Quantum objects

SeeMPS is built around tensor network representations of vectors and linear operators in exponentially large vector spaces. The core data structures are:

• MPS: Matrix Product States represent vectors using a chain of three-legged tensors. They can encode quantum states of composite systems or, more generally, any high-dimensional vector with subexponential memory when correlations are bounded.

• CanonicalMPS: A specialized MPS in canonical form, where tensors satisfy orthonormality conditions that simplify many operations and improve numerical stability.

• MPSSum: A lazy representation of weighted sums of MPS, useful for intermediate computations before simplification.

• MPO: Matrix Product Operators represent linear transformations using a chain of four-legged tensors. They can encode Hamiltonians, evolution operators, or any linear map between MPS.

These structures form the foundation for all algorithms in SeeMPS, from basic linear algebra operations to advanced eigensolvers and PDE integrators.

• Matrix-product states (MPS)
• Canonical form MPS (CanonicalMPS)
• MPS combination (MPSSum)
• Matrix-product operators (MPO, MPOList)
• Hamiltonians