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National Conference on Emerging Trends and Applications in Computer Science (NCETACS)

Towards implementation of fault tolerant reversible circuits

Anugrah Jain, Sushil Chandra Jain

Published Sep 1, 2013• 3 citations
Publisher

Abstract

Reversible computing is gaining importance in order to achieve low power consumption, high speed and packaging density in VLSI circuits. It has applications in various other fields such as quantum computing, nanotechnology, DNA computing, optical computing, cryptography and informatics. In order to achieve reliable circuits in reversible computing provision for fault tolerance is necessary. To achieve fault tolerance, the first stage is to identify occurrence of fault. To detect the occurrence, parity preserving technique has been reported in literature. This paper presents a new 4*4 parity preserving reversible logic gate PPTG (Parity Preserving Toffoli Gate) and its quantum realization. After that two new parity preserving implementations are presented in this paper. These implementations are used towards the development of fault tolerant reversible circuits. By which substitution becomes efficient and minimum in terms of constant inputs and garbage outputs. It permits us to use existing benchmarks preserving parity with only one additional circuit line.

DOI
10.1109/icetacs.2013.6691401

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Reversible computing is gaining importance in order to achieve low power consumption, high speed and packaging density in VLSI circuits. It has applications in various other fields such as quantum computing, nanotechnology, DNA computing, optical computing, cryptography and informatics. In order to achieve reliable circuits in reversible computing provision for fault tolerance is necessary. To achieve fault tolerance, the first stage is to identify occurrence of fault. To detect the occurrence, parity preserving technique has been reported in literature. This paper presents a new 4*4 parity preserving reversible logic gate PPTG (Parity Preserving Toffoli Gate) and its quantum realization. After that two new parity preserving implementations are presented in this paper. These implementations are used towards the development of fault tolerant reversible circuits. By which substitution becomes efficient and minimum in terms of constant inputs and garbage outputs. It permits us to use existing benchmarks preserving parity with only one additional circuit line.
Reversible logic is an emerging area of research, having applications in nanotechnology, low power CMOS design, quantum computing, and DNA computing. In this paper, two different parity-preserving reversible error coding and detection circuits are studied. First we propose two new reversible Hamming code generator circuits. One of them is parity-preserve. We also propose a new parity-preserving reversible Hamming code error detector circuit. The proposed parity-preserving reversible Hamming code generator (PPHCG) and error detector circuits provide single error correction–double error detection (SEC–DED). The designs are better than the existing counterparts in terms of quantum cost (QC), number of constant inputs, and number of garbage outputs. Then we propose parity-preserving reversible cyclic code encoder/decoder circuits for the first time. A parity-preserving reversible D flip-flop is also proposed. Equivalent quantum representation of two parity-preserving 4 ∗ 4 reversible gates, IG, and PPHCG, are also proposed. We show for the first time that IG has a QC of only 7 and PPHCG has a QC of only 6.
Reversible logic is characterized by its feature of being a prominent application in low-power conventional computers and the most compatible logic in quantum computers. Quantum circuits executes quantum algorithms and are important in a new generation of advanced computing. However, they are highly error-prone and also subject to the use of limited and sensitive physical resources like qubits and quantum gates. This paper introduces a comprehensive fault tolerant quantum-based reversible circuit which can calculate a high variety number of arithmetic and logic operations. It uses both: parity preserving method for detecting one or an odd number of bit errors, and Clifford + T implementation for protecting circuits against decoherence faults. First, we propose a new fault-tolerant (parity preserving and Clifford + T) adder/subtractor and derive a quantum reversible Arithmetic and Logic Unit (ALU). These modules reach the most optimized extent of circuit line, ancilla inputs, and garbage outputs according to the logical analysis done in this work. This article focuses on reducing T-cost metrics in conjunction with enhancing the number of operations and quantum costs in proposed circuits compared to other counterparts. We propose 4-bit fault tolerant ALU derived from our proposed single-bit module to show the proposed circuit can be extended to any larger size. The proposed circuit is implemented in the Qiskit simulation tool, and output results confirm the accuracy of our design functionality. The proposed full adder/ subtractor achieves an average of 64% and 43%, and the proposed ALU circuit achieves an average of 38% and 27% improvement in T-count and T-depth, respectively compared to their counterparts. The proposed reversible quantum-optimized fault tolerant adder/subtractor and ALU units can be applied as the basic part of DSP systems and quantum processor units in quantum computing devices.
The fault tolerant reversible Hamming code circuits were designed in order to test the reliability of the data in the transmission process.A new reversible gate named four variables parity preserving gate(FVG) was proposed,and the quantum equivalent implementations of FVG was also given.Fault tolerant reversible code encoding and detection circuits were designed using FVG and existing gates.Taking the design of the(7,4) Hamming code as an example,its circuit performance was evaluated in terms of quantum cost and delay.The results prove that its performance is improved by 10%to 20%than existing counterparts.Simulation results indicate that the logic structures of circuit are correct and their performances are reliable.
The performance of existing technology for implementing digital circuits based on irreversible logic is closely reaching its limit. Conventional logic circuits result in heat dissipation whenever there is an information loss. Hence reversible logic is attaining major consideration in the perspective of evolving technologies such as quantum computing as there isno information loss and there is a unique mapping between the input vectors and output vectors. A reversible gate is supposed to be parity preserving if there existsimilarity between input parityand the outputparity.To construct reliable fault-tolerant reversible systems elements should be of fault-tolerant reversiblestructures.Adder circuits are studied extensively since their performance can directly affect the entire digital system. This paper presents a Toffoli gate (TG) based fulladderwhich serves as a fundamental component in constructing a ripple carry adder. Further a parity preserving Toffoligate based full adder is presented which was utilized to develop a fault-tolerant Ripple Carry Adder without compromising on its performance.The proposed designs have been simulated using IBM Quantum Simulator and have been verified for their correctness. The proposed adders will serve as vital design components in developing fault-tolerant reversible arithmetic and logic unit.
In recent years reversible logic has offered a promising alternative to traditional logic circuits. Reversible logic introduces a mechanism which allows theoretically zero energy \ndissipation by eliminating the possibility of information loss. However, it is also desirable \nthat all computation should ideally be done in a fault tolerant manner. To address this we \npropose techniques to achieve fault tolerance in reversible logic based on a passive hardware redundancy technique. We propose two new designs for a reversible majority voter circuit that can be used to implement fault masking. Comparisons to existing designs are presented in terms of cost metrics such as gate count, garbage outputs, constant inputs, and quantum cost. Comparative failure probability analysis of the proposed voter circuits is also provided. Simulation results of the voter circuit failure probabilities over different numbers of trials are also presented. Our approach can be used to determine the circuit failure probability by using the gate failure probabilities. The proposed methodology can provide useful information for future reversible gate fabrication and designing future fault tolerant reversible circuits.
Reversible logic circuits have received emerging attentions in recent years. Reversible logic is widely applied in some new technical fields, such as quantum computing, nanocomputing and optical computing and so on. In this paper, three fault tolerant gates are proposed, ZPL gate, ZQC gate and ZC gate. By using the proposed gates, fault tolerant quantum and reversible BCD adder and skip carry BCD adder are designed, which overcome the limitations of the existing methods. The proposed reversible BCD adders have also parity-preserving property. They are better than the existing counterparts, especially in the quantum cost. Proposed designs have been compared with existing designs with respect to the number of gates, number of garbage outputs and quantum cost.