Improved Ternary Reversible Logic Synthesis Using Group Theoretic Approach

2020 ◽  
Vol 29 (12) ◽  
pp. 2050192 ◽  
Author(s):  
P. Mercy Nesa Rani ◽  
Kamalika Datta
Keyword(s):  
Binary Systems ◽  
Logic Synthesis ◽  
Quantum Systems ◽  
Theoretic Approach ◽  
Quantum Cost ◽  
Decomposition Approach ◽  
Gate Count ◽  
Higher Dimensional ◽  
Significant Attention ◽  
Computing Element

Quantum computation relies on exploiting quantum mechanical phenomena, and has received significant attention in recent years. Higher-dimensional quantum systems increase the density of encoded information per computing element (e.g., qutrit for three-level system), resulting in less resource overhead. For instance, 63% reduction in the number of qutrits is possible for ternary quantum systems as compared to the corresponding binary systems. The proposed work exploits this fact to synthesize ternary reversible circuits employing a cycle-based technique. The method starts from the ternary reversible specification of a given function in the form of a permutation. The permutation cycles are factored into simpler three-cycles and two-cycles, which are then mapped to ternary reversible gates. Different gate libraries are used to synthesize three-cycles and two-cycles, respectively. A gate decomposition approach is also proposed to synthesize a quantum gate netlist in terms of elementary ternary quantum gates, viz. Muthukrishnan–Stroud gate and shift gate. Synthesis results on benchmark functions indicate that the proposed method results in 27% and 6% improvements in quantum cost and gate count, respectively, over existing works in the literature.

scholarly journals A shared-cube approach to ESOP-based synthesis of reversible logic

2011 ◽  
Vol 24 (3) ◽  
pp. 385-402 ◽  
Author(s):  
Noor Nayeem ◽  
Jacqueline Rice
Keyword(s):  
Power Loss ◽  
Heat Dissipation ◽  
Logic Synthesis ◽  
Reversible Logic ◽  
Experimental Results ◽  
Quantum Cost ◽  
Toffoli Gate ◽  
Gate Count ◽  
Computing Industry ◽  
Synthesis Approach

Reversible logic is being suggested as a possibility for overcoming potential power loss and heat dissipation problems that the computing industry may soon be at a loss to overcome. However, for reversible logic to be a solution we must have techniques for synthesizing function descriptions to reversible circuits. This paper presents an improved ESOP-based reversible logic synthesis approach which leverages situations where cubes are shared by multiple outputs and ensures that the implementation of each cube requires just one Toffoli gate. It has the potential to minimize both gate count and quantum cost, and in fact our experimental results show that this technique can reduce the quantum cost up to 75% compared to results from the existing work.

scholarly journals Reversible logic synthesis by quantum rotation gates

2013 ◽  
Vol 13 (9&10) ◽  
pp. 771-792
Author(s):  
Afshin Abdollahi ◽  
Mehdi Saeedi ◽  
Massoud Pedram
Keyword(s):  
Logic Synthesis ◽  
Canonical Representation ◽  
Reversible Logic ◽  
Boolean Logic ◽  
Decision Diagrams ◽  
Multiple Control ◽  
Decomposition Approach ◽  
Binary Decision ◽  
Gate Count ◽  
Toffoli Gates

A rotation-based synthesis framework for reversible logic is proposed. We develop a canonical representation based on binary decision diagrams and introduce operators to manipulate the developed representation model. Furthermore, a recursive functional bi-decomposition approach is proposed to automatically synthesize a given function. While Boolean reversible logic is particularly addressed, our framework constructs intermediate quantum states that may be in superposition, hence we combine techniques from reversible Boolean logic and quantum computation. {The proposed approach results in quadratic gate count for multiple-control Toffoli gates without ancillae, linear depth for quantum carry-ripple adder, and $O(n\log^2 n)$ size for quantum multiplexer.

