Purpose The purpose of this paper is to introduce an approach form‐valued classical and non‐classical (reversible and quantum) optical computing. The developed approach utilizes new multiplexer‐based optical devices and circuits within switch logic to perform the required optical computing. The implementation of the new optical devices and circuits in the optical regular logic synthesis using new lattice and systolic architectures is introduced, and the extensions to quantum optical computing are also presented. Design/methodology/approach The new linear optical circuits and systems utilize coherent light beams to perform the functionality of the basic logic multiplexer. The 2‐to‐1 multiplexer is a basic building block in switch logic, where in switch logic a logic circuit is implemented as a combination of switches rather than a combination of logic gates as in the gate logic, which proves to be less‐costly in synthesizing wide variety of logic circuits and systems. The extensions to quantum optical computing using photon spins and the collision of Manakov solitons are also presented. Findings New circuits for the optical realizations ofm‐valued classical and reversible logic functions are introduced. Optical computing extensions to linear quantum computing using photon spins and nonlinear quantum computing using Manakov solitons are also presented. Three new multiplexer‐based linear optical devices are introduced that utilize the properties of frequency, polarization and incident angle that are associated with any light‐matter interaction. The hierarchical implementation of the new optical primitives is used to synthesize regular optical reversible circuits such as them‐valued regular optical reversible lattice and systolic circuits. The concept of parallel optical processing of an array of input laser beams using the new multiplexer‐based optical devices is also introduced. The design of regular quantum optical systems using regular quantum lattice and systolic circuits is introduced. New graph‐based quantum optical representations using various types of quantum decision trees are also presented to efficiently represent quantum optical circuits and systems. Originality/value The introduced methods for classical and non‐classical (reversible and quantum) optical regular circuits and systems are new and interesting for the design of several future technologies that require optimal design specifications such as super‐high speed, minimum power consumption and minimum size such as in quantum computing and nanotechnology.
Purpose The purpose of this paper is to introduce an approach form‐valued classical and non‐classical (reversible and quantum) optical computing. The developed approach utilizes new multiplexer‐based optical devices and circuits within switch logic to perform the required optical computing. The implementation of the new optical devices and circuits in the optical regular logic synthesis using new lattice and systolic architectures is introduced, and the extensions to quantum optical computing are also presented. Design/methodology/approach The new linear optical circuits and systems utilize coherent light beams to perform the functionality of the basic logic multiplexer. The 2‐to‐1 multiplexer is a basic building block in switch logic, where in switch logic a logic circuit is implemented as a combination of switches rather than a combination of logic gates as in the gate logic, which proves to be less‐costly in synthesizing wide variety of logic circuits and systems. The extensions to quantum optical computing using photon spins and the collision of Manakov solitons are also presented. Findings New circuits for the optical realizations ofm‐valued classical and reversible logic functions are introduced. Optical computing extensions to linear quantum computing using photon spins and nonlinear quantum computing using Manakov solitons are also presented. Three new multiplexer‐based linear optical devices are introduced that utilize the properties of frequency, polarization and incident angle that are associated with any light‐matter interaction. The hierarchical implementation of the new optical primitives is used to synthesize regular optical reversible circuits such as them‐valued regular optical reversible lattice and systolic circuits. The concept of parallel optical processing of an array of input laser beams using the new multiplexer‐based optical devices is also introduced. The design of regular quantum optical systems using regular quantum lattice and systolic circuits is introduced. New graph‐based quantum optical representations using various types of quantum decision trees are also presented to efficiently represent quantum optical circuits and systems. Originality/value The introduced methods for classical and non‐classical (reversible and quantum) optical regular circuits and systems are new and interesting for the design of several future technologies that require optimal design specifications such as super‐high speed, minimum power consumption and minimum size such as in quantum computing and nanotechnology.
