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We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In particular, we construct translational invariant matrix product operators suitable for time evolution, and show how such descriptions are possible for Hamiltonians with long-range interactions. We illustrate how those tools can be exploited for constructing new algorithms for simulating quantum spin systems.
We provide an exact construction of interaction Hamiltonians on a one-dimensional lattice which grow as a polynomial multiplied by an exponential with the lattice site separation as a matrix product operator (MPO), a type of one-dimensional tensor ne
We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications in a purely matrix p
We define quantum phase in terms of inverses of annihilation and creation operators. We show that like Susskind - Glogower phase operators, the measured phase operators and the unitary phase operators can be defined in terms of the inverse operators.
We demonstrate that the optimal states in lossy quantum interferometry may be efficiently simulated using low rank matrix product states. We argue that this should be expected in all realistic quantum metrological protocols with uncorrelated noise an
A variational ansatz for momentum eigenstates of translation invariant quantum spin chains is formulated. The matrix product state ansatz works directly in the thermodynamic limit and allows for an efficient implementation (cubic scaling in the bond