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BQP is contained in the complexity class # P ( or more precisely in the associated class of decision problems P < sup ># P </ sup >), which is a subclass of PSPACE.
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BQP and is
In computational complexity theory, BQP ( 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.
A language L is in BQP if and only if there exists a polynomial-time uniform family of quantum circuits, such that
Just like P and BPP, BQP is low for itself, which means BQP < sup > BQP </ sup > = BQP.
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 instantly, an indication of the possible difference in power between these similar classes.
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.
Adding postselection to BQP results in the complexity class PostBQP which is equal to PP.
It is known to be in BQP because of Shor's algorithm.
The class of problems that can be efficiently solved by quantum computers is called BQP, for " bounded error, quantum, polynomial time ".
Quantum computers only run probabilistic algorithms, so BQP on quantum computers is the counterpart of BPP (" bounded error, probabilistic, polynomial time ") on classical computers.
If that solution runs in polynomial time, then that problem is in BQP.
BQP is suspected to be disjoint from NP-complete and a strict superset of P, but that is not known.
Specifically it takes time, demonstrating that the integer factorization problem can be efficiently solved on a quantum computer and is thus in the complexity class BQP.
The class BQP is based on another machine with randomness: the quantum computer.
If the Grover's search problem was solvable with log < sup > c </ sup > N applications of U < sub > ω </ sub >, that would imply that NP is contained in BQP, by transforming problems in NP into Grover-type search problems.
Grover's algorithm suggests ( but does not prove ) that NP is not contained in BQP.
Simon's algorithm is with respect to an oracle separating BQP from BPP.
BQP and contained
However, there is some evidence that BQP, the class of problems solvable in polynomial time by a quantum computer, is not contained in PH ( Aaronson 2010 ).
BQP and class
PP also contains BQP, the class of decision problems solvable by efficient polynomial time quantum computers.
BQP and P
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:
BQP and problems
The suspected shape of the range of problems BQP | solvable by quantum computers in polynomial time ( BQP ).
In fact, BQP is low for PP, meaning that a PP machine achieves no benefit from being able to solve BQP problems instantly.
* BQP is low for PP In other words, a randomized algorithm that can be run an unbounded number of times can easily solve all the problems that a quantum computer can solve efficiently.
BQP and which
Furthermore, PP contains QMA, which subsumes inclusions of MA and BQP.
BQP and .
BQP can also be viewed as a bounded-error uniform family of quantum circuits.
The suspected relationship of BQP to other problem spaces.
Both integer factorization and discrete log are in BQP.
This tells us nothing about BPP or BQP, though.
is and contained
It is not possible to reconstruct fully the arrangements whereby these honors lists were then made up or even how the names that they contained assumed the order in which we find them.
What we will be sacrificing in any such arrangement will be our power to be selective which is contained in the reciprocal trade principle under which we now operate.
A good example of the results obtainable with ultrasonic radiation is contained in papers presented by Dr. G. Baum who has explored the human eye.
Freeman, Cameron and McGhie, in their description of the disturbances of thinking found in chronic schizophrenic patients, say, in regard to condensation, that `` the lack of adequate discrimination between the self and the environment, and the objects contained therein in itself is the prototypical condensation ''.
If each text form is marked when matched with a dictionary form, the text forms not contained in the dictionary can be identified when all dictionary forms have been read.
A full description of the DIOCS, DTF, and DUF statements is contained in the 7070 Data Processing System Bulletin `` IBM 7070 Input/Output Control System '', form Aj.
The publication form is that of loose-leaf sheets ( Af ) contained in binders.
The name and order Asterales is botanically venerable, dating back to at least 1926 in the Hutchinson system of plant taxonomy when it contained only five families, of which only two are retained in the APG III classification.
Many theorems which are provable using choice are of an elegant general character: every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact.
** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.
The gases are contained in a test-tube ( A ) standing over a large quantity of weak alkali ( B ), and the current is conveyed in wires insulated by U-shaped glass tubes ( CC ) passing through the liquid and round the mouth of the test-tube.
As Jacques Revel notes, the success of the Annales School, especially its use of social structures as explanatory forces contained the seeds of its own downfall, for there is " no longer any implicit consensus on which to base the unity of the social, identified with the real.
For an adiabatic free expansion of an ideal gas, the gas is contained in an insulated container and then allowed to expand in a vacuum.
Lastly, his Mouseion ( a word invoking the Muses ) seems to have contained the narrative of the Contest of Homer and Hesiod, of which the version that has survived is the work of a grammarian in the time of Hadrian, based on Alcidamas.
Some folk etymologies argue that the original forms of these symbols indicated their value through the number of angles they contained, however there is no proof of any such origin.
In the United Kingdom, the number of units contained in a typical serving of an alcoholic beverage is publicised and printed on bottles.
They are known in this context as control tables and are used in conjunction with a purpose built interpreter whose control flow is altered according to values contained in the array.
Some of the epistemic basis for Steiner's later anthroposophical work is contained in the seminal work, Philosophy of Freedom.
This high pressure is achieved by burning the propellant in a contained area, either the chamber of a gun barrel or the combustion chamber of a rocket motor.
A response of Abba Mari on a ritual question is contained in MS. Ramsgate, No. 136 ; and Zunz ( Literaturgeschichte der Synagogalen Poesie, p. 498 ), mentions a ḳinah composed by Abba Mari.
Hydride generation occurs by adding an acidified aqueous solution of the sample to a 1 % aqueous solution of sodium borohydride, all of which is contained in a glass vessel.
To see this, note that if L is any algebraic extension of K, then the algebraic closure of L is also an algebraic closure of K, and so L is contained within the algebraic closure of K.
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