Realizing symmetry-protected topological phases in a spin-1/2 chain with next-nearest-neighbor hopping on superconducting qubits

Abstract

Quantum simulation on near-term quantum hardware is a topic of intense interest. The preparation of novel quantum states of matter provides a quantitative assessment of the capabilities of near-term digital quantum computers to implement circuits with structure of relevance to quantum simulation. Here, we conduct a benchmark study by realizing symmetry-protected topological (SPT) phases of a spin-1/2 Hamiltonian with next-nearest-neighbor hopping on up to 11 qubits on a programmable superconducting quantum processor using adiabatic state preparation. Using recompilation techniques to reduce the gate count to around 50 two-qubit gates, we observe clear signatures of the two distinct SPT phases, such as excitations localized to specific edges and finite string-order parameters. We identify a parasitic phase associated with the two-qubit gate as the dominant imperfection that limits the depth of the circuits, indicating a research topic of interest for future hardware development.