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Inverse Fourier transform

As explained in Building Quantum Software with Python

The inverse discrete Fourier transform is the mathematical operation that reconstructs a discrete signal from its frequency components.

The inverse discrete Fourier transform reconstructs a length-N discrete signal from frequency components by summing complex amplitudes after angle rotations. In the quantum formulation, the QFT performs the same computation up to a constant, while the IQFT uses a negative sign in its exponents. section 7.3.2

A practical simulation represents the input as a state vector, constructs normalized Fourier basis states, and computes one inner product per output entry. Each resulting amplitude corresponds to the matching Fourier basis frequency. section 7.3.2

How Building Quantum Software with Python covers it

How deep it goes
Explains basis construction and inner-product computation, then stops short of detailing the full controlled-rotation circuit.
Examples
Uses normalized Fourier-basis vectors and a Python function that transforms each state entry through an inner product.
What it assumes
Assumes complex-number sequences and quantum state vectors while introducing Fourier bases through executable classical code.
What you can do after
Build it from scratch using Fourier-basis generation and inner products over a complex state vector.
How it connects
Connects inverse DFT with QFT, IQFT, Fourier basis states, state vectors, complex-number rotations, and controlled phase rotations.
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This explainer was generated by Manning's knowledge graph from the text of Building Quantum Software with Python. The section links point to the parts of the book it draws on.