In computational complexity theory, bounded-error quantum polynomial time is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances. It is the quantum analogue of the complexity class BPP. A decision problem is a member of BQP if there exists a quantum algorithm that solves the decision problem with high probability and is guaranteed to run in polynomial time. A run of the algorithm will solve the decision problem with a probability of at least 2/3. BQP can be viewed as the languages associated with certain bounded-error uniform families of quantum circuits. A language L is in BQP if and only if there exists a polynomial-time uniform family of quantum circuits, such that For all n ∈ N, Qn takes n qubits as input and outputs 1 bit For all x in L, P r ≥ 2 3 For all x not in L, P r ≥ 2 3 Alternatively, one can define BQP in terms of quantum Turing machines. A language L is in BQP if and only if there exists a polynomial quantum Turing machine that accepts L with an error probability of at most 1/3 for all instances.

To other "bounded error" probabilistic classes the choice of 1/3 in the definition is arbitrary. We can run the algorithm a constant number of times and take a majority vote to achieve any desired probability of correctness less than 1, using the Chernoff bound; the complexity class is unchanged by allowing error as high as 1/2 − n−c on the one hand, or requiring error as small as 2−nc on the other hand, where c is any positive constant, n is the length of input. The number of qubits in the computer is allowed to be a polynomial function of the instance size. For example, algorithms are known for factoring an n-bit integer using just over 2n qubits. Computation on a quantum computer ends with a measurement; this leads to a collapse of quantum state to one of the basis states. It can be said. Quantum computers have gained widespread interest because some problems of practical interest are known to be in BQP, but suspected to be outside P; some prominent examples are: Integer factorization Discrete logarithm Simulation of quantum systems Approximating the Jones polynomial at certain roots of unity This class is defined for a quantum computer and its natural corresponding class for an ordinary computer is BPP.

Just like P and BPP, BQP is low for itself, which means BQPBQP = BQP. Informally, this is true. If a polynomial time algorithm calls as a subroutine polynomially many polynomial time algorithms, the resulting algorithm is still polynomial time. BQP contains P and BPP and is contained in AWPP, PP and PSPACE. In fact, BQP is low for PP, meaning that a PP machine achieves no benefit from being able to solve BQP problems an indication of the possible difference in power between these similar classes; the known relationships with classic complexity classes are: P ⊆ B P P ⊆ B Q P ⊆ A W P P ⊆ P P ⊆ P S P A C E As the problem of P ≟ PSPACE has not yet been solved, the proof of inequality between BQP and classes mentioned above is supposed to be difficult. The relation between BQP and NP is not known. In May 2018, computer scientists Ran Raz of Princeton University and Avishay Tal of Stanford University published a paper which showed that, relative to an oracle, BQP was not contained in PH. Adding postselection to BQP results in the complexity class PostBQP, equal to PP.

Hidden subgroup problem Polynomial hierarchy Quantum complexity theory QMA, the quantum equivalent to NP. Complexity Zoo link to BQP

Cima d'Asta

Cima d’Asta at 2,847 metres is the highest mountain of the Fiemme Mountains in the eastern part of the Italian province of Trentino. It is situated between the Vanoi valley to the north and the Tesino valley to the south and is 18 km north-east of the town of Borgo Valsugana, it is over 21 km away from the nearest higher summit, the Cimon della Pala. Just south of the summit is a mountain lake at 2460 m, the Lago di Cima d’Asta, from which the river Grigno originates, it is unclear. On his ascent in 1882, Gustav Euringer did not find evidence of earlier visits, but was aware that the summit had been a triangulation point since 1816 and assumed it had been reached at or before that time

Jastrabie nad Top─żou

Jastrabie nad Topľou is a village and municipality in Vranov nad Topľou District in the Prešov Region of eastern Slovakia. In historical records the village was first mentioned in 1363; the municipality lies at an altitude of 170 metres and covers an area of 6.779 km². It has a population of about 414 people; the records for genealogical research are available at the state archive "Statny Archiv in Presov, Slovakia" Roman Catholic church records: 1769-1910 Greek Catholic church records: 1852-1940 Lutheran church records: 1830-1902 List of municipalities and towns in Slovakia Surnames of living people in Jastrabie nad Toplou