The Hilbert-Polya approach 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 Physics of the Riemann Hypothesis.

The Hilbert-Polya approach 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 Physics of the Riemann Hypothesis.

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 Quantum Proofs for Classical Theorems. An example, is a proof of Jackson's inequality by means of a quantum probabilistic approach to polynomial approximation.