The Deutsch-Jozsa algorithm is a quantum algorithm, proposed by David Deutsch and Richard Jozsa in It was one of first examples of a. Ideas for quantum algorithm. ▫ Quantum parallelism. ▫ Deutsch-Jozsa algorithm. ▫ Deutsch’s problem. ▫ Implementation of DJ algrorithm. The Deutsch-Jozsa algorithm can determine whether a function mapping all bitstrings to a single bit is constant or balanced, provided that it is one of the two.

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First, do Hadamard transformations on n 0s, forming all possible inputs, and a single 1, which will be the answer qubit. Archived from the original on A Hadamard transform is applied to each bit to obtain the state.

Applying the quantum oracle gives.

## Deutsch–Jozsa algorithm

Applying this function to our current state we obtain. Read the Docs v: If it is 0, the function is constant, otherwise the function is balanced. Nielsen and Isaac L. It preceded other quantum algorithms such as Shor’s algorithm and Grover’s algorithm.

The Deutsch-Jozsa quantum algorithm produces an answer that is always correct with just 1 evaluation of f. References David Deutsch, Richard Jozsa.

The algorithm is as follows. Charge qubit Flux qubit Phase qubit Transmon. The algorithm builds on an earlier work by David Deutsch which gave a similar algorithm for the special case when the function aogorithm x1 has one valued variable instead of n.

## Deutsch-Jozsa algorithm

At this point the last qubit may be ignored. Next, run the function once; this XORs the result with the answer qubit. This is partially based on the public domain information found here: The best case occurs where the function is balanced and the first two output values that happen to be selected are different.

We apply a Hadamard transform to each qubit to obtain. A constant function always maps to either 1 or 0, and a balanced function maps to 1 for half of the inputs and maps to 0 for the other half.

Finally, do Hadamards on the n inputs again, and measure the answer qubit. It is also a deterministic algorithmmeaning that it always produces an answer, and that answer is always correct.

Unlike Deutsch’s Algorithm, this algorithm required two function evaluations instead of only one. The Deutsch—Jozsa Algorithm generalizes earlier work by David Deutsch, which provided a solution for the simple case. Views Read Edit View history.

### [] An elementary derivation of the Deutsch-Jozsa algorithm

In the Deutsch-Jozsa problem, we are given a black box quantum computer known as an oracle that implements some function f: Specifically we were given a boolean function whose input is 1 bit, f: Further improvements to the Deutsch—Jozsa algorithm were made by Cleve et al. The motivation is to show a black box problem that can be solved efficiently by a quantum computer with no error, whereas a deterministic classical computer would need a large number of queries to the black box to solve the problem.

The algorithm as Deutsch had originally proposed it was not, in fact, deterministic. For a conventional deterministic algorithm, 2n-1 evaluations of f algorithhm be required in the worst case.

This matrix is exponentially large, and thus even generating the program will take exponential time. The black box deutdch n bits x1, x2, Retrieved from ” https: The algorithm was successful with a probability of one half.