We describe a many-body quantum system that can be made to quantum compute by the adiabatic application of a large applied field to the system. Prior to the application of the field, quantumâ€¦ (More)

A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite stateâ€¦ (More)

A new type of diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product states and complex weighted finite state automata. It is thenâ€¦ (More)

There is a fundamental difficulty in generalizing weighted automata to the case of infinite words: in general the infinite sum-of-products from which the weight of a given word is derived willâ€¦ (More)