Related papers: Efficient conversion from fermionic Gaussian state…
It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I…
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…
Entanglement between the constituents of a quantum system is an essential resource in the implementation of many quantum processes and algorithms. Indeed, universal quantum computation is possible by measuring individual qubits comprising…
Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most…
Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network…
Density matrix renormalization group (DMRG) or matrix product states (MPS) is the most effective and accurate method for studying one-dimensional quantum many-body systems. However, the application of DMRG to two-dimensional systems is not…
Quadratic programming over orthogonal matrices encompasses a broad class of hard optimization problems that do not have an efficient quantum representation. Such problems are instances of the little noncommutative Grothendieck problem…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
We propose a universal transformation from a many-boson state to a corresponding many-fermion state in the lowest Landau level approximation of rotating many-body systems, inspired by the Laughlin wave function and by the Jain…
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…
We study the capacity of entanglement as an alternative to entanglement entropies in estimating the degree of entanglement of quantum bipartite systems over fermionic Gaussian states. In particular, we derive the exact and asymptotic…
Since Fermions are based on anti-commutation relations, their entanglement can not be studied in the usual way, such that the available theory has to be modified appropriately. Recent publications consider in particular the structure of…
We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors…
We introduce TeMFpy, a Python library for converting fermionic mean-field states to finite or infinite matrix product state (MPS) form. TeMFpy includes new, efficient, and easy-to-understand algorithms for both Slater determinants and…
We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this…
Fermions, as a major class of quantum particles, provide platforms for quantum information processing beyond the possibilities of spins or bosons which have been studied more extensively. One particularly interesting model to study, in view…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then…
For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can…
Tensor network quantum states are powerful tools for strongly correlated systems, tailored to capture local correlations such as in ground states with entanglement area laws. When applying tensor network states to interacting fermionic…