Quantum Fourier Transform (QFT) and Inverse QFT (IQFT) implementation.
The QFT is a fundamental quantum algorithm that transforms quantum states into their frequency domain representation. It is widely used in various quantum algorithms, including Shor's factoring algorithm and quantum phase estimation.
This namespace provides functions to create QFT and IQFT circuits for a given number of qubits.
Quantum Fourier Transform (QFT) and Inverse QFT (IQFT) implementation. The QFT is a fundamental quantum algorithm that transforms quantum states into their frequency domain representation. It is widely used in various quantum algorithms, including Shor's factoring algorithm and quantum phase estimation. This namespace provides functions to create QFT and IQFT circuits for a given number of qubits.
(inverse-quantum-fourier-transform-circuit n)Create an Inverse Quantum Fourier Transform (IQFT) circuit.
The IQFT undoes the QFT and is critical for quantum phase estimation in Shor's algorithm and other quantum algorithms.
Parameters:
Returns: Quantum circuit implementing the complete IQFT
Example: (def iqft-circuit (inverse-quantum-fourier-transform-circuit 3))
Create an Inverse Quantum Fourier Transform (IQFT) circuit. The IQFT undoes the QFT and is critical for quantum phase estimation in Shor's algorithm and other quantum algorithms. Parameters: - n: Number of qubits Returns: Quantum circuit implementing the complete IQFT Example: (def iqft-circuit (inverse-quantum-fourier-transform-circuit 3))
(quantum-fourier-transform-circuit n)Create a Quantum Fourier Transform (QFT) circuit.
Creates a complete QFT circuit that transforms computational basis states into their quantum Fourier transformed states. The QFT is the quantum analog of the discrete Fourier transform and is essential for many quantum algorithms including Shor's factoring algorithm and quantum phase estimation.
The QFT algorithm consists of:
Parameters:
Returns: Quantum circuit implementing the complete QFT
Example: (def qft-circuit (quantum-fourier-transform-circuit 3)) ;=> Complete 3-qubit QFT circuit
Create a Quantum Fourier Transform (QFT) circuit. Creates a complete QFT circuit that transforms computational basis states into their quantum Fourier transformed states. The QFT is the quantum analog of the discrete Fourier transform and is essential for many quantum algorithms including Shor's factoring algorithm and quantum phase estimation. The QFT algorithm consists of: 1. Apply Hadamard gate to each qubit 2. Apply controlled rotation gates with angles π/2^k 3. Reverse qubit order with SWAP gates Parameters: - n: Number of qubits Returns: Quantum circuit implementing the complete QFT Example: (def qft-circuit (quantum-fourier-transform-circuit 3)) ;=> Complete 3-qubit QFT circuit
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