Preentangling Quantum Algorithms -- the Density Matrix Renormalization Group-assisted Quantum Canonical Transformation

TL;DR

This paper introduces a novel quantum algorithm approach that combines classical density matrix renormalization group methods with quantum canonical transformations, reducing parameters needed for electronic structure calculations near multi-reference points.

Contribution

It presents a parameter-free preentangler method integrated with quantum algorithms and a new Matrix Product State preparation algorithm, enhancing efficiency in quantum chemistry simulations.

Findings

Requires fewer parameters than generalized unitary coupled cluster circuits near multi-reference points.

Demonstrates effectiveness on systems like H2O, N2, BeH2, and P4.

Proposes a new MPS preparation algorithm based on the Linear Combination of Unitaries.

Abstract

We propose the use of parameter-free preentanglers as initial states for quantum algorithms. We apply this idea to the electronic structure problem, combining a quantized version of the Canonical Transformation by Yanai and Chan [J. Chem. Phys. 124, 194106 (2006)] with the Complete Active Space Density Matrix Renormalization Group. This new ansatz allows to shift the computational burden between the quantum and the classical processor. In the vicinity of multi-reference points in the potential energy surfaces of H$_2$O, N$_2$, BeH$_2$ and the P4 system, we find this strategy to require significantly less parameters than corresponding generalized unitary coupled cluster circuits. We propose a new algorithm to prepare Matrix Product States based on the Linear Combination of Unitaries and compare it to the Sequential Unitary Algorithm proposed by Ran in [Phys. Rev. A 101, 032310 (2020)].