Preparing 100-qubit symmetry-protected topological order on a digital quantum computer

TL;DR

This paper demonstrates the preparation and detection of 100-qubit symmetry-protected topological phases on a quantum computer using shallow circuits, enabling large-scale studies of complex quantum matter.

Contribution

It introduces a tensor network based approximate quantum compiling protocol to create shallow circuits for large-scale SPT states on quantum hardware.

Findings

Achieved high-fidelity preparation of 100-site SPT ground states.

Observed key signatures of SPT order on IBM quantum hardware.

Established a practical method for studying large-scale quantum matter phenomena.

Abstract

Symmetry-protected topological (SPT) phases extend the Landau paradigm of quantum matter by admitting distinct symmetry-preserving phases that lack any local order parameter. Demonstrating these phases at scale on programmable quantum processors is a key milestone in using quantum hardware to probe emergent many-body phenomena, yet it is impeded by the circuit depth normally required to capture non-trivial entanglement. Here we use a tensor network based approximate quantum compiling (AQC) protocol to construct shallow quantum circuits (18-39 CNOT depth), which prepare 100-site ground states of the spin-1/2 bond-alternating Heisenberg chain in both SPT phases, to 97.9-99.0% fidelity. Upon executing the circuits on IBM quantum hardware, the resulting states exhibit all defining signatures of SPT order including non-local string order for strings of up to length 20, characteristic degeneracies in the entanglement spectrum and clear evidence of symmetry-protected edge modes. The simultaneous observation of these independent diagnostics establishes current quantum computers as versatile platforms for large-scale studies of symmetry-protected quantum matter. More broadly, our results establish a practical foundation for probing non-equilibrium quench dynamics of such systems in regimes that challenge classical computational methods.