Tensor network
A representation of a high-rank tensor as a contracted network of lower-rank tensors, whose graph structure encodes which degrees of freedom are directly correlated.
Concept record →Concept library
16 concept records. Each states what the term means, why it matters, and — where it applies — what the term is routinely taken to establish but does not.
Matrix product state (MPS)
A one-dimensional chain of tensors in which each physical site carries one tensor joined to its neighbours by virtual bonds.
Concept record →Bond dimension (D)
The rank retained on each virtual index of a tensor network, bounding the entanglement the state can carry across a cut at log(D).
Concept record →SVD truncation and discarded weight
Reducing a bond to the D largest singular values, discarding the remaining tail of the Schmidt spectrum.
Concept record →Area law
A scaling property in which the entanglement entropy of a region grows with the size of its boundary rather than its volume.
Concept record →DMRG
A variational sweep algorithm that optimizes a state site by site, later understood as optimization over the MPS manifold.
Concept record →PEPS
A projected entangled pair state: the generalization of MPS to two and higher dimensions, with tensors arranged on a lattice.
Concept record →MERA
A multiscale entanglement renormalization ansatz: a layered network alternating disentanglers and isometries, coarse-graining a system scale by scale.
Concept record →Disentangler
A unitary applied across block boundaries before coarse-graining, removing short-range entanglement that the isometry would otherwise have to carry to the next layer.
Concept record →Scale invariance
Reusing the same disentangler and isometry at every layer, giving a renormalization-group transformation with no preferred length scale.
Concept record →AdS/MERA correspondence (conjecture)
The proposal that the layered geometry of a MERA network is a discretization of a holographic bulk spacetime, with the extra network direction playing the role of a radial bulk coordinate.
Concept record →QUBO and Ising models
Quadratic unconstrained binary optimization, and its equivalent spin form in which binary variables become ±1 spins with couplings and local fields.
Concept record →Penalty term
A term added to an objective so that violating a hard constraint costs more than any feasible improvement, converting a constrained problem into an unconstrained one.
Concept record →Contraction complexity
The cost of evaluating a tensor network, governed by the contraction order chosen and by structural properties of the network graph such as its treewidth.
Concept record →Quantum-inspired optimization
Classical algorithms — tensor-network contraction among them — that borrow structure from quantum many-body methods and run on conventional hardware.
Concept record →QAOA
The quantum approximate optimization algorithm: a variational circuit alternating problem and mixing Hamiltonians, with classical outer-loop parameter optimization.
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