The Quantum Iterated Function Systems (QIFS) theory establishes an exponential relation q = e−Γtc linking the quantum group deformation parameter q withthe open system decoherence rate Γ and characteristic coherence time tc, offering anew perspective for understanding the emergence mechanism of quantum symmetries. This paper proposes concrete experimental schemes to implement the QIFSof su(2) generators in superconducting qubit and ion trap systems, aiming to testthis theoretical relation. First, we construct QIFS generators based on amplitudedamping and phase damping channels, and present their physical realizations insuperconducting circuits and ion trap systems. Second, we define two methodsto extract the quantum group parameter qexp from experimental data—quantumstate tomography based on entanglement spectra and time-series analysis based ondynamical correlation functions—and elaborate on their operational steps and error control. Finally, we establish a falsification criteria system including absolutedeviation criterion, goodness-of-fit criterion, self-consistency criterion, and limitingbehavior test. It is explicitly stated that if the deviation between qexp and thetheoretical prediction qth = e−Γtc exceeds 5%, the core proposition of the QIFSframework regarding quantum group emergence is invalidated. This experimentaldesign directly connects abstract quantum group algebraic structures with observable quantum open system dynamics, providing operable experimental criteria fortesting generative quantum theories.
The Quantum Iterated Function Systems (QIFS) theory establishes an exponential relation q = e−Γtc linking the quantum group deformation parameter q withthe open system decoherence rate Γ and characteristic coherence time tc, offering anew perspective for understanding the emergence mechanism of quantum symmetries. This paper proposes concrete experimental schemes to implement the QIFSof su(2) generators in superconducting qubit and ion trap systems, aiming to testthis theoretical relation. First, we construct QIFS generators based on amplitudedamping and phase damping channels, and present their physical realizations insuperconducting circuits and ion trap systems. Second, we define two methodsto extract the quantum group parameter qexp from experimental data—quantumstate tomography based on entanglement spectra and time-series analysis based ondynamical correlation functions—and elaborate on their operational steps and error control. Finally, we establish a falsification criteria system including absolutedeviation criterion, goodness-of-fit criterion, self-consistency criterion, and limitingbehavior test. It is explicitly stated that if the deviation between qexp and thetheoretical prediction qth = e−Γtc exceeds 5%, the core proposition of the QIFSframework regarding quantum group emergence is invalidated. This experimentaldesign directly connects abstract quantum group algebraic structures with observable quantum open system dynamics, providing operable experimental criteria fortesting generative quantum theories.
The mathematical structure of quantum groups, as q-deformations of Lie algebras, has been extensively studied, yet their deep connection with the dynamicsof open quantum systems remains to be elucidated. Based on the framework ofQuantum Iterated Function Systems (QIFS), this paper establishes an emergencemechanism from quantum groups to classical Lie groups. We first construct a concrete QIFS whose generators are a family of completely positive maps acting onthe space of quantum states, and prove that the Lie algebra structure of its lowenergy effective theory corresponds to the Drinfeld–Jimbo quantum group Uq(g).Next, we derive the relation between the q-parameter and the decoherence rate Γ,characteristic coherence time τc as q = e−Γτc, revealing the physical origin of theq-deformation. Based on this, we prove that in the limit of vanishing decoherencerate Γ → 0, the quantum group degenerates to the classical Lie group g. Finally, weestablish a correspondence between the representation theory of quantum groupsand the spectrum of QIFS, providing a unified mathematical framework for understanding the emergence mechanism of quantum symmetries. This result links theconcept of decoherence in quantum information theory with the algebraic structureof quantum groups, revealing a deeper picture where classical Lie group symmetriesemerge as the semiclassical limit of open quantum system dynamics.
The computational advantage of quantum algorithms over classical algorithmshas been partially proven, but its deep connection with the dynamics of open quantum systems has yet to be elucidated. This paper establishes a formal correspondence between quantum algorithm complexity and dissipative dynamics based onthe framework of Quantum Iterated Function Systems (QIFS). We first prove thatthe convergence rate of a QIFS—governed by the spectral gap ∆—directly determines the query complexity and time complexity of the corresponding quantumalgorithm. Second, we establish an exponential relationship between the quantumgroup parameter q and the success probability of the algorithm, revealing the dualrole played by decoherence in quantum search algorithms: moderate decoherenceaccelerates convergence, while excessive decoherence causes the algorithm to fail.Building on this, we propose the “dissipative speedup” theorem: there exists an optimal decoherence rate Γopt such that the quantum algorithm described by the QIFSachieves minimal time complexity, and this optimal value satisfies Γopt = −lnq/tc.Finally, we explore the connections between this framework and adiabatic quantum computation as well as quantum walk algorithms, and propose experimentalschemes to test the theoretical predictions on superconducting quantum processors.This work unifies the theory of open quantum systems, quantum group algebra,and quantum computational complexity into a common generative framework, providing a new perspective for understanding the persistence of quantum advantagein noisy environments.
