dorsal/arxiv
View SchemaA Number Theoretic Interpolation Between Quantum and Classical Complexity Classes
| Authors | J. Maurice Rojas |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604089 |
| URL | https://arxiv.org/abs/quant-ph/0604089 |
Abstract
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.
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"abstract": "We reveal a natural algebraic problem whose complexity appears to interpolate\nbetween the well-known complexity classes BQP and NP:\n (*) Decide whether a univariate polynomial with exactly m monomial terms has\na p-adic rational root. In particular, we show that while (*) is doable in\nquantum randomized polynomial time when m=2 (and no classical randomized\npolynomial time algorithm is known), (*) is nearly NP-hard for general m: Under\na plausible hypothesis involving primes in arithmetic progression (implied by\nthe Generalized Riemann Hypothesis for certain cyclotomic fields), a randomized\npolynomial time algorithm for (*) would imply the widely disbelieved inclusion\nNP \\subseteq BPP. This type of quantum/classical interpolation phenomenon\nappears to new.",
"arxiv_id": "quant-ph/0604089",
"authors": [
"J. Maurice Rojas"
],
"categories": [
"quant-ph",
"math.NT"
],
"title": "A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes",
"url": "https://arxiv.org/abs/quant-ph/0604089"
},
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