Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor networks
Quantum algorithms reformulate computational problems as quantum evolutions in a large
Hilbert space. Most quantum algorithms assume that the time evolution is perfectly unitary …
Hilbert space. Most quantum algorithms assume that the time evolution is perfectly unitary …
Learning tensor networks with tensor cross interpolation: new algorithms and libraries
The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing
low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns …
low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns …
Tensor networks enable the calculation of turbulence probability distributions
Predicting the dynamics of turbulent fluids has been an elusive goal for centuries. Even with
modern computers, anything beyond the simplest turbulent flows is too chaotic and …
modern computers, anything beyond the simplest turbulent flows is too chaotic and …
Real-frequency quantum field theory applied to the single-impurity Anderson model
A major challenge in the field of correlated electrons is the computation of dynamical
correlation functions. For comparisons with experiment, one is interested in their real …
correlation functions. For comparisons with experiment, one is interested in their real …
[HTML][HTML] Efficient MPS representations and quantum circuits from the Fourier modes of classical image data
Abstract Machine learning tasks are an exciting application for quantum computers, as it has
been proven that they can learn certain problems more efficiently than classical ones …
been proven that they can learn certain problems more efficiently than classical ones …
Cross-extrapolation reconstruction of low-rank functions and application to quantum many-body observables in the strong coupling regime
We present a general-purpose algorithm to extrapolate a low-rank function of two variables
from a small domain to a larger one. It is based on the cross-interpolation formula. We apply …
from a small domain to a larger one. It is based on the cross-interpolation formula. We apply …
Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
Two-particle response functions are a centerpiece of both experimental and theoretical
quantum many-body physics. Yet, due to their size and discontinuity structure, they are …
quantum many-body physics. Yet, due to their size and discontinuity structure, they are …
Strong coupling impurity solver based on quantics tensor cross interpolation
AJ Kim, P Werner - arxiv preprint arxiv:2411.19026, 2024 - arxiv.org
Numerical methods capable of handling nonequilibrium impurity models are essential for
the study of transport problems and the solution of the nonequilibrium dynamical mean field …
the study of transport problems and the solution of the nonequilibrium dynamical mean field …
Compactness of quantics tensor train representations of local imaginary-time propagators
Abstract Space-time dependence of imaginary-time propagators, vital for ab initio and many-
body calculations based on quantum field theories, has been revealed to be compressible …
body calculations based on quantum field theories, has been revealed to be compressible …
Two-particle calculations with quantics tensor trains--solving the parquet equations
We present the first application of quantics tensor trains (QTTs) and tensor cross
interpolation (TCI) to the solution of a full set of self-consistent equations for multivariate …
interpolation (TCI) to the solution of a full set of self-consistent equations for multivariate …