OPTIMIZED REVERSIBLE MULTIPLIER CIRCUIT

2009 ◽  
Vol 18 (02) ◽  
pp. 311-323 ◽  
Author(s):  
MAJID HAGHPARAST ◽  
MAJID MOHAMMADI ◽  
KEIVAN NAVI ◽  
MOHAMMAD ESHGHI
Keyword(s):  
Dna Computing ◽  
Full Adder ◽  
Logic Circuits ◽  
Optical Information ◽  
Quantum Cost ◽  
Hardware Complexity ◽  
Cmos Design ◽  
Fair Comparison ◽  
Low Power Cmos ◽  
Significant Attention

Reversible logic circuits have received significant attention in quantum computing, low power CMOS design, optical information processing, DNA computing, bioinformatics, and nanotechnology. This paper presents two new 4 × 4 bit reversible multiplier designs which have lower hardware complexity, less garbage bits, less quantum cost and less constant inputs than previous ones, and can be generalized to construct efficient reversible n × n bit multipliers. An implementation of reversible HNG is also presented. This implementation shows that the full adder design using HNG is one of the best designs in term of quantum cost. An implementation of MKG is also presented in order to have a fair comparison between our proposed reversible multiplier designs and the existing counterparts. The proposed reversible multipliers are optimized in terms of quantum cost, number of constant inputs, number of garbage outputs and hardware complexity. They can be used to construct more complex systems in nanotechnology.

scholarly journals Advanced exact synthesis of Clifford+T circuits

2020 ◽  
Vol 19 (9) ◽  
Author(s):  
Philipp Niemann ◽  
Robert Wille ◽  
Rolf Drechsler
Keyword(s):  
Large Scale ◽  
Fault Tolerant ◽  
Logic Synthesis ◽  
Research Problem ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Research Attention ◽  
Small Quantum ◽  
Significant Research ◽  
Important Research Problem

Abstract Quantum systems provide a new way of conducting computations based on the so-called qubits. Due to the potential for significant speed-ups, this field received significant research attention in recent years. The Clifford+T library is a very promising and popular gate library for these kinds of computations. Unlike other libraries considered so far, it consists of only a small number of gates for all of which robust, fault-tolerant realizations are known for many technologies that seem to be promising for large-scale quantum computing. As a consequence, (logic) synthesis of Clifford+T quantum circuits became an important research problem. However, previous work in this area has several drawbacks: Corresponding approaches are either only applicable to very small quantum systems or lead to circuits that are far from being optimal. The latter is mainly caused by the fact that current synthesis realizes the desired circuit by a local, i.e., column-wise, consideration of the underlying unitary transformation matrix to be synthesized. In this paper, we analyze the conceptual drawbacks of this approach and propose to overcome them by taking a global view of the matrices and perform a separation of concerns regarding individual synthesis steps. We precisely describe a corresponding algorithm as well as its efficient implementation on top of decision diagrams. Experimental results confirm the resulting benefits and show improvements of up to several orders of magnitudes in costs compared to previous work.

scholarly journals Synthesis of quantum circuits in Linear Nearest neighbor Model using Positive Davio Lattices

2011 ◽  
Vol 24 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Marek Perkowski ◽  
Martin Lukac ◽  
Dipal Shah ◽  
Michitaka Kameyama
Keyword(s):  
Nearest Neighbor ◽  
Dimensional Space ◽  
Synthesis Method ◽  
Logic Synthesis ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Synthesis Methods ◽  
Cost Models ◽  
Quantum Cost ◽  
One Dimensional

We present a logic synthesis method based on lattices that realize quantum arrays in One-Dimensional Ion Trap technology. This means that all gates are built from 2x2 quantum primitives that are located only on neighbor qubits in a one-dimensional space (called also vector of qubits or Linear Nearest Neighbor (LNN) architecture). The Logic circuits designed by the proposed method are realized only with 3*3 Toffoli, Feynman and NOT quantum gates and the usage of the commonly used multi-input Toffoli gates is avoided. This realization method of quantum circuits is different from most of reversible circuits synthesis methods from the literature that use only high level quantum cost based on the number of quantum gates. Our synthesis approach applies to both standard and LNN quantum cost models. It leads to entirely new CAD algorithms for circuit synthesis and substantially decreases the quantum cost for LNN quantum circuits. The drawback of synthesizing circuits in the presented LNN architecture is the addition of ancilla qubits.

