imclab / deutsch-josza

Simulate the Deutsch-Josza quantum algorithm.

Deutsch-Josza Quantum Algorithm Simulation

dj is a Matlab function that simulates the Deutsch-Josza quantum algorithm. quarter_dj can simulate the algorithm for 3/4-balanced functions.

Usage

These functions have the following syntax:

dj(n, f)
quarter_dj(n, f)

To use these functions in the Matlab prompt, simply run Matlab in the same directory, and then call these functions.

>> dj(5, @(x) 1)

ans =

CONST

In this example, we applied the constant function to the algorithm. We put n=5 so the function must return 0 or 1 for any input in 0,...,2^5 - 1. For this function that always return 1, the algorithm detected that f was constant. Here is another example that f is balanced.

>> dj(8, @(x) rem(x, 2))

ans =

BALANCED

The function

@(x) rem(x, 2)

is balanced because it returns 1 if x is odd, and it return 0 if x is even.

for 3/4-balanced functions

quarter_dj can be used exactly the same as dj.

>> quarter_dj(5, @(x) 0)

ans =

CONST

We prepared quarter_balanced function that simulates a 3/4-balanced function.

>> quarter_dj(5, @quarter_balanced)

ans =

BALANCED

Since it has error rate 1/4, it sometimes output CONST for 3/4-balanced functions.

>> quarter_dj(5, @quarter_balanced)

ans =

CONST