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.
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.
This paper proposes a theoretical framework of ”Spatiotemporal TopologicalOrder” based on time-space dual topological quantum field theory (TQFT) andhigher-order categorical syntax, aiming to provide a unified description of spatialtopological orders (e.g., anyon theory) and temporal topological structures (e.g.,barcodes in persistent homology). By constructing a monoidal equivalence functor, this work rigorously proves the isomorphism between the modular S-matrix oftopological orders and the persistent homology pairing matrix, and demonstratesthat both constitute a unitary representation of SL(2,Z). To validate the theory, a”dual-encoding” lattice model is designed, which compiles higher-order categoricalstructures into local interaction Hamiltonians, and the duality is preliminarily verified via numerical simulations (isomorphism error < 1%). Furthermore, this paperproposes a three-stage verification roadmap from mathematical formalization toquantum simulation experiments, laying the foundation for testing spatiotemporaltopological orders in controllable quantum systems.
This paper addresses key bottlenecks in spatiotemporal topological order research, namely the difficulty of experimental verification, the complexity of higherdimensional theories, and the lack of automated tools, by proposing a unified framework for three-pronged extension encompassing defects, higher dimensions, and algorithms. First, we generalize semisimple categories to non-semisimple categorieswith boundaries and defects, establishing an algebraic duality between defect braiding and defect merging, and provide phase signals measurable via quantum interference. Second, we elevate the duality between (2+1)-dimensional topological orderand single-parameter persistent homology to a duality between (3+1)-dimensionalorder and three-parameter persistent homology, proving that the high-dimensionalbarcode merging algebra and the 3-category data of (3+1)-dimensional topological order satisfy the same set of higher-order Verlinde equations. Finally, wedevelop and open-source the “TDA-TopoOrder” algorithm library, implementingan end-to-end automated pipeline from quantum many-body dynamical data totopological order classification. This paper further integrates a ten-year technicalroadmap, specifying verifiable parameters, error thresholds, and toolchains, providing a plug-and-play standardized scheme for quantum simulation and cosmologicalobservation.
This paper proposes a theoretical and experimental scheme for experimentallysimulating the phenomenon of ”temporal structure emergence” on near-term quantum processors (such as superconducting qubit arrays). By translating the theoretical framework of ”time emerging from quantum information” into executablequantum circuits and algorithms, this research designs a set of hybrid quantumclassical algorithms based on variational quantum simulation (VQS) to simulatethe dynamics of simplified spacetime tensor networks and extract order parameterscharacterizing the arrow of time and causal structure. The experimental objectivesinclude preparing initial entangled states with no preset time direction, realizing evolution akin to renormalization group flow through parameterized quantumcircuits, and measuring causal correlation functions to observe the emergence ofthe arrow of time as a spontaneous symmetry-breaking phenomenon. The articleelaborates on the physical implementation, algorithmic steps, error analysis, andexpected results, demonstrating the feasibility of a proof-of-principle verification onnoisy intermediate-scale quantum (NISQ) devices, thereby providing an actionableexperimental entry point for testing quantum gravity and foundational theories ofspacetime
Systems displaying topological quantum order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of systems displaying topological order including, in particular, their anyon excitations. Here, we investigate systems that lie outside this common purview, and present a rich class of models exhibiting topological orders with distance-dependent interactions between anyons. As we illustrate, in some instances, . This leads to behaviors not typically described by topological quantum field theories. We examine these models by performing exact dualities to systems displaying conventional (i.e., Landau) orders. Our approach enables a general method for mapping Landau-type theories to dual models with topological order, while preserving the same spatial dimension. The low-energy subspaces of our models can be made more resilient to thermal effects than those of surface codes.
Abstract Quantum many-body systems with a non-Abelian topological order can host anyonic quasiparticles. It has been proposed that anyons could be used to encode and manipulate information in a topologically protected manner that is immune to local noise, with quantum gates performed by braiding and fusing anyons. Unfortunately, realizing non-Abelian topologically ordered states is challenging, and it was not until recently that the signatures of non-Abelian statistics were observed through digital quantum simulation approaches. However, not all forms of topological order can be used to realize universal quantum computation. Here we use a superconducting quantum processor to simulate non-Abelian topologically ordered states of the Fibonacci string-net model and demonstrate braidings of Fibonacci anyons featuring universal computational power. We demonstrate the non-trivial topological nature of the quantum states by measuring the topological entanglement entropy. In addition, we create two pairs of Fibonacci anyons and demonstrate their fusion rule and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. Our results establish a digital approach to explore non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.
This paper systematically explores the experimental verification pathways forTranscendental Topological Order (TTO). TTO theory predicts novel phenomena marked by transcendental numbers (such as e, π) as quantum dimensions,resonant dependence of system properties on size (scale resonance), and time crystallization. This paper argues for the feasibility of testing these predictions using artificial quantum systems (quantum simulators), focusing on evaluating thetechnical advantages and limitations of three major platforms: cold-atom optical lattices, superconducting qubit arrays, and topological photonic crystals. Acomplete experimental framework is proposed, including engineering schemes forkey theoretical elements (e.g., transcendental number coupling), measurement protocols for core observables (e.g., topological entanglement entropy, time crystalresponse), strategies to address experimental challenges (e.g., parameter precision,decoherence, finite-size effects), and an auxiliary verification pipeline integratinghigh-fidelity numerical simulation with interpretable machine learning. Finally,the paper outlines a progressive experimental roadmap from proof-of-principle tomulti-platform collaborative confirmation, aiming to provide a feasibility analysisframework based on current technology levels for translating the highly abstractmathematical conception of TTO into concrete physical experimental goals.