__Keywords:__bit-stream computing associative memory quantum computers

G. M. Alakoz, A. S. Dobrotvorsky

Key feature of quantum computing lies in the fact that they are based on coherent superposition of 2R linearly independent boolean states, which is possible only in a quantum system of R two-level quantum elements (qubits), and cannot be reproduced at macrolevel. Thanks to this fact, operation in the quantum computing corresponds to rotation in 2R-dimensional Hilbert space of states and therefore R q-bit quantum computing device can perform 2R operations simultaneously. The main argument for quantum computers bases on the fact that quantum superposition description in the traditional computer engineering requires to set 2R complex numbers, so that when R=100 (2R≈1030) such a task becomes intractable technical problem. Hence it appears that the instrumental platform, ensuring quantum computers usage, can only be quantum computer itself.
Indeed the problem lies not in macroconditions for such a superposition creation, but in fact that it is linearly indistinguishable at the microelectronics physical processes level so it is calculated by the principle of «wired OR», following which it is impossible to determine "correct" response state at the output. But except the physical control level there are circuit and systems engineering control levels in microelectronics, on which is possible to select any of multiple memory states. Particularly in associative memory multiple response is not mixed by the principle of «wired OR» at the output, so that prerequisites for its usage as macroscopic analog of q-bit computing organization are established.
To confirm this fact two bit-stream addition schemes were used. One of which processes symbolic formatted data and theoretically provides any calculation accuracy, while the other one processes integer data preserving digital-analog converter specificity. Significantly that in both cases ambiguous response is inevitable, and its proper elimination ensures correct operation conditions of corresponded bit-stream operational units.
In the first case the associative q-bit analog is gained on the basis of adding Turing machine, operating with symbolic format of input and output operands. In this case, as in «q-bit», it is necessary to initiate two memory cells «simultaneously», which will store two sum symbol Si values, representing two «transfer unit» from previous decade indicator (e–) values: Si/e–=0 and Si/e–=1. However in contrast to q-bit both associative memory responses are not mixed in linear superposition and are separated in space.
In the second case so-called digital analogs were used, which are devices the structure and operational principle of which corresponds with investigating object or with solving mathematical equations. In such an approach computing organization inherent to analog computers is preserved, however, physical quantities such as voltage, current and charges on capacitors are replaced by digital equivalents represented by streams of «zeros» and «unities». As a result it is succeeded to improve computing accuracy and noise immunity which are stumbling block to use analog computers.
The basic element of digital analogs is digital integrator which is usually presented by integer accumulators or counters, in which transfers to high-order bit form functional output. As in bit-stream associative memory, bit-stream counters realization specificity is determined by obligatory one cycle delay while transforming data passage through each bit-processor. As a result feedback circuits, ensuring triggers with complementing input performance, form two-cycle loops, which decrease «unities» cutoff frequency feed to complementing input two times. Therefore such a negative effect allows combining two independently performing by even and odd cycles counters, which content can be divided by independent result states reading circuits, on the same equipment that is in space.
The obtained simulation data shows:
1. Both in quantum and in traditional computers large-scale boolean states superposition generation is and by all appearance will be rather intricate technical problem, although by different reasons. That is why it is possible to expect that even in quantum computer it will have to resort to current task decomposition, decreasing coherent boolean states superpositions space dimension. As a result computing paralleling coefficients will be decreased and there will appear enumerative procedures, which are peculiar to all computers performing with limited memory without exception.
2. Traditional for neurocomputers associative methods and tools for organization of computing with multiple space-time response may be used as quantum computers with independent bitwise q-bit output response macroanalogs. This fact simplifies both instrumental platform building and practical mastering.
3. Drawn analogy shows that for quantum computer the basic computing paralleling mode is SIMD, what is determined by homogeneous q-bits response to turn in 2R-dimensional Hilbert states space. (SIMD – computing organization in which «single instruction stream – multiple data stream»). Hence, increasing paralleling coefficient of classical computers assembler instructions microprogram algorithm it is possible to increase q-bit output response dimension of PD-associative symbolic quantum computers simulators.
4. It should be spoken not about quantum and non-quantum computers, but about large- and small-scale quantum computers. The first of which is determined by boolean states superposition physical realization level, while the second one is determined by more expensive circuit or systems engineering level.
5. Neural MIMD-bit-stream computing technology requires very simple and already being implemented in practice, a hardware platform based on the 3 – 8 bit qubit registers, controlled from outside by the system of orthogonal space-time switching on the "short-range" and distributed system of status identification of each register, which can accumulate and dissipate excess heat.

References: