Scaling and Better Approximating Quantum Fourier Transform by Higher Radices
IEEE Transactions on Computers
| Hi-index | 0.00 |
We present the role that spectral methods play in the developmentof the most impressive quantum algorithms, such as thepolynomial time number factoring algorithm by Shor. While thefast transform algorithms reduce the number of operations neededin obtaining the transforms from O(2^2n) to O(n^2n), quantumtransforms are in comparison super-fast. The Quantum FourierTransform can be performed in O(n^2) time, while the specificcases of Walsh-Hadamard and Chrestenson Transforms requireonly O(n) operations. We derive Quantum Fourier Transform overnon-binary quantum digits using the Chrestenson gate, which canserve as a basic block for quantum transforms.implication of making the number factorization-basedencryption methods breakable. Several classes of quantumtransform implementations are presented. Further, weconsider the issue of the multiple-valued logic quantumgates. As most quantum computing results have so far beenobtained for binary logic, we consider the problem of thedesign of non-binary quantum logic gates and demonstratethe usefulness of the Chrestenson gate, which can serve asa basic block for quantum transforms.