A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes
| dc.creator | Rojas, J. Maurice | |
| dc.date | 2006-04-12 | |
| dc.date | 2006-04-12 | |
| dc.date.accessioned | 2026-07-07T07:11:51Z | |
| dc.date.available | 2026-07-07T07:11:51Z | |
| dc.description | We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In particular, we show that while (*) is doable in quantum randomized polynomial time when m=2 (and no classical randomized polynomial time algorithm is known), (*) is nearly NP-hard for general m: Under a plausible hypothesis involving primes in arithmetic progression (implied by the Generalized Riemann Hypothesis for certain cyclotomic fields), a randomized polynomial time algorithm for (*) would imply the widely disbelieved inclusion NP \subseteq BPP. This type of quantum/classical interpolation phenomenon appears to new. | |
| dc.description | 14 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0604089 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0604089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111916 | |
| dc.subject | Quantum Physics | |
| dc.subject | Number Theory | |
| dc.title | A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes | |
| dc.type | text |