NQP = co-C=P
نویسندگان
چکیده
Adleman, Demarrais, and Huang introduced the nondeterministic quantum polynomial-time complexity class NQP as an analogue of NP. It is known that, with restricted amplitudes, NQP is characterized in terms of the classical counting complexity class C=P. In this paper we prove that, with unrestricted amplitudes, NQP indeed coincides with the complement of C=P. As an immediate corollary, with unrestricted amplitudes BQP differs from NQP. key words: computational complexity, theory of computation
منابع مشابه
NQPC = co-C=P
Adleman, DeMarrais, and Huang introduced the nondeterministic quantum polynomial-time complexity class NQP as an analogue of NP. Fortnow and Rogers showed that, when the amplitudes are rational numbers, NQP is contained in the complement of C=P. Fenner, Green, Homer, and Pruim improved this result by showing that, when the amplitudes are arbitrary algebraic numbers, NQP coincides with co-C=P. I...
متن کاملQuantum and Classical Complexity Classes: Separations, Collapses, and Closure Properties
Separations, Collapses, and Closure Properties Holger Spakowski1?, Mayur Thakur2??, and Rahul Tripathi2? ? ? 1 Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany. [email protected] 2 Department of Computer Science, University of Rochester, Rochester, NY 14627, USA. fthakur,[email protected] Abstract. We study the complexity of quantum c...
متن کاملQuantum Np Is Hard for Ph
In analogy with NP, a language L is in the class NQP if the strings in L are exactly those accepted by a polynomial-time quantum machine with non-zero probability. Previously, Adleman, Demarrais and Huang showed that NQP PP. The sharper upper bound NQP coC=P is implicit in Adleman et al. and results of Fortnow and Rogers. Here we prove that in fact NQP and coC=P are the same class, by showing t...
متن کاملQuantum Computation Relative to Oracles
The study of the power and limitations of quantum computation remains a major challenge in complexity theory. Key questions revolve around the quantum complexity classes EQP, BQP, NQP and their derivatives. This paper presents new relativized worlds in which (i) co-RP * NQE, (ii) P = BQP and UP = EXP, (iii) P = EQP and RP = EXP, and (iv) EQP * Σ 2 ∪Π P 2 . We also show a partial answer to the q...
متن کاملExact Non-identity check is NQP-complete
We define a problem “exact non-identity check”: Given a classical description of a quantum circuit with an ancilla system, determine whether it is strictly equivalent to the identity or not. We show that this problem is NQP-complete. In a sense of the strict equivalence condition, this problem is different from a QMA-complete problem, non-identity check defined in [1]. As corollaries, it is der...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electronic Colloquium on Computational Complexity (ECCC)
دوره 5 شماره
صفحات -
تاریخ انتشار 1998