The <A HREF="https://en.wikipedia.org/wiki/Hilbert–Pólya_conjecture">Hilbert-Polya approach</A> to the Riemann hypothesis follows this path, by attempting to relate the zeroes of the Riemann zeta function to a quantum mechanical scattering problem. The probability distribution of the energy levels of a chaotic quantum system with broken time-reversal symmetry is conjectured to describe the local statistics of the zeta-function zeroes, see for example <A HREF="https://arxiv.org/abs/1101.3116">Physics of the Riemann Hypothesis.</A>

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Quantum algorithms provide a different area of quantum physics that is used to prove deterministic mathematical theorems. Drucker and De Wolf given an overview in <A HREF="https://arxiv.org/abs/0910.3376">Quantum Proofs for Classical Theorems</A>. An example, is a proof of <A HREF="https://en.wikipedia.org/wiki/Jackson%27s_inequality">Jackson's inequality</A> by means of a quantum probabilistic approach to polynomial approximation.