Renormalization-group-based preparation of matrix product states on up to 80 qubits

TL;DR

This paper demonstrates an RG-based quantum algorithm for preparing matrix product states on up to 80 qubits, showing advantages over sequential methods in noise resilience and circuit depth.

Contribution

It introduces a renormalization-group-based protocol for efficient large-scale MPS preparation on quantum hardware, surpassing traditional sequential methods.

Findings

RG-based circuits are more noise-resilient.

They outperform sequential circuits for large systems.

Successful preparation of SPT-ordered states beyond the fixed point.

Abstract

A key challenge for quantum computers is the efficient preparation of many-body entangled states across many qubits. In this work, we demonstrate the preparation of matrix product states (MPS) using a renormalization-group(RG)-based quantum algorithm on superconducting quantum hardware. Compared to sequential generation, it has been shown that the RG-based protocol asymptotically prepares short-range correlated MPS with an exponentially shallower circuit depth (when scaling system size), but it is not yet clear for which system sizes it starts to convey an advantage. We thus apply this algorithm to prepare a class of MPS exhibiting a phase transition between a symmetry-protected topological (SPT) and a trivial phase for systems of up to 80 qubits. We find that the reduced depth of the RG-based circuits makes them more resilient to noise, and that they generally outperform the sequential circuits for large systems, as we showcase by measuring string-order-like local expectation values and energy densities. We thus demonstrate that the RG-based protocol enables large-scale preparation of MPS and, in particular, SPT-ordered states beyond the fixed point.