and associated binor calculus to the level of a formal diagrammatic language. The power of doing so is illustrated by the variety of scientific areas we apply it to:…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further understanding of essential features in such systems. Quantum Monte Carlo…
We present a fermionic description of non-equilibrium multi-level systems. Our approach uses the Keldysh path integral formalism and allows us to take into account periodic drives, as well as dissipative channels. The technique is based on…
Precise understanding of strongly interacting fermions, from electrons in modern materials to nuclear matter, presents a major goal in modern physics. However, the theoretical description of interacting Fermi systems is usually plagued by…
Thermal properties of quantum fields at finite temperature are crucial to understanding strongly interacting matter and recent development in quantum computing has provided an alternative and promising avenue of study. In this work, we…
We compare the structures and methods in the theory of causal fermion systems with approaches to fundamental physics based on division algebras, in particular the octonions. We find that octonions and, more generally, tensor products of…