Index of algorithms

This section documents the algorithms implemented in SeeMPS, organized by category.

Tensor operations

Low-level operations for decomposing and manipulating tensors within MPS.

• Schmidt decomposition
• Tensor splitting
• Canonical form
• Creating an MPS from a state vector
• MPS update
• MPS simplification

Optimization and eigensolvers

Algorithms for finding ground states and solving eigenvalue problems.

• Gradient descent
• Power method
• Restarted Arnoldi iteration
• Density-Matrix Renormalization Group

Linear system solvers

Methods for solving systems of linear equations \(A \psi = b\).

• Conjugate gradient (CGS)
• Biconjugate gradient stabilized (BiCGSTAB)
• Generalized minimal residual (GMRES)
• DMRG linear solver

Time evolution and PDE operators

Methods for evolving MPS states under generic linear, time-dependent, or problem-specific operators.

• Restarted Arnoldi iteration
• Runge-Kutta methods
• Implicit time evolution methods
• Split-step HDAF method
• TEBD Time evolution
• Time-Dependent Variational Principle (TDVP)

Fourier transform

The Quantum Fourier Transform for MPS representations.

• Quantum Fourier Transform

Function approximation

Algorithms for constructing MPS representations of functions.

• Polynomial expansions
• Tensor cross-interpolation (TCI)
• Multiscale interpolative constructions
• Sketching constructions
• Computation-tree constructions