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Algorithmic Holography on Noisy Quantum Hardware:Testing Boundary-Kernel Information Processing via Spectral Resonance

Jewon Moon

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.29674.58564

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Twisted Topological Operators: Closure, Openness, and Compression as a Unified Spectral Structure

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Twisted Topological Operators: Closure, Openness, and Compression as a Unified Spectral Structure develops a minimal operator-theoretic framework in which circulation, resonance decay, and information compression arise as a single coherent spectral phenomenon. Rather than treating topology, dissipation, and holography as independent mechanisms, this work demonstrates that they emerge from a common structural origin once boundary conditions, openness, and projection are treated at the operator level. The paper proceeds through three tightly connected constructions: Twisted Topological ClosureStarting from self-adjoint operators on compact ring domains with twisted boundary conditions, the work shows that persistent probability currents and time-reversal symmetry breaking are enforced purely by topology, without invoking external forcing or dissipation. Circulation is therefore structural, not dynamical. Controlled Openness and ResonanceIntroducing bounded non-self-adjoint perturbations yields intrinsic decay and complex spectra. Resonances are identified as resolvent poles rather than eigenstates, providing a clean operator interpretation of quasinormal modes and irreversible relaxation. Holography as Operator CompressionApparent information loss is reinterpreted as projection onto inaccessible subspaces. Entropy and decay quantify compression due to restricted boundary access, not physical destruction of information. Throughout, the paper deliberately avoids arithmetic input or number-theoretic assumptions. Its aim is to isolate the minimal operator skeleton capable of simultaneously supporting circulation, dissipation, and compression. This operator framework serves as a structural prelude to subsequent spectral and arithmetic applications. In particular, it prepares the ground for an operator-theoretic reduction of the Riemann spectrum, where time-reversal symmetry breaking, self-adjoint domain selection, and spectral stability become unavoidable consequences of topology and openness. In this view, circulation, decay, and holography are not separate phenomena—but different projections of a single underlying operator structure.

•Dec 16, 2025•0 citations
Variational quantum algorithms (VQAs) aim at solving classical or quantum optimization problems by optimizing parametrized trial states on a quantum device, based on the outcomes of noisy projective measurements. The associated optimization process benefits from an accurate modeling of the cost function landscape using Gaussian process models (GPMs), whose performance is critically affected by the choice of their kernel. Here, we introduce specialized trigonometric kernels, inspired by the observation that typical VQA cost functions display oscillatory behavior with only few frequencies. Appropriate scores to benchmark the reliability of a GPM are defined, and a systematic comparison between different kernels is carried out on prototypical problems from quantum chemistry and combinatorial optimization. We further introduce RotoGP, a sequential line-search optimizer equipped with a GPM, and test how different kernels can help mitigate noise and improve optimization convergence. Overall, we observe that the trigonometric kernels show the best performance in most of the cases under study.
The use of quantum computing for machine learning is among the most exciting applications of quantum technologies. Researchers are developing quantum models inspired by classical ones to find some possible quantum advantages over classical approaches. Although such a clear quantum advantage has not yet been achieved, the need for rigorous methodologies to test quantum machine learning (QML) algorithms is an evident requirement. A major challenge in QML development and testing is the lack of datasets specifically designed for quantum algorithms. Existing datasets, often borrowed from classical machine learning, need modifications to be compatible with current noisy quantum hardware. In this work, we use a dataset produced by internet-of-things (IoT) devices in a form usable for quantum algorithms without the need for feature reductions. Among quantum-inspired machine learning algorithms, the Projected Quantum Kernel (PQK) stands out for its elegant solution of projecting the data encoded in Hilbert space into classical space. In this paper, we detail how a PQK approach can be used to develop a prediction model on IoT data using quantum machine learning.
Twisted Topological Operators: Closure, Openness, and Compression as a Unified Spectral Structure develops a minimal operator-theoretic framework in which circulation, resonance decay, and information compression arise as a single coherent spectral phenomenon. Rather than treating topology, dissipation, and holography as independent mechanisms, this work demonstrates that they emerge from a common structural origin once boundary conditions, openness, and projection are treated at the operator level. The paper proceeds through three tightly connected constructions: Twisted Topological ClosureStarting from self-adjoint operators on compact ring domains with twisted boundary conditions, the work shows that persistent probability currents and time-reversal symmetry breaking are enforced purely by topology, without invoking external forcing or dissipation. Circulation is therefore structural, not dynamical. Controlled Openness and ResonanceIntroducing bounded non-self-adjoint perturbations yields intrinsic decay and complex spectra. Resonances are identified as resolvent poles rather than eigenstates, providing a clean operator interpretation of quasinormal modes and irreversible relaxation. Holography as Operator CompressionApparent information loss is reinterpreted as projection onto inaccessible subspaces. Entropy and decay quantify compression due to restricted boundary access, not physical destruction of information. Throughout, the paper deliberately avoids arithmetic input or number-theoretic assumptions. Its aim is to isolate the minimal operator skeleton capable of simultaneously supporting circulation, dissipation, and compression. This operator framework serves as a structural prelude to subsequent spectral and arithmetic applications. In particular, it prepares the ground for an operator-theoretic reduction of the Riemann spectrum, where time-reversal symmetry breaking, self-adjoint domain selection, and spectral stability become unavoidable consequences of topology and openness. In this view, circulation, decay, and holography are not separate phenomena—but different projections of a single underlying operator structure.