The reversible logic has promising applications in emerging computing paradigms, such as quantum computing, quantum dot cellular automata, optical computing, etc. In reversible logic gates, there is a unique one-to-one mapping between the inputs and outputs. To generate a useful gate function, the reversible gates require some constant ancillary inputs called ancilla inputs. Also to maintain the reversibility of the circuits some additional unused outputs are required that are referred to as the garbage outputs. The number of ancilla inputs, the number of garbage outputs and quantum cost plays an important role in the evaluation of reversible circuits. Thus minimizing these parameters are important for designing an efficient reversible circuit. Reversible circuits are of highest interest in optical computing, quantum dot cellular automata and quantum computing. The quantum gates perform an elementary unitary operation on one, two or more two-state quantum systems called qubits. Any unitary operation is reversible in nature, and hence, quantum networks are also reversible, to conclude the quantum computers must be built from reversible logic components. The main contribution of this dissertation is the design exploration and application of reversible circuits in emerging nanotechnologies. The emerging technologies explored in this work are 1) Optical quantum computing 2) Quantum computing. The first contribution of this dissertation is Mach-Zehnder interferometer based design of all optical reversible binary adder. The all optical reversible adder design is based on two new optical reversible gates referred as optical reversible gate I (ORG-I) and optical reversible gate II (ORG-II) and the existing all optical Feynman gate. The two new reversible gates ORG-I and ORGI-II have been proposed and can implement a reversible adder with a reduced optical cost which is equal to the number of MZI switches required, less propagation delay, and with zero overhead in terms of number of ancilla inputs and the garbage outputs. The proposed all optical reversible adder design based on the ORG-I and ORG-II reversible gates are compared and shown to be better than the other existing designs of reversible adder proposed in the non-optical domain in terms of number of MZI switches, delay, the number of ancilla inputs and the garbage outputs. The proposed all optical reversible adder will be a key component of an all optical reversible arithmetic logical unit (ALU), that is a quite essential component in a wide variety of optical signal processing applications. In the existing literature, the NAND logic based implementation is the only known implementation available for reversible gates and its functions. There is a lack of research in the direction of NOR logic based implementation of reversible gates and functions. The second contribution of this dissertation is the design of NOR logic based n-input and n-output reversible gates, one of which can be efficiently mapped into optical computing using the Mach-Zehnder interferometer (MZI), while the other can be mapped efficiently in optical computing using the linear optical quantum gates. The proposed reversible NOR gates work as a corresponding NOR counterpart of NAND logic based Toffoli gates. The proposed optical reversible NOR logic gates can implement the reversible boolean logic functions with less number of linear optical quantum logic gates with reduced optical cost and propagation delay compared to the implementation using existing optical reversible NAND gates. It is illustrated that an optical reversible gate library having both optical Toffoli gate and the proposed optical reversible NOR gate is superior compared to the library containing only the optical Toffoli gate: (i) in terms of number of linear optical quantum gates when implemented using linear optical quantum computing (LOQC), (ii) in terms of optical cost and delay when implemented using the Mach-Zehnder interferometer. The third contribution of this dissertation is a binary tree-based design methodology for a NxN reversible multiplier. The proposed binary tree-based design methodology for a NxN reversible multiplier performs the addition of partial products in parallel using the reversible ripple adders with zero ancilla bit and zero garbage bit; thereby, minimizing the number of ancilla and garbage bits used in the design. The proposed design methodology shows improvements in terms of number of ancilla inputs and garbage outputs compared to all the existing reversible multiplier designs. The methodology is also extended to the design of NxN reversible signed multiplier based on modified Baugh-Wooley multiplication methodology.
Considering the benefits of Quantum and Optics, if the logic gates in the quantum field and electronic structure are implemented using optical elements, then it will be benefited from advantages of Quantum and design, and these processing circuits can be used in optical computing and quantum computing, genetic processes, and other useful nanotechnology applications. Advantages of reversible logic systems and circuits have drawn a significant interest in recent years as a promising computing paradigm having application in low power CMOS, quantum computing, nanotechnology, and optical computing. In this study, we have introduced reversible optical Double Feynman gate using optical Mach-Zehnder interferometer (MZI) switches with new design. The proposed optical Double Feynman gate will be optical logic gate and reversible. As the proposed gate is a complete one, it can implement all the MZI-based quantum circuits.
Abstract — Reversible logic is one of the most vital issue at present time and it has different areas for its application, those are low power CMOS, quantum computing, nanotechnology, cryptography, optical computing, DNA computing, digital signal processing (DSP), quantum dot cellular automata, communication, computer graphics. It is not possible to realize quantum computing without implementation of reversible logic. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs. This paper provides the basic reversible logic gates, which in designing of more complex system having reversible circuits as a primitive component and which can execute more complicated operations using quantum computers. The reversible circuits form the basic building block of quantum computers as all quantum operations are reversible. This paper presents the data relating to the primitive reversible gates which are available in literature and helps researches in designing higher complex computing circuits using reversible gates.
The biggest problems in system design today, and in the future, are the high rate of power consumption, and the emergence of quantum effects for highly dense ICs. The real challenge is to design reliable systems that consume as little power as possible and in which the signals are processed and transmitted at very high speeds with very high signal integrity. Current tools are used to design ICs using only classical design methodologies that apply conventional synthesis constraints such as area, delay, and power.
