Quantum Fourier transform
The quantum Fourier transform is a quantum circuit implementing the discrete Fourier transform on the amplitudes of a quantum state.
Building Quantum Software with Python
The quantum Fourier transform is a quantum algorithm that applies the Fourier transform to amplitudes of a quantum state, converting encoded phase relationships into measurable amplitude patterns.
- How it is used
- Converts phase-encoded periodic information into measurable magnitude patterns and prepares useful quantum-state distributions.
- How deep it goes
- Works from a one-qubit Hadamard example through Fourier bases and executable QFT/IQFT circuits, while deferring a rigorous equivalence proof.
- Examples
- Uses a π/3 single-qubit phase encoding, Fourier-basis state vectors, four-qubit QFT circuits, and phased discrete sinc states.
- What you can do after
- Build it from scratch as QFT and IQFT circuits using Hadamard gates, controlled phase rotations, and optional register swaps.
Read how Building Quantum Software with Python explains quantum Fourier transform →
Quantum Programming in Depth
The quantum Fourier transform is the quantum analogue of the discrete Fourier transform, mapping amplitudes between computational bases.
- How it is used
- Supports phase estimation by transforming amplitude-encoded information into phase-encoded information.
- How deep it goes
- Defines one- and two-qubit behavior but stops short of the general form and arbitrary-qubit implementation.
- Examples
- Uses the one-qubit Hadamard gate and one- or two-bit phase-precision scenarios as concrete cases.
- What you can do after
- Apply QFT as a phase-estimation building block while recognizing its classical input-output overhead.
Read how Quantum Programming in Depth explains quantum Fourier transform →
Related concepts
- discrete Fourier transformequivalent to · The discrete Fourier transform converts a finite sequence of sampled values into its frequency components.
- inverse Fourier transformequivalent to · The inverse discrete Fourier transform is the mathematical operation that reconstructs a discrete signal from its frequency-domain coefficients.
- quantum parallelismuses · Quantum parallelism is the ability of a quantum instruction to perform corresponding elementary operations simultaneously across many affected value pairs.
- inverse quantum Fourier transformcontrasts with · The inverse quantum Fourier transform is the inverse unitary transformation of the quantum Fourier transform, mapping encoded phase information toward computational-basis information.
- Shor's algorithmused by · Shor's algorithm is a quantum algorithm that efficiently factors integers and solves discrete logarithms using quantum period finding.
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