Previous work, starting from hierarchical iterated function systems (HierarchicalIFS), proved that discrete Lie algebras converge to affine Kac-Moody algebras in therescaling limit, with the central charge uniquely determined by the topological dataof inter-level gluing rules. This paper proposes to numerically verify this theoreticalprediction using the multiscale entanglement renormalization ansatz (MERA). Byestablishing a structural correspondence between the MERA network and the hierarchical IFS, we interpret the isometries of MERA as inter-level gluing rules, andthe ultraviolet degrees of freedom as fine-level generators, and introduce a gluingstrength parameter that directly links the winding number to the variational parameters of MERA. Taking the SU(2) Heisenberg model as an example, we designnumerical protocols to extract the central charge from the ground-state entanglement entropy and entanglement spectrum, and demonstrate that as the MERAdepth increases, the effective central charge converges exponentially to the theoretical value of conformal field theory, with the convergence rate controlled by thespectral gap of the hierarchical IFS. We explicitly give falsification thresholds consisting of three criteria: absolute deviation, convergence rate, and self-consistency,and introduce cross-validation with exact diagonalization and DMRG. Finally, weextend the verification framework to SU(2)k WZW models and non-diagonal conformal field theories, elucidating the central role of the double matching of windingnumber and central charge in theoretical tests. This work positions tensor networks as a numerical experimental platform for testing core ideas of generativemathematical physics.
Description: This paper introduces a thermodynamic time parameter τ = ∫C dt, where C[ρ,𝒜] quantifies the information accessibility of quantum state ρ within observable set 𝒜. We prove that entropy decrease with respect to τ is equivalent to information recovery from inaccessible degrees of freedom—a process realizable in quantum error correction (QEC) cycles. The framework predicts a measurable signature: QEC should exhibit 10-15% fidelity enhancement relative to standard quantum dynamics, arising from negative coarse-graining rates (dC/dt < 0) during syndrome measurement. The time-dependent field C(t) can be reconstructed from fidelity data via C(t) = -(1/Γ) d ln F(t)/dt, providing a falsifiable experimental observable. We present a detailed experimental protocol for trapped-ion systems, achievable with current technology. Statistical discrimination criteria distinguish this effect from conventional mechanisms (non-Markovian baths, leakage errors, SPAM errors, dynamical decoupling). The combined statistical power enables rigorous falsification. This work establishes quantum error correction as a testbed for emergent time dynamics and provides concrete predictions testable with current trapped-ion quantum computing platforms. Key contributions: Theoretical framework linking coarse-graining to emergent time Quantitative prediction: 10-15% fidelity enhancement in QEC Experimental protocol for trapped-ion systems Falsification criteria distinguishing from alternative mechanisms Document type: Preprint / Working Paper Date: December 2025
This paper establishes a rigorous correspondence between quantum generativedynamics and quantum algorithmic complexity, reducing the query complexity andtime complexity of algorithms to the spectral properties of the generative process.Byembedding quantum algorithms within the framework of quantum iterated function systems, it is proven that the convergence rate of an algorithm is uniquely determined by the spectral gap ∆ of the Markov operator: the required number of iterations T ∼ (1/∆)ln(1/ε). Furthermore, the dual role of decoherence in quantumsearch is revealed-the competition between coherent and dissipative contributionsleads to the existence of an optimal decoherence rate, given by Γopt ∼ −(1/4)lnN,which corresponds to the optimal complexity of Grover’s algorithm. By relatingthe spectral gap to the quantum group parameter q = e−Γtc, we derive ∆ = 1−q2,establishing a direct correspondence between algebraic parameters and computational resources. This framework unifies open quantum system theory, quantumgroup algebra, and quantum computational complexity under the language of generative dynamics, providing a new theoretical foundation for understanding thebehavior of quantum algorithms in noisy environments.
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