|
| related topics |
| {let, theorem, proof} |
| {algorithm, log, probability} |
| {group, space, representation} |
| {equation, function, exp} |
| {qubit, qubits, gate} |
| {time, systems, information} |
| {phase, path, phys} |
| {state, algorithm, problem} |
| {classical, space, random} |
| {cos, sin, state} |
|
Quantum Computing and Zeroes of Zeta Functions
Wim van Dam
abstract: A possible connection between quantum computing and Zeta functions of finite
field equations is described. Inspired by the 'spectral approach' to the
Riemann conjecture, the assumption is that the zeroes of such Zeta functions
correspond to the eigenvalues of finite dimensional unitary operators of
natural quantum mechanical systems. The notion of universal, efficient quantum
computation is used to model the desired quantum systems.
Using eigenvalue estimation, such quantum circuits would be able to
approximately count the number of solutions of finite field equations with an
accuracy that does not appear to be feasible with a classical computer. For
certain equations (Fermat hypersurfaces) it is show that one can indeed model
their Zeta functions with efficient quantum algorithms, which gives some
evidence in favor of the proposal of this article.
- oai_identifier:
- oai:arXiv.org:quant-ph/0405081
- categories:
- quant-ph math.AG
- comments:
- 18 pages, AMS-LaTeX
- arxiv_id:
- quant-ph/0405081
- created:
- 2004-05-17
Full article ▸
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