Welcome to SeeMPS’s documentation!#
SeeMPS is a Python library dedicated to implementing tensor network algorithms based on the Matrix Product States (MPS) and Quantized Tensor Train (QTT) formalisms. SeeMPS is implemented as a complete finite-precision linear algebra package where exponentially large vector spaces are compressed using the MPS/TT formalism, enabling both low-level operations—such as vector (MPS) addition, linear transformations and Hadamard products—as well as high-level algorithms—approximation of linear equations, eigenvalue and eigenstate computations, and exponentially efficient Fourier transforms.
This library can be used for traditional quantum many-body physics applications and also for quantum-inspired numerical analysis problems, such as solving PDEs, interpolating and integrating multidimensional functions, sampling multivariate probability distributions, etc.
Features#
MPS-BLAS: Low-level linear algebra operations
Vector representation using MPS/TT with controlled truncation
Matrix representation using MPO
Vector addition, scaling, inner products
Matrix-vector products and Hadamard (element-wise) products
Tensor products and simplification algorithms
MPS-LAPACK: High-level linear algebra algorithms
Eigenvalue search: Power method, Arnoldi, DMRG
Linear system solvers: CGS, BiCGS, GMRES, DMRG
Quantum Fourier Transform as MPO
Functional analysis: Quantum-inspired numerical methods
Function loading: direct constructions, polynomial expansions, tensor cross-interpolation (TCI)
Differentiation: finite differences, Fourier differentiation, HDAF
Integration: Newton-Cotes, Clenshaw-Curtis quadratures
Interpolation: finite differences, Fourier methods
PDE solvers for eigenvalue and source problems
Time evolution: explicit Runge-Kutta, implicit Crank-Nicolson/Radau, TDVP
Quantum many-body physics and computing
Hamiltonian construction using interaction graphs
Ground state search with DMRG
Time evolution with TEBD
Parameterized quantum circuits