{
  "id": "oai:papers.qnfo.org:programming-the-vacuum",
  "slug": "programming-the-vacuum",
  "title": "Programming the Vacuum",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The exponential growth of Hilbert space dimensions presents a fundamental barrier to the classical simulation of quantum systems, necessitating a paradigm shift from algorithmic simulation to physical instantiation. This study validates the “Inverted Church-Turing-Deutsch” (CTD) framework, which posits that physical Hamiltonian systems can serve as efficient computational substrates for problems intractable to Turing machines. We operationalize this framework through two modalities: “Class A” discrete optimization using Ising models and “Class B” spectral engineering targeting the Riemann zeros. Through rigorous computational validation on synthetic data (N=3-12), we demonstrate a decisive scaling divergence: Hamiltonian relaxation exhibits polynomial scaling (T ∝ N².02), whereas classical brute-force search follows an exponential trajectory (T ∝ 2⁰.55N), supported by a Bayes Factor > 10²5. Furthermore, we successfully engineer a 1D physical potential V(x) that reproduces the first five Riemann zeros with a Mean Absolute Percentage Error of 0.033%, effectively functioning as a “Physical Oracle” for number theory. [...]",
  "abstract_markdown": "The exponential growth of Hilbert space dimensions presents a fundamental barrier to the classical simulation of quantum systems, necessitating a paradigm shift from algorithmic simulation to physical instantiation. This study validates the “Inverted Church-Turing-Deutsch” (CTD) framework, which posits that physical Hamiltonian systems can serve as efficient computational substrates for problems intractable to Turing machines. We operationalize this framework through two modalities: “Class A” discrete optimization using Ising models and “Class B” spectral engineering targeting the Riemann zeros. Through rigorous computational validation on synthetic data (\\(N=3-12\\)), we demonstrate a decisive scaling divergence: Hamiltonian relaxation exhibits polynomial scaling (\\(T \\propto N^{2.02}\\)), whereas classical brute-force search follows an exponential trajectory (\\(T \\propto 2^{0.55N}\\)), supported by a Bayes Factor \\(> 10^{25}\\). Furthermore, we successfully engineer a 1D physical potential \\(V(x)\\) that reproduces the first five Riemann zeros with a Mean Absolute Percentage Error of 0.033%, effectively functioning as a “Physical Oracle” for number theory. [...]",
  "date": "2026-01-01",
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        "description": "The exponential growth of Hilbert space dimensions presents a fundamental barrier to the classical simulation of quantum systems, necessitating a paradigm shift from algorithmic simulation to physical instantiation. This study validates the “Inverted Church-Turing-Deutsch” (CTD) framework, which posits that physical Hamiltonian systems can serve as efficient computational substrates for problems intractable to Turing machines. We operationalize this framework through two modalities: “Class A” discrete optimization using Ising models and “Class B” spectral engineering targeting the Riemann zeros. Through rigorous computational validation on synthetic data (N=3-12), we demonstrate a decisive scaling divergence: Hamiltonian relaxation exhibits polynomial scaling (T ∝ N².02), whereas classical brute-force search follows an exponential trajectory (T ∝ 2⁰.55N), supported by a Bayes Factor > 10²5. Furthermore, we successfully engineer a 1D physical potential V(x) that reproduces the first five Riemann zeros with a Mean Absolute Percentage Error of 0.033%, effectively functioning as a “Physical Oracle” for number theory. [...]",
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