Is PH a Pspace?
PH contains almost all well-known complexity classes inside PSPACE; in particular, it contains P, NP, and co-NP. However, there is some evidence that BQP, the class of problems solvable in polynomial time by a quantum computer, is not contained in PH.
What is BQP complexity?
BQP, in computational complexity theory, stands for “Bounded error, Quantum, Polynomial time”. It denotes the class of problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/4 for all instances.
Is BQP equal to NP?
The relation between BQP and NP is not known, though we do know that NP is not contained in BQP. 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.
Is BQP in pspace?
In the next section we will prove that BQP ⊆ PSPACE. It is believed that BQP contains problems that aren’t in BPP, for example factoring large integers: this problem (or rather decision-version thereof) is in BQP because of Shor’s algorithm, and is generally believed not to be in BPP.
What is quantum query?
Similar to the case of graphing problems, the quantum query complexity of a black-box problem is the smallest number of queries to the oracle that are required in order to calculate the function.
Who invented complexity theory?
This conceptual framework, developed by Descartes in the 17th century, was made complete by the genius of Isaac Newton, who developed a comprehensive system of mathematics that would synthesize and validate the works of Copernicus, Kepler, Galileo, and Descartes.
Is a quantum computer a Turing machine?
The Church-Turing limit restricts all current computation, including quantum computers, to rational number computation. This is because quantum computer designs (still not scalable even with high parallelism), are still Turing machines, which are limited by Turing machine constraints.
Who is the father of complexity theory?