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SeeMPS 3.0.0 documentation

  • Getting started
  • Quantum objects
  • Index of algorithms
  • Quantum registers
  • Quantum-inspired numerical analysis
    • Reading and writing
    • Other tools
    • Contributing
    • Examples and Bibliography
    • API Reference
  • Getting started
  • Quantum objects
  • Index of algorithms
  • Quantum registers
  • Quantum-inspired numerical analysis
  • Reading and writing
  • Other tools
  • Contributing
  • Examples and Bibliography
  • API Reference

Section Navigation

  • Schmidt decomposition
  • Tensor splitting
    • Schmidt decomposition
    • Creating an MPS from a state vector
    • Canonical form
    • MPS update
  • Canonical form
  • Creating an MPS from a state vector
  • MPS update
  • MPS simplification
  • Gradient descent
  • Power method
  • Restarted Arnoldi iteration
  • Density-Matrix Renormalization Group
  • Conjugate gradient (CGS)
  • Biconjugate gradient stabilized (BiCGSTAB)
  • Generalized minimal residual (GMRES)
  • DMRG linear solver
  • Restarted Arnoldi iteration
  • Runge-Kutta methods
  • Implicit time evolution methods
  • Split-step HDAF method
  • TEBD Time evolution
  • Time-Dependent Variational Principle (TDVP)
  • Quantum Fourier Transform
  • Polynomial expansions
  • Tensor cross-interpolation (TCI)
  • Multiscale interpolative constructions
  • Sketching constructions
  • Computation-tree constructions
  • Index of algorithms
  • Tensor splitting

Tensor splitting#

One of the most basic algorithms for tensor network manipulation is to approximate a tensor with multiple legs, by a contraction of tensors with smaller numbers of legs. There are various criteria to do this, but in this section we will discuss thosed based on the Schmidt decomposition.

Contents:

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

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Schmidt decomposition

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Creating an MPS from a state vector

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