Related papers: Fermion determinants on a quantum computer
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
A quantum algorithm for computing the determinant of a unitary matrix $U\in U(N)$ is given. The algorithm requires no preparation of eigenstates of $U$ and estimates the phase of the determinant to $t$ binary digits accuracy with…
Some algorithms for the numerically exact treatment of fermion determinants are summarised. This is not supposed to be a review, rather a concise handbook. The audience is expected to have a basic understanding of how to put fermions on a…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
The fermion determinant is a highly non-local object and its logarithm is an extensive quantity. For these reasons it is widely believed that the determinant cannot be treated in acceptance steps of gauge link configurations that differ in…
Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and…
A formula expressing the fermionic determinant (a large order polynomial) as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and…
An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a…
We show in detail how the Jordan-Wigner transformation can be used to simulate any fermionic many-body Hamiltonian on a quantum computer. We develop an algorithm based on appropriate qubit gates that takes a general fermionic Hamiltonian,…
Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubit-based quantum computers can potentially tackle this…
The non-local dependence of the fermion determinant on the gauge field limits our ability of simulating Quantum Chromodynamics on the lattice. Here we present a factorization of the gauge field dependence of the fermion determinant based on…
A formula expressing the fermionic determinant as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and are indexed by loops of…
We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and…
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic…
We define a model of quantum computation with local fermionic modes (LFMs) -- sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of $m$ LFMs and the Hilbert space of $m$ qubits,…
Given a nonsingular $n \times n$ matrix of univariate polynomials over a field $\mathbb{K}$, we give fast and deterministic algorithms to compute its determinant and its Hermite normal form. Our algorithms use…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
The matrix logarithm is one of the important matrix functions. Recently, a quantum algorithm that computes the state $|f\rangle$ corresponding to matrix-vector product $f(A)b$ is proposed in [Takahira, et al. Quantum algorithm for matrix…
In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum…