Spatiotemporal Topological Order C, Quantum Chip Spatiotemporal Topological Order: Anyon-Time Barcode Dual Encoding Experiment

This paper proposes and designs a quantum simulation experiment scheme forverifying the duality of ”spatiotemporal topological order” on a superconductingquantum processor. The core of the scheme lies in ”dual encoding”: within thesame chip, using the physical qubits of the surface code to encode and manipulatethe braiding process of spatial anyons, while simultaneously using auxiliary timequbits and delay operations to encode the barcodes of persistent homology and theirmerging process in the temporal dimension. By designing a specialized quantumcircuit containing a ”quantum switch” protocol, the experiment aims to achieve acontrollable mapping and comparison between anyon worldlines and barcode intervals. The theory predicts that, under the framework of spatiotemporally dualtopological quantum field theory, the geometric phase ϕanyon induced by spatialbraiding should be precisely equal to the topological phase ϕtime induced by temporal barcode merging. This paper details the overall objectives of the experiment,the specific quantum circuit implementation, targeted error mitigation strategies,and analyzes feasibility and fidelity thresholds under typical noise through numerical simulations. This research provides a concrete and operational experimentalblueprint for testing the unity of spatiotemporal topological structures on mediumscale noisy intermediate-scale quantum (NISQ) devices.