Derivatives of Perkowski’s Gate k f2 g h t t...... De Vos gates  f1f1  A B P Q Feynman gates A B P f 2f 2  C Q R Toffoli gates Q P f 2 A C R B S D 0.

Slides:

Advertisements

Similar presentations

Reversible Gates in various realization technologies

Advertisements

Synthesis of Reversible Synchronous Counters Mozammel H A Khan Department of Computer Science and Engineering, East West University, 43 Mohakhali, Dhaka.

ECE 2110: Introduction to Digital Systems Chapter 6 Combinational Logic Design Practices Encoders.

Logic Circuits Design presented by Amr Al-Awamry

Realization of Incompletely Specified Reversible Functions Manjith Kumar Ying Wang Natalie Metzger Bala Iyer Marek Perkowski Portland Quantum Logic Group.

Quantum Phase Estimation using Multivalued Logic.

Midterm Exam for Quantum Computing Class Marek Perkowski.

SYNTHESIS OF REVERSIBLE CIRCUITS WITH NO ANCILLA BITS FOR LARGE REVERSIBLE FUNCTIONS SPECIFIED WITH BIT EQUATIONS Nouraddin Alhagi, Maher Hawash, Marek.

ECE 667 Synthesis & Verification - Boolean Functions 1 ECE 667 Spring 2013 ECE 667 Spring 2013 Synthesis and Verification of Digital Circuits Boolean Functions.

ECE 331 – Digital System Design

Designing Oracles for Grover Algorithm

GF(4) Based Synthesis of Quaternary Reversible/Quantum Logic Circuits

A Transformation Based Algorithm for Reversible Logic Synthesis D. Michael Miller Dmitri Maslov Gerhard W. Dueck Design Automation Conference, 2003.

Marek Perkowski Reversible Logic Synthesis with Garbage Bits Lecture 6.

Regular Realization of Symmetric Binary and Ternary Reversible Logic Functions.

08/07/041 CSE-221 Digital Logic Design (DLD) Lecture-8:

Marek Perkowski Reversible Logic Models: Billiard Ball and Optical Lecture 4.

1 COMP541 Combinational Logic Montek Singh Jan 16, 2007.

Reversible Circuit Synthesis Vivek Shende & Aditya Prasad.

Synthesis of Reversible Synchronous Counters Mozammel H. A. Khan East West University, Bangladesh Marek Perkowski Portland State University,

A Transformation Based Algorithm for Ternary Reversible Logic Synthesis using Universally Controlled Ternary Gates Erik Curtis, Marek Perkowski.

Boolean Functions and their Representations

Multi-Valued Input Two-Valued Output Functions. Multi-Valued Input Slide 2 Example Automobile features 0123 X1X1 TransManAuto X2Doors234 X3ColourSilverRedBlackBlue.

Rolf Drechlser’s slides used

Ternary Deutsch’s, Deutsch-Jozsa and Affine functions Problems All those problems are not published yet.

Engineering Models and Design Methods for Quantum State Machines.

How to realize many-input AND gates a 0 d c b X ab abc  X 0 acd  abc  X 0 cd We need just one row to create all three-input ANDs.

April 25, A Constructive Group Theory based Algorithm for Reversible Logic Synthesis.

Review of basic quantum and Deutsch-Jozsa. Can we generalize Deutsch-Jozsa algorithm? Marek Perkowski, Department of Electrical Engineering, Portland State.

2002/10/08 SeonPil Kim Layout-Driven Synthesis For Submicron Technology : Mapping Expansions To Regular Lattices High Level Synthesis Homework #2.

Regular Structures. Levelized Structures Standard Lattice Diagrams for continuous, multiple-valued and binary logic.

Classical and Quantum Circuit Synthesis An Algorithmic Approach.

Design of Regular Quantum Circuits

 2001 CiesielskiBDD Tutorial1 Decision Diagrams Maciej Ciesielski Electrical & Computer Engineering University of Massachusetts, Amherst, USA

Minimization Techniques for Reversible Logic Synthesis.

 2000 M. CiesielskiPTL Synthesis1 Synthesis for Pass Transistor Logic Maciej Ciesielski Dept. of Electrical & Computer Engineering University of Massachusetts,

Grover’s Algorithm in Machine Learning and Optimization Applications

Introduction to Quantum logic (2) Yong-woo Choi.

New Approach to Quantum Calculation of Spectral Coefficients Marek Perkowski Department of Electrical Engineering, 2005.

Research Potential We should develop a set of unified standardized CAD tools for synthesizing, verifying, testing and simulating of quantum computers.

Fast Spectral Transforms and Logic Synthesis DoRon Motter August 2, 2001.

Digital Logic Lecture 08 By Amr Al-Awamry. Combinational Logic 1 A combinational circuit consists of an interconnection of logic gates. Combinational.

Classical Versus Quantum. Goal: Fast, low-cost implementation of useful algorithms using standard components (gates) and design techniques Classical Logic.

REVERSIBLE LOGIC SYNTHESIS. Overview of the Presentation 1. Introduction 2. Design of a Reversible Full-adder Circuit.

Digital Computer Concept and Practice Copyright ©2012 by Jaejin Lee Logic Circuits I.

Combinational Logic 1.

Copyright © 2004 by Miguel A. Marin1 COMBINATIONAL CIRCUIT SYNTHESIS CLASSIC TWO-LEVEL CIRCUIT SYNTHESIS MULTILEVEL-CIRCUIT SYNTHESIS FACTORIZATION DECOMPOSITION.

