A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes Institutional Repository Document uri icon


  • 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.

author list (cited authors)

  • Rojas, J. M.

complete list of authors

  • Rojas, J Maurice

Book Title

  • arXiv

publication date

  • April 2006