Concise Guide to Quantum Computing by Sergei Kurgalin & Sergei Borzunov

Author:Sergei Kurgalin & Sergei Borzunov
Language: eng
Format: epub
ISBN: 9783030650520
Publisher: Springer International Publishing

Components of Fourier transform are calculated according to the formula

(8.10)

for all , or

(8.11)

After algebraic transformations, let us write the components of the vector in the following form:

(8.12)

The implementation of a parallel program based on the obtained expression for is easy. Using a possible parallelism over the variable l, there is calculated the inner sum

(8.13)

for . The values are then multiplied by ; then another FFT with the possibility of parallelism over the variable L is applied, where . The values form the final answer .

The Quantum Fourier Transform is a component of many quantum algorithms, including the quantum algorithm of the decomposition of a compound number into prime multipliers, the algorithm of phase evaluation for finding unitary operator eigenvalues, etc.

Let us consider the orthonormalized computational basis

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