As it was proven, physical processes have to be logically reversible in order to reduce (theoretically eliminate) power consumption. Logical reversibility requires that one can obtain the vector of inputs from the vector of outputs (i.e., backward process) as well as the vector of outputs from the vector of inputs (i.e., forward process). Since only ad-hoc methods were used previously for the reversible synthesis of logic functions, and since systematic and efficient reversible logic synthesis methodologies were significantly missing from previous literature, this dissertation provides several original contributions to reversible logic synthesis by providing a set of tools that can be systematically used to synthesize and evaluate logic functions using reversible logic. This includes, among other new results, Reversible Lattice Structures, Reversible Modified Reconstructability Analysis, Reversible Nets, Reversible Decision Diagrams, and Reversible Cascades.
To solve the problem of high signal integrity when processing (computing and transmitting) information using extremely high dense circuits one needs to incorporate the physical quantum mechanical effects that are unavoidable in the nano scales. Since quantum circuits are reversible, and since many of the underlying theorems and formalisms for multiple-valued quantum computing were significantly missing from previous literature, new fundamental foundations for such computations had to be established. These new results include, but not limited to, Quantum Chrestenson Operator, new types of Quantum Decision Trees and Quantum Decision Diagrams as efficient representations for quantum computing, new Composite Basis States, new multiple-valued Einstein-Podolsky-Rosen (EPR) Basis States, and new classes of quantum primitives.
Initial evaluations and conclusions for the comparative advantages and disadvantages of the new reversible and quantum computing methodologies are also provided.
Reversible logic is becoming more and more popular due to the fact that many novel technologies such as quantum computing, low power CMOS circuit design or quantum optical computing are becoming more and more realistic. In quantum computing, reversible computing is the main venue for the realization and design of classical functions and circuits. We present a new approach to synthesis of reversible circuits using Kronecker Functional Lattice Diagrams (KFLD). Unlike many of contemporary algorithms for synthesis of reversible functions that use n×n Toffoli gates, our method synthesizes functions using 3×3 Toffoli gates, Feynman gates and NOT gates. This reduces the quantum cost of the designed circuit but adds additional ancilla bits. The resulting circuits are always regular in a 4-neighbor model and all connections are predictable. Consequently resulting circuits can be directly mapped in to a quantum device such as quantum FPGA [14]. This is a significant advantage of our method, as it allows us to design optimum circuits for a given quantum technology.
Emerging quantum computing technologies are poised to replace standard CMOS logic when the exponential size reduction reaches sub-atomic dimensions. Quantum circuits are reversible and therefore promise the potential of computation without energy loss. This research considers computer aided design (CAD) methods for all major aspects of quantum computing circuit design including logic synthesis, simulation, verification, and testing.
The technologies we investigate include quantum cell automata (QCA) and general quantum circuits (QC), with significantly more emphasis on the later. The recently introduced quantum multi-valued decision diagram (QMDD) provides an efficient method to represent and simulate quantum (and other classical reversible) circuits. A major contribution of this dissertation is the development of a sift-like minimization as well as structure metrics based minimization techniques for QMDD. We have used the enhanced QMDD to efficiently simulate quantum circuits as well as quantum vectors.
Our early investigation of reversible logic is concerned with a virtual implementation that uses a direct translation of relatively complex binary functions into circuits composed of Fredkin reversible gates. This allowed us to project size and speed complexity of complex reversible circuits, although this direct translation approach fails to minimize garbage inputs and outputs. To achieve proper garbage minimization, one must synthesize reversible logic using gate cascades with appropriate optimization methods embedded that attempt to minimize the total number of lines in the circuit. To that end, we developed a novel QMDD-based tool for cascade logic synthesis that utilizes the QMDD minimized variable order for lexicographical synthesis with garbage minimization included as an optimization criterion.
We developed a synthesis tool that investigates the QCA native 3-input majority gates ability to implement complex logic circuits. In particular, we explore the benefit of transforming the logic description into exclusive sum of products (ESOP) forms prior to implementation in the majority gates.
We survey recent efforts in establishing the foundation for QC testing and fault tolerant QC. We project the potential use of random tests as well as built in self test (BIST) techniques for future QC. A major contribution of this dissertation is the investigation of partially redundant reversible logic. Detection of partially redundant logic within any design, reversible or irreversible, has ramifications for logic synthesis, for design verification, and for design for test (DFT) issues.