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We investigate quantum algorithms derived from tensor networks to simulatethe static and dynamic properties of quantum many-body systems. Using asequentially prepared quantum circuit representation of a matrix product state(MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms toprepare ground and excited states on a quantum computer and apply them tomolecular nanomagnets (MNMs) as a paradigmatic example. In this setting, wedevelop two approaches for extracting the spectral correlation functionsmeasured in neutron scattering experiments: (a) a generalization of the SWAPtest for computing wavefunction overlaps and, (b) a generalization of thenotion of matrix product operators (MPOs) to the QTN setting which generates alinear combination of unitaries. The latter method is discussed in detail fortranslationally invariant spin-half systems, where it is shown to reduce thequbit resource requirements compared with the SWAP method, and may begeneralized to other systems. We demonstrate the versatility of our approachesby simulating spin-1/2 and spin-3/2 MNMs, with the latter being anexperimentally relevant model of a Cr$^{3+}_8$ ring. Our approach has qubitrequirements that are independent of the number of constituents of themany-body system and scale only logarithmically with the bond dimension of theMPS representation, making them appealing for implementation on near-termquantum hardware with mid-circuit measurement and reset.

Quantum tensor networks algorithms for evaluation of spectral functions on quantum computers