Inverse quantum Fourier transform
The inverse quantum Fourier transform is the inverse unitary transformation of the quantum Fourier transform, mapping encoded phase information toward computational-basis information.
Building Quantum Software with Python
The inverse quantum Fourier transform is the inverse unitary transformation of the quantum Fourier transform, mapping frequency-encoded amplitudes back to the corresponding computational-basis representation.
- How it is used
- Converts phase-encoded frequencies into measurable magnitude patterns for frequency decoding, phase estimation, and function-value encoding.
- How deep it goes
- Explains Fourier-basis inner products, classical simulation, gate construction, and digit-by-digit recovery without a rigorous circuit-equivalence proof.
- Examples
- Uses F13 on four qubits, three-qubit frequencies 4 and 4.7, phase-estimation circuits, and knapsack value and weight registers.
- What you can do after
- Apply it via QuantumCircuit methods to decode phase-encoded frequencies and append inverse Fourier transforms to selected registers.
Read how Building Quantum Software with Python explains inverse quantum Fourier transform →
Quantum Programming in Depth
The inverse quantum Fourier transform is the inverse unitary transformation of the quantum Fourier transform, mapping encoded phase information back toward computational-basis information.
- How it is used
- Uses inverse QFT in quantum phase estimation to convert eigenphase information into measurable computational-basis outcomes.
- How deep it goes
- Defines inverse QFT as the QFT adjoint and traces its role in phase estimation, but does not derive its gate decomposition.
- Examples
- Demonstrates two control qubits, controlled-U applications, big-endian phase bits, and measurement after inverse QFT.
- What you can do after
- Apply inverse QFT to a phase-encoded control register and read out an eigenphase approximation by measurement.
Read how Quantum Programming in Depth explains inverse quantum Fourier transform →
Related concepts
- quantum phase estimationused by · Quantum phase estimation is a quantum algorithm that estimates the eigenphase of a unitary operator given a corresponding eigenstate.
- quantum amplitude estimationused by · Quantum amplitude estimation is a quantum algorithm that estimates the probability or count associated with marked outcomes by estimating a rotation angle of a Grover operator.
- function encodingused by · Function encoding is a technique for representing a function's inputs and outputs in linked quantum registers.
- Hadamard gateuses · The Hadamard gate is a single-qubit quantum gate that transforms computational-basis states into equal superpositions with relative phase differences.
- quantum Fourier transformcontrasts with · The quantum Fourier transform is a quantum circuit implementing the discrete Fourier transform on the amplitudes of a quantum state.
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