High-fidelity realization of the AKLT state on a NISQ-era quantum processor

TL;DR

This paper demonstrates the first successful preparation of the AKLT state on a NISQ quantum processor using a novel, shallow, parametrized circuit approach with high fidelity, advancing quantum simulation capabilities.

Contribution

The authors developed a non-deterministic, shallow circuit method for AKLT state preparation on IBM quantum hardware, achieving over 99.99% fidelity and enabling practical quantum simulations.

Findings

Achieved AKLT state preparation with >99.99% fidelity

Developed a shallow, nearest-neighbor circuit for state preparation

Enhanced accuracy with readout error mitigation

Abstract

The AKLT state is the ground state of an isotropic quantum Heisenberg spin-$1$ model. It exhibits an excitation gap and an exponentially decaying correlation function, with fractionalized excitations at its boundaries. So far, the one-dimensional AKLT model has only been experimentally realized with trapped-ions as well as photonic systems. In this work, we successfully prepared the AKLT state on a noisy intermediate-scale quantum (NISQ) era quantum device for the first time. In particular, we developed a non-deterministic algorithm on the IBM quantum processor, where the non-unitary operator necessary for the AKLT state preparation is embedded in a unitary operator with an additional ancilla qubit for each pair of auxiliary spin-1/2's. Such a unitary operator is effectively represented by a parametrized circuit composed of single-qubit and nearest-neighbor $CX$ gates. Compared with the conventional operator decomposition method from Qiskit, our approach results in a much shallower circuit depth with only nearest-neighbor gates, while maintaining a fidelity in excess of $99.99\%$ with the original operator. By simultaneously post-selecting each ancilla qubit such that it belongs to the subspace of spin-up $|\uparrow \rangle$, an AKLT state can be systematically obtained by evolving from an initial trivial product state of singlets plus ancilla qubits in spin-up on a quantum computer, and it is subsequently recorded by performing measurements on all the other physical qubits. We show how the accuracy of our implementation can be further improved on the IBM quantum processor with readout error mitigation.