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

TL;DR

This paper introduces quantum tensor network algorithms for simulating spectral functions of quantum many-body systems on quantum computers, demonstrating efficient state preparation and spectral function extraction methods applicable to molecular nanomagnets.

Contribution

It develops novel quantum algorithms based on tensor networks for preparing states and extracting spectral functions, reducing resource requirements and applicable to near-term quantum hardware.

Findings

Algorithms successfully simulate spin-1/2 and spin-3/2 molecular nanomagnets.

Qubit requirements are independent of system size and scale logarithmically with bond dimension.

The methods are suitable for implementation on near-term quantum hardware.

Abstract

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example. In this setting, we develop two approaches for extracting the spectral correlation functions measured in neutron scattering experiments: (a) a generalization of the SWAP test for computing wavefunction overlaps and, (b) a generalization of the notion of matrix product operators (MPOs) to the QTN setting which generates a linear combination of unitaries. The latter method is discussed in detail for translationally invariant spin-half systems, where it is shown to reduce the qubit resource requirements compared with the SWAP method, and may be generalized to other systems. We demonstrate the versatility of our approaches by simulating spin-1/2 and spin-3/2 MNMs, with the latter being an experimentally relevant model of a Cr$^{3+}_8$ ring. Our approach has qubit requirements that are independent of the number of constituents of the many-body system and scale only logarithmically with the bond dimension of the MPS representation, making them appealing for implementation on near-term quantum hardware with mid-circuit measurement and reset.