Related papers: Graphical Calculus for Fermionic Tensors
In this work we present a method for generating a fermionic encoding tailored to a set of target fermionic operators and to a target hardware connectivity. Our method uses brute force search, over the space of all encodings which map from…
The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces, to transport through nanojunctions, and offer a prime target for quantum computing applications. Here we…
We present a unified fermionic approach to compute the tau-functions and the n-point functions of integrable hierarchies related to some infinite-dimensional Lie algebras and their representations.
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…
In recent years, the variational Monte Carlo (VMC) calculations of projected entangled pair states (PEPS) has emerged as a competitive method for computing the ground states of many-body quantum systems. This method is particularly…
This paper is an introduction to the language of Feynman Diagrams. We use Reshetikhin-Turaev graphical calculus to define Feynman diagrams and prove that asymptotic expansions of Gaussian integrals can be written as a sum over a suitable…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
Partition- and moment functions for a general (not necessarily Gaussian) functional measure that is perturbed by a Gibbs factor are calculated using generalized Feynman graphs. From the graphical calculus, a new notion of Wick ordering…
We propose a method of simulating efficiently many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily distant couplings. We map products of…
We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…
Efficient encoding of electronic operators into qubits is essential for quantum chemistry simulations. The majority of methods map single electron states to qubits, effectively handling electron interactions. Alternatively, pairs of…
Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the…
The many-body Hamiltonians and other fermionic physical observables are expressed in terms of fermionic creation and annihilation operators, which form the algebra of canonical anti-commutation relations (CAR). In this work we use a…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
Continuous-time determinantal algorithm is proposed for the quantum Monte Carlo simulation of the interacting fermions. The scheme does not invoke Hubbard-Stratonovich transformation. The fermionic action is divided into two parts. One of…
We relaxe the constraint on the domains of combinatorial HHS machinery so combinatorial HHS machinery works for most cubical curve graphs. As an application we extend the factor system machinery of the CAT(0) cube complex to the…
We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large $N$ limit this system describes a $c=1/2$ chiral fermion in $1+1$ dimensions. The Gauss' law constraint implies that to obtain a physical state,…
Fermion-to-qubit mappings are used to represent fermionic modes on quantum computers, an essential first step in many quantum algorithms for electronic structure calculations. In this work, we present a formalism to design flexible…
It is commonly believed that in quantum Monte Carlo approaches to fermionic many- body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point…
The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limited to k-ary representations of length L and arithmetic modulo k^{L}. An abstract representation on an L fold tensor…