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Is the Deutsch-Jozsa problem hard or easy?
The Deutsch–Jozsa problem is specifically designed to be easy for a quantum algorithm and hard for any deterministic classical algorithm.
Is the Deutsch Jozsa algorithm constant or balanced?
The function takes n-digit binary values as input and produces either a 0 or a 1 as output for each such value. We are promised that the function is either constant (0 on all outputs or 1 on all outputs) or balanced (returns 1 for half of the input domain and 0 for the other half). The task then is to determine if
How is the Jozsa algorithm related to EQP?
More formally, it yields an oracle relative to which EQP, the class of problems that can be solved exactly in polynomial time on a quantum computer, and P are different.
What is the history of the Deutsch-Jozsa algorithm?
History. The Deutsch–Jozsa Algorithm generalizes earlier (1985) work by David Deutsch, which provided a solution for the simple case. Specifically we were given a boolean function whose input is 1 bit, and asked if it is constant. The algorithm as Deutsch had originally proposed it was not, in fact, deterministic.
Which is a special case of the Deutsch algorithm?
Deutsch’s algorithm is a special case of the general Deutsch–Jozsa algorithm. We need to check the condition f ( 0 ) = f ( 1 ) {\\displaystyle f(0)=f(1)} .
When is the Deutsch Jozsa algorithm a special case?
If it is 0, the function is constant, otherwise the function is balanced. The algorithm builds on an earlier 1985 work by David Deutsch which gave a similar algorithm for the special case when the function f (x1) has one 0-1 valued variable instead of n. It preceded other quantum algorithms such as Shor’s algorithm and Grover’s algorithm.
Why is the Deutsch oracle problem so interesting?
The Deutsch oracle problem is interesting to complexity theorists because the quantum algorithm only has to query the black box once, but the classical algorithm has to query it twice.