相关论文: Fermionic functionals without Grassmann numbers

We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…

Lattice field theory (LFT) is the standard non-perturbative method to perform numerical calculations of quantum field theory. However, the typical bottleneck of fermionic lattice calculations is the inversion of the Dirac matrix. This…

The partition functions of Hermitian one-matrix models are known to be tau-functions of the KP hierarchy. In this paper we explicitly compute the elements in Sato grassmannian these tau-functions correspond to, and use them to compute the…

The fermionic Gaussian operator basis provides a representation for treating strongly correlated fermion systems, as well as playing an important role in random matrix theory. We prove that a resolution of unity exists for any even…

We present a quantum algorithm to compute the logarithm of the determinant of the fermion matrix, assuming access to a classical lattice gauge field configuration. The algorithm uses the quantum eigenvalue transform, and quantum mean…

A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on…

For a quantum system of N identical, harmonically interacting particles in a one-dimensional harmonic trap we calculate for the bosonic and fermionic ground state the corresponding 1-particle reduced density operator $\rho_1$ analytically.…

Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic…

Fermionic formulae originate in the Bethe ansatz in solvable lattice models. They are specific expressions of some q-polynomials as sums of products of q-binomial coefficients. We consider the fermionic formulae associated with general…

Deriving the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially when improvement terms are present. This physically important task is, however, suitable for automation. We describe a flexible…

We review some aspects of the fermionic interpretation of the two-dimensional Ising model. The use is made of the notion of the integral over the anticommuting Grassmann variables. For simple and more complicated 2D Ising lattices, the…

We present a method to compute the Fermi function of the Hamiltonian for a system of independent fermions, based on an exact decomposition of the grand-canonical potential. This scheme does not rely on the localization of the orbitals and…

A recent paper by Jones-Smith and Mathur extends PT-symmetric quantum mechanics from bosonic systems (systems for which $T^2=1$) to fermionic systems (systems for which $T^2=-1$). The current paper shows how the formalism developed by…

We delve into the in-in formalism and derive general expressions for the computation of n-point functions for a self-interacting scalar field by means of a probability density functional (PDF). Even though in typical situations these…

We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…

We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian…

We investigate the dividing line between classical and quantum computational power in estimating properties of matrix functions. More precisely, we study the computational complexity of two primitive problems: given a function $f$ and a…

We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. Our work is inspired by a recent experimental demonstration of large-scale quantum registers, where…

In this paper, we present numerical schemes for evaluating the matrix elements of Gaussian/non-Gaussian operators in the Fock state basis, which are identified as multivariate Hermite polynomials (MHPs). Using the integral transformation…

We discuss the inclusion of fermionic loops contributions in Numerical Stochastic Perturbation Theory for Lattice Gauge Theories. We show how the algorithm implementation is in principle straightforward and report on the status of the…