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...
