Another Way to Perform the Quantum Fourier Transform in Linear Parallel Time
نویسنده
چکیده
Abstract. We exhibit a quantum circuit that performs the Quantum Fourier Transform on n qubits in O(n) depth. Thus, a parallel quantum computer can carry out the QFT in linear time. Griffiths and Niu have already shown this, so this paper is little more than an exercise in quantum circuit design; but perhaps it illustrates a worthwhile idea. We also speculate as to whether the QFT might be in the class QNC of problems solvable in logarithmic parallel time.
منابع مشابه
Another Way to Perform the Quantum
We exhibit a quantum circuit that performs the Quantum Fourier Transform on n qubits in O(n) depth. Thus, a parallel quantum computer can carry out the QFT in linear time. Griiths and Niu have already shown this, so this paper is little more than an exercise in quantum circuit design; but perhaps it illustrates a worthwhile idea. We also speculate as to whether the QFT might be in the class QNC...
متن کاملSampling Rate Conversion in the Discrete Linear Canonical Transform Domain
Sampling rate conversion (SRC) is one of important issues in modern sampling theory. It can be realized by up-sampling, filtering, and down-sampling operations, which need large complexity. Although some efficient algorithms have been presented to do the sampling rate conversion, they all need to compute the N-point original signal to obtain the up-sampling or the down-sampling signal in the tim...
متن کاملQuantum Algorithms to Solve the Hidden Shift Problem for Quadratics and for Functions of Large Gowers Norm
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor’s algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular exponentiation function. In a generalization of this idea, quantum Fourier sampling can be used to discover hidden subgroup structures of some functions much mo...
متن کاملDetecting buried channels using linear least square RGB color stacking method based on deconvolutive short time Fourier transform
Buried channels are one of the stratigraphic hydrocarbon traps. They are often filled with a variety of porous and permeable sediments so they are important in the exploration of oil and gas reservoirs. In reflection seismic data, high-frequency components are sensitive to the channel thickness, whereas, low-frequency components are sensitive to the channel infill materials. Therefore, decompos...
متن کاملA Comparison Between Fourier Transform Adomian Decomposition Method and Homotopy Perturbation ethod for Linear and Non-Linear Newell-Whitehead-Segel Equations
In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...
متن کامل