We report experimental implementation of discrete Fourier transformation(DFT) on a nuclear magnetic resonance(NMR) quantum computer. Experimental results agree with theoretical results. Using the pulse sequences we introduced, DFT can be realized on any L-bit quantum number in principle.
A quantum Fourier transform (QFT) has been implemented on a three qubit nuclear magnetic resonance (NMR) quantum computer to extract the periodicity of an input state. Implementation of a QFT provides a first step towards the realization of Shor's factoring and other quantum algorithms. The experimental implementation of the QFT on a periodic state is presented along with a quantitative measure of its efficiency measured through state tomography. Experimentally realizing the QFT is a clear demonstration of the ability of NMR to control quantum systems.
We report the realization of a nuclear magnetic resonance quantum computer which combines the quantum Fourier transform with exponentiated permutations, demonstrating a quantum algorithm for order finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.
The remarkable capability of quantum Fourier transformation (QFT) to extract the periodicity of a given periodic function has been exhibited by using nuclear magnetic resonance (NMR) techniques. Two separate sets of experiments were performed. In a full QFT, the periodicity were validated with state tomography and fidelity measurements. For a simplified QFT, the three-qubit pseudo-pure state was created by introducting an additional observer spin, and the spectra recorded on the observer spin showed intuitively the power of QFT\ to find the periodicity. Experimentally realizing the QFT provides a critical step to implement the renowned Shor's quantum factoring algorithm and many other algorithms. Moveover, it can be applied to the study of quantum chaos and other quantum information processing.
At present, it is one of various effective approaches for quantum algorithm to using the nuclear magnetic resonance (NMR) experiment technology. NMR uses radio frequency (RF) electromagnetic pulses to rotate the spins. By tuning the frequency of the RF-field to the precession frequency of a particular spin, the power of the applied pulse controls how much the spin will rotate. The axis of the rotation is determined by the direction of the applied RF-field. By selecting the appropriate RF pulses, arbitrary single-spin rotation can be carried out. In other words, using RF pulses we can perform any single-qubit operation. Communication between the qubits is accomplished through the spin-spin interaction in model. A simulation approach in this paper is described to realize quantum Fourier transform algorithm (QFT).