A Quantum Waveguide Array Generator For Performing Fourier Transforms


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Recently, quantum computing has gained attention as a possible means of greatly increasing the speed of certain calculations when compared with traditional, binary computing. A key part of many quantum computing algorithms is the performance of a Fourier transform. Inspired by ideas from electromagnetics and acoustics, we propose a quantum waveguide array generator that can perform such operations quickly but with but classical approach that uses the analog properties of waves and rather than the qubit concept. The proposed device is illustrated in Fig. 1(a). The first split is one-half of an Aharonov-Bohm loop (such loops are used to create wave interference in nanostructures), each arm of which is split once again to create 4 radiating elements. Each waveguide should emit a wave with the same relative phase (in the absence of a magnetic field). Hence, an interference pattern, representative of the Fourier transform of the input sources, should be formed at any detection plane to the right of the sources. The figure shows the interference pattern that arises from a simulation of such an array, in which Schrödinger’s equation is solved on a finite-difference grid using a stabilized variant of the transfer-matrix technique. Pictured is a region 1.4 mm long by 0.6 mm wide. All the quantum wire segments are each 0.04 mm wide, allowing a single propagating mode when the Fermi energy is 80 meV. The diameter of the smaller semicircles is 4 times this, while the larger semicircle is 8 times this width. When all the elements are driven in phase and have constant amplitude, the Fourier frequency is zero, resulting in a peak at _ = π /2. Such a dominant peak is evident in the figure and labeled A. The use of only a few radiators causes significant side lobes to be present, however the reduction of these for any given number of elements have been extensively studied for both antenna arrays and for surface acoustic waves. The array pattern can be shifted if we now use a nanomagnet or an electrostatic structure to shift the relative phase of the sources. We have chosen to incorporate the former, using a modest magnetic field to controllably change the angle at which the dominant lobe appears, as shown in Fig. 1(b). A modest field can sweep the pattern to almost any desired angle. Similar changes could be achieved by application of a gate voltage. For detection of this interference pattern, one could use a scanning probe, as has been recently done in the case of a quantum point contact1, to probe the interfering wave functions, or one could construct an array of quantum point contacts to detect the deflected wave pattern. Detecting of this interference pattern is likely to be difficult, however, this detection problem is one faced by any approach to quantum computing.

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Journal: TechConnect Briefs
Volume: 2, Technical Proceedings of the 2003 Nanotechnology Conference and Trade Show, Volume 2
Published: February 23, 2003
Pages: 210 - 213
Industry sectors: Advanced Materials & Manufacturing | Sensors, MEMS, Electronics
Topic: Modeling & Simulation of Microsystems
ISBN: 0-9728422-1-7