Related papers: Towards a better understanding of the matrix produ…
Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-$\frac{1}{2}$ systems. Here, we instead consider…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
Tensor networks have historically proven to be of great utility in providing compressed representations of wave functions that can be used for calculation of eigenstates. Recently, it has been shown that a variety of these networks can be…
We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on…
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…
Quantum state tomography is a key technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. In this work, we propose an algorithm which iteratively finds the best…
In the path integral formulation of the evolution of an open quantum system coupled to a Gaussian, non-interacting environment, the dynamical contribution of the latter is encoded in an object called the influence functional. Here, we…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
We consider the class of non-Hermitian operators represented by infinite tridiagonal matrices, selfadjoint in an indefinite inner product space with one negative square. We approximate them with their finite truncations. Both infinite and…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
We perform a Nf = 2 + 1 lattice QCD simulation to determine the quark spin fractions of hadrons using the Feynman-Hellmann theorem. By introducing an external spin operator to the fermion action, the matrix elements relevant for quark spin…
A mathematical proposition with a trainable pair, operator and quantum circuit, are introduced to approximate functions expressed as cubic Taylor polynomials, numerical simulations illustrate three cases.
The theory of low-rank tensor-train approximation is well understood when the approximation error is measured in the Frobenius norm. The entrywise maximum norm is equally important but is significantly weaker for large tensors, making the…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…
Gradient-based algorithms are one of the methods of choice for the optimisation of Markov Decision Processes. In this article we will present a novel approximate Newton algorithm for the optimisation of such models. The algorithm has…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…