A matrix product state represents one-dimensional amplitudes as products of finite matrices. Its bond dimension bounds the Schmidt rank across a cut.
An MPS tensor is injective after blocking when products of its physical matrices span the full virtual matrix algebra.
An MPS parent Hamiltonian is a sum of local projectors onto the orthogonal complement of the tensor's local support. The MPS is a frustration-free ground state.
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A Matrix Product State (MPS) is a mathematical representation commonly used in quantum physics and quantum computing to describe quantum many-body systems. It provides an efficient way to represent and manipulate states of quantum systems that may have an exponentially large dimension in the standard basis. ### Description An MPS is expressed as a product of matrices, which allows for the encoding of quantum states in a way that maintains a manageable computational complexity.