Abdullah Said Alkalbani University of Buraimi

Garbage in Reversible Designs of Multiple Output Functions

CLASSICAL LOGIC SRFPGA layout With I/O pins.

ECE 301 – Digital Electronics Logic Circuit Design (Lecture #9)

Quantum Cost Calculation of Reversible Circuit Sajib Mitra MS/ Department of Computer Science and Engineering University of Dhaka

Online Testable Fault Tolerant Full Adder in Reversible Logic Synthesis Sajib Kumar Mitra MS/ Department of Computer Science and Engineering University.

Controlled- Controlled NOTControlled- Controlled NOT = Toffoli Gate.

Circuit Synthesis A logic function can be represented in several different forms:  Truth table representation  Boolean equation  Circuit schematic 

BDD-based Synthesis of Reversible Logic for Large Functions Robert Wille Rolf Drechsler DAC’09 Presenter: Meng-yen Li.

Combinational Design, Part 2: Procedure. 2 Topics Positive vs. negative logic Design procedure.

Very good news for People who know Reed-Muller Logic 1.Quantum XOR 1.Quantum XOR is the most important gate in Quantum Logic 2.Synthesis of Quantum Circuits.

Overview Part 1 – Gate Circuits and Boolean Equations

Fredkin/Toffoli Templates for Reversible Logic Synthesis

Lecture 6 Topics Combinational Logic Circuits

Kerntopf Gate and Regular Structures for Symmetric Functions

Introduction to Quantum logic (2)

Chapter 2 Introduction to Logic Circuits

Homework 2 This homework is the first use of quantum gates. In lectures we learned about the following gates: inverter, Feynman (controlled NOT), Toffoli.

Design of new quantum primitives

Fuzzy Reversible Logic using Toffoli-like gates

Sajib Kumar Mitra, Lafifa Jamal and Hafiz Md. Hasan Babu*

SYEN 3330 Digital Systems Chapter 2 – Part 1 SYEN 3330 Digital Systems.

Presentation transcript:

Derivatives of Perkowski’s Gate k f2 g h t t De Vos gates  f1f1  A B P Q Feynman gates A B P f 2f 2  C Q R Toffoli gates Q P f 2 A C R B S D Fredkin gates Kerntopf gates Many other gate families Generalized multi- input multiplexer Generalized Maitra gates Maitra gates CMOS gates

Structure of Wave Cascade The definitions presented in this section are based on and, with some modifications. Definition. A complex Maitra term is recursively defined as follows: (1)Constant 0 (1) Boolean function is a Maitra term. (2)A literal is a Maitra term. (3)If M i is a Maitra term, a is a literal, and G is an arbitrary two-input Boolean function, then M i+1 = G( a, M i+1 ) is a Maitra term. –Additionally, it is required that each variable appears in each Maitra term only once and that the same variable ordering is used to represent all Maitra terms. Previous authors restricted the two-input functions used in the Maitra terms to only functions AND, OR, and EXOR. For the purposes of reversible logic synthesis, on the other hand, it is better to use the above more general definition. In a variation of our algorithm targeting low-power CMOS implementation, G cannot be an EXOR function and its complement, NEXOR.

Generalized Maitra Gate, Maitra Gate or CMOS Gate Reversible Wave Cascade

Material for exam 1.Definition of reversible functions. 2.Balanced and Conservative functions. Interaction and other optically-realizable reversible gates that are not n*n gates. 3.Toffoli, Feynman, Peres, Fredkin, Miller, Margolus and Kerntopf gates. Properties. Be able to synthesize one from another one. SWAP gates. 4.Convertion of irreversible circuit to reversible quantum array. 5.Concepts of garbage, input constants and ancilla bits. 6.Mirrors, local mirrors, spies, folding of constants. 7.Generalized controlled gates (so-called Perkowski’s gates). 8.Transposition vector, vs set of cycles, vs Kmap vs truth table vs BDD notations. Go from one to another. 9.MMD algorithm and synthesis without ancilla bits. 10.EXOR Lattice for symmetric and non-symmetric functions. Understanding of symmetry and its uses. 11.Naïve methods of converting from irreversible netlist to reversible quantum cascade. 12.Billard Ball model. 13.KFDD and function graphs with linear and nonlinear preprocessors. Davio versus Shannon expansions. 14.Synthesis of linear reversible circuits. 15.Nets versus lattices, single-output versus multi-output 16.Multiple-valued reversible logic. Fundamentals. (no advanced methods).

Material for exam 17. PPRM, FPRM and ESOP. Synthesis and use in reversible logic. 18. Kronecker Products and matrix representation of logic. 19. QUIDDs. 20. Analyze a circuit with CV, CV+ and CNOT gates. 21. Analyze Mitra cascades or other complex realizations. No synthesis. 22. Being able to use symmetry or other properties such as balancedness, or NPNP classification classes in problems formulated in natural language. 23. Being able to combine several methods to design a practical quantum oracle, such as a spectral transform or arithmetic circuit. 24. Being able to combine several methods, or at least select one good method to analyze a reversible circuit. Binary of multi-valued. 25. Being able to analyze a reversible fuzzy circuit. 26. Being able to solve linear equations to solve some problem in reversible logic. (1) expansions of non-symmetric functions. (2) inverse gate. (3) find inputs states from output states. 27. Testability of simple cascades. EXOR cascade. Cascade from PPRM.