Estimation of Power for Reversible Subtractors

2018 ◽  
Vol 7 (4.5) ◽  
pp. 102
Author(s):  
E. V.Naga Lakshmi ◽  
Dr. N.Siva Sankara Reddy
Keyword(s):  
Low Power ◽  
Power Dissipation ◽  
Logic Gates ◽  
Logic Circuits ◽  
Reversible Logic ◽  
Quantum Cost ◽  
Gate Count ◽  
Garbage Output ◽  
Reversible Logic Gates

In recent years Reversible Logic Circuits (RLC) are proved to be more efficient in terms of power dissipation. Hence, most of the researchers developed Reversible logic circuits for low power applications. RLC are designed with the help of Reversible Logic Gates (RLG).   Efficiency of the Reversible gates is measured in terms of Quantum cost, gate count, garbage output lines, logic depth and constant inputs. In this paper, measurement of power for RLG is done. Basic RLGs are designed using GDI technology and compared in terms of power dissipation. 1 bit Full subtractor is designed using EVNL gate [1] and also with TG& Fy [6] gates. The power dissipation is compared with 1 bit TR gate [5] full subtractor.  Then 2 bit, 4 bit and 8 bit subtractors are designed and compared the powers. Proposed 4 bit and 8 bit full subtractors are dissipating less power when compared to TR gate 4 bit and 8 bit subtractors.  

Quantum Gate Entangler and Entangling Capacity of a General Multipartite Quantum System

2008 ◽  
Vol 15 (03) ◽  
pp. 213-222 ◽  
Author(s):  
Hoshang Heydari
Keyword(s):  
Quantum System ◽  
Quantum Systems ◽  
Quantum Gate ◽  
Projective Varieties ◽  
Multipartite Quantum Systems ◽  
Higher Dimensional ◽  
Multipartite States ◽  
Complex Projective

We construct quantum gate entangler for general multipartite states based on the construction of complex projective varieties. We also discuss in detail the construction of quantum gate entangler for higher dimensional bipartite and multipartite quantum systems. Moreover, we construct and discuss entangling capacity of general multipartite quantum systems.

scholarly journals Experimental access to higher-dimensional entangled quantum systems using integrated optics

Optica ◽  
2015 ◽  
Vol 2 (6) ◽  
pp. 523 ◽  
Author(s):  
Christoph Schaeff ◽  
Robert Polster ◽  
Marcus Huber ◽  
Sven Ramelow ◽  
Anton Zeilinger
Keyword(s):  
Integrated Optics ◽  
Quantum Systems ◽  
Higher Dimensional

Efficient designs of reversible BCD to EX-3 Converter with low quantum cost in nanoscale

2020 ◽  
Vol 18 (05) ◽  
pp. 2050020 ◽  
Author(s):  
Mojtaba Noorallahzadeh ◽  
Mohammad Mosleh
Keyword(s):  
Quantum Computing ◽  
Optical Computing ◽  
Reversible Logic ◽  
Quantum Cost ◽  
Computing Systems ◽  
Gate Count ◽  
Reversible Gate ◽  
Significant Research ◽  
Research Domain ◽  
Better Than

As an interesting and significant research domain, reversible logic is massively utilized in technologies, including optical computing, cryptography, quantum computing, nanotechnology, and so on. The realization of quantum computing is not possible without the implementation of reversible logic, and reversible designs are presented mainly to minimize the thermal loss because of the data input bits lost in the irreversible circuit. Digital converters, as the most important logic circuits, are used to connect computing systems with different binary codes. This paper first proposes a new reversible gate called Reversible Noorallahzadeh[Formula: see text]Mosleh Gate (RNMG). Then, using the proposed RNMG gate as well as existing NMG1, NMG6, and PG gates, three different designs of reversible Binary-Coded Decimal (BCD) to EX-3 code converter are proposed. Our results indicate that the proposed BCD to EX-3 code converters are superior to previous designs in terms of quantum cost. Moreover, the proposed converters are comparable or better than previous designs in terms of gate count, constant inputs, and garbage outputs.

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