API reference

Generated from the docstrings of the package. The package exports the main classes at the top level (from torch_vn_algebra import TypeIAlgebra, SpinChain, SU2Chain, ...); the modules are:

module	contents
torch_vn_algebra.algebra	Type I von Neumann algebra M = ⊕_{c=1}^{C} M_{n_c}(ℂ) with subspace dimensions k_c.
torch_vn_algebra.functional	Functional calculus on stacks of blocks (n, k, k), at four levels of generality.
torch_vn_algebra.hilbert_space	Hilbert space H of dimension n with a distinguished k-dimensional subspace H0.
torch_vn_algebra.states	States (density matrices) on M = (+)_c M_{k_c} and information-theoretic quantities.
torch_vn_algebra.channels	Quantum channels on a Type I algebra M = (+)_c M_{k_c} that preserve the sectors.
torch_vn_algebra.composite	Tensor products of Type I algebras.
torch_vn_algebra.dynamics	Time evolution on M = (+)_c M_{k_c} for Hamiltonians and Lindblad generators in M.
torch_vn_algebra.chains	Spin-1/2 chains with a conserved number of up spins (U(1) symmetry, total S^z).
torch_vn_algebra.krylov	Krylov-subspace methods for large sectors, where dense matrices no longer fit.
torch_vn_algebra.su2	SU(2) symmetry of spin-1/2 chains: spin multiplets, highest-weight vectors and the Wigner-Eckart theorem.
torch_vn_algebra.decompose	From symmetries or generators to the algebra: numerical Wedderburn decomposition.
torch_vn_algebra.inclusions	Unital inclusions of finite-dimensional von Neumann algebras, conditional expectations and index.
torch_vn_algebra.divergences	Quantum Renyi divergences, Petz recovery maps and noncommutative L^p norms on M = (+)_c M_{k_c}.
torch_vn_algebra.jordan	Jordan structure of finite-dimensional von Neumann algebras: Jordan products, the quadratic representation, Jordan subalgebras of Hermitian matrices and spin factors.
torch_vn_algebra.optimize	Batched gradient-based optimisation over operators of a Type I algebra.
torch_vn_algebra.cost	Safeguards against unexpectedly long or memory-hungry computations.

The tutorial shows every module at work, with tested code.