REVERSIBLE SYSTOLIC ARRAYS: m-ARY BIJECTIVE SINGLE-INSTRUCTION MULTIPLE-DATA (SIMD) ARCHITECTURES AND THEIR QUANTUM CIRCUITS

Abstract

New type of m-ary systolic arrays called reversible systolic arrays is introduced in this paper. The m-ary quantum systolic architectures' realizations and computations of the new type of systolic arrays are also introduced. A systolic array is an example of a single-instruction multiple-data (SIMD) machine in which each processing element (PE) performs a single simple operation. Systolic devices provide inexpensive but massive computation power, and are cost-effective, high-performance, and special-purpose systems that have wide range of applications such as in solving several regular and computebound problems containing repetitive multiple operations on large arrays of data. Similar to the classical case, information in a reversible and quantum systolic circuit flows between cells in a pipelined fashion, and communication with the outside world occurs only at the boundary cells. Since basic PEs used in the construction of arithmetic systolic arrays are the add-multiply cells, the results introduced in this paper are general and apply to a very wide range of add-multiply-based systolic arrays. Since the reduction of power consumption is a major requirement for the circuit design in future technologies, such as in quantum computing, the main features of several future technologies will include reversibility. Consequently, the new systolic circuits can play an important task in the design of future circuits that consume minimal power. It is also shown that the new systolic arrays maintain the high level of regularity while exhibiting the new fundamental bijectivity (reversibility) and quantum superposition properties. These new properties will be essential in performing super-fast arithmetic-intensive computations that are fundamental in several future applications such as in multi-dimensional quantum signal processing (QSP). IntroductionDue to the anticipated failure of Moore's law around the year 2020, quantum computing will hopefully play an increasingly crucial role in building more compact and less power consuming computers. 1,7,23,30,65,66,82 Due to this fact, and because all quantum computer gates (i.e., fundamental building blocks) should be reversible, [1][2][3]7,9,18,23,30,57,65,66,72,82 reversible computing will have an increasingly more existence in the future design of regular, compact, and universal circuits. (k, k) reversible circuits are circuits that have the same number of inputs k and outputs k and are one-to-one mappings between vectors of inputs and outputs, thus the vector of input states can be always uniquely reconstructed from the vector of output states. 1,9,18,23,57,66 As was proven in Ref. 57, it is a necessary (but not sufficient) condition for not dissipating power in any physical circuit that all system circuits must be built using fully reversible logical components. For this reason, different technologies have been studied to implement reversible logic in hardware like adiabatic CMOS, 78 optical, 72 and quantum. 1,66 Fully reversible digital systems will greatly reduce the power co...

Parallel Bijective Processing of Regular Nano Systolic Grids via Carbon Field Emission Controlled - Switching

“…After the substitution of Equations (3) - (11) in Equation (2), and after the minimization of the terms according to the axioms of the Galois field, one obtains the following Equations:…”

“…Systolic arrays are single-instruction multiple-data (SIMD) machines in which each processing element (PE) is only capable of performing a simple single operation [2,27,28]. In systolic computing, computations are synchronized by a global clock signal, and data flows in a rhythmic fashion from the host through the array where data items are pumped out from a memory.…”

“…This is due to the fact that reversible logic leads to the design of computer systems that consume much less power and occupy much less space [1,3,9,20,29,32,34], where it was shown that if all physical subcircuits were designed to be reversible then the whole system composed of inter-connecting these reversible sub-systems will minimize its operational need for power consumption [29]. For this purpose, various important technologies have been investigated to implement reversibility such as adiabatic CMOS circuits [36], optical computing [4] and quantum computation circuits and systems [1,2,4,15,20,[32][33][34].…”

“…Systolic systems provide parallel computation and inexpensive computing power, and provide a model of computation which captures the important features of parallelism, interconnection sub-systems and pipelining, which has been utilized in wide range of implementations [2,27,28,38], and provide a good model of computation for investigating concurrent algorithms for VLSI circuits and systems.…”

“…Recently, carbon nanotubes have attracted much attention not only for their unique morphologies and relatively small dimensions, but also for their potential applications in several current and emerging technologies [8,[16][17][18]. CNT is made from graphite that is shaped in three forms within nano dimensions: (1) Carbon nanoball (or buckyball) with the shape of a soccer ball, (2) Carbon nanotube that is shaped as multi-wall CNT (MWCNT) and single-wall CNT (SWCNT), and (3) Carbon nanocoil. Field electron emission is defined as electron emission under the influence of the applied electric field from the surface of a cathode which is highly dependent upon the emitting material work function [10,21,23,25].…”