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

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. 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 |↑>, 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.

Observation of the non-Hermitian skin effect and Fermi skin on a digital quantum computer

“…Default decompositions provided by Qiskit's transpile function often result in exceedingly deep circuits, which is not ideal for robust noisy simulations. To overcome these obstacles, we employ variational quantum algorithms (VQAs) and optimize stacked ansatz circuits [38,46], providing for an approximation of the target dynamics with shorter and more manageable circuit structure (See Methods). Since CX gates are a primary source of gate errors, our approach offers a significant advantage by substantially reducing the num-ber of CX gates compared to the default decomposition provided by Qiskit's tool.…”