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Is BPP contained in BQP?
BQP contains P and BPP and is contained in 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 vast difference in power between these similar classes.
Is measurement a unitary operator?
The question of why measurement itself is not unitary is more related to quantum computation. A measurement is a projection on to a basis; in essence, it must “answer” with one or more basis states as the state itself.
What is BPP computer science?
In computational complexity theory, bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded away from 1/3 for all instances.
Can a quantum computer solve P vs NP?
Lieuwe Vinkhuijzen gave a different interpretation of your question: Will quantum computers be able to solve NP-complete problems efficiently? The expected answer is: no. So even in this sense, physical quantum computers won’t enable us to solve NP-complete problems at will.
What is the difference between BQP and BPP?
BQP is defined for quantum computers; the corresponding complexity class for classical computers (or more formally for probabilistic Turing machines) is BPP. Just like P and BPP, BQP is low for itself, which means BQPBQP = BQP.
How is BQP related to bounded error complexity?
In computational complexity theory, bounded-error quantum polynomial time ( BQP) 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 .
Which is the natural corresponding class of BQP?
This class is defined for a quantum computer and its natural corresponding class for an ordinary computer (or a Turing machine plus a source of randomness) is BPP. Just like P and BPP, BQP is low for itself, which means BQP BQP = BQP. Informally, this is true because polynomial time algorithms are closed under composition.
Is there such a thing as a BQP complete problem?
A BQP-complete problem Similar to the notion of NP-completeness and other complete problems, we can define a BQP-complete problem as a problem that is in BQP and that every problem in BQP reduces to it in polynomial time. Here is an intuitive BQP-complete problem, which stems directly from the definition of BQP.