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Mustafa Altun Electronics & Communication Engineering Istanbul Technical University Web: http://www.ecc.itu.edu.tr/. ELE 523E COMPUTATIONAL NANOELECTRONICS. W2 : Emerging Computing, 23 /9/2013. FALL 2013. Outline. Overview of Boolean algebra Overview of computational complexity

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ele 523e computational nanoelectronics

MustafaAltun

Electronics & Communication Engineering

Istanbul Technical University

  • Web: http://www.ecc.itu.edu.tr/

ELE 523E COMPUTATIONALNANOELECTRONICS

W2: Emerging Computing, 23/9/2013

FALL 2013

outline
Outline
  • Overview of Boolean algebra
  • Overview of computational complexity
  • Quantum computing
  • DNA computing
  • Computing with nano arrays
  • Emerging transistors
boolean gates
Boolean Gates

How to implementgates, extensivelyanygivenBooleanfunction, with emerging devices?

NAND and

NOR are

universal.

computational complexity
ComputationalComplexity
  • Focuson classifying computational problems according to their inherent difficulty.
    • Time
    • Circuit size
    • Number of processors
  • Determine the practical limits regardingthe restrictions on resources.
  • Based on algorithms
    • Reaching optimal solutions.

Emergingdevicesaimto improvecomputational complexity of importantproblems.

notations
Notations

Big O notation

C is a positive real number.

Example:

time complexity examples
Time ComplexityExamples

Example:

Countingtheclass of nstudents

Onebyone

Everyrow has a constantA number of students.

Example:

Findingtheintersection of twosetswithnandmelements.

Example:

Travellingsalesman problem: Given a list of n cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?

time complexity examples1
Time ComplexityExamples

Travelling Salesman Problem

time complexity examples2
Time Complexity Examples

Example:

Factorizing semi-prime (RSA) numbers. For each RSA number n, there exist prime numbers p and q such that n = p × q.

15 = 3 × 5

4633 = 41 × 113

The prize for RSA-1024 is $100.000.

RSA-2048 takes approximately 10 billion years with the bestknown algorithm.

What isPvs NP?

quantum computing
Quantum Computing
  • Theoretically, quantum computers solve RSA-2048 problem in seconds compared to 10 billion years.
  • Shor’salgorithm.
  • Cracking RSA keys.
  • Would be a breakthrough in cryptology.

Practically, where are we now?

Erik Lucero’scircuittofactorize 15

quantum computing1
Quantum Computing
  • February 2012: IBM scientists achieved several breakthroughs in quantum computing with superconducting integrated circuits
  • September 2012: The first working "quantum bit" based on a single atom in silicon suitable for the building blocks of modern computers.
  • October 2012: Nobel Prizes were presented to David J. Wineland and Serge Haroche for their basic work on understanding the quantum world - work which may eventually help makequantum computing possible.
  • May 2013: Google launching the Quantum Artificial Intelligence Lab with 512-qubit quantum computer.
bits vs qubits
Bits vs. Qubits

Bits

  • 0 or 1 at a time
  • Deterministic
  • Discrete and stable states
  • State of a bit:
  • In state 0 or 1 with a probability of
  • Qubits
  • 0 or 1 at thesame time
  • Probabilistic
  • Superposition of states
  • State of a qubit:
  • In state 0 with a probability of
  • In state 1 with a probability of
quantum gates
Quantum Gates

Classical NOT gate

Quantum NOT gate

quantum gates1
Quantum Gates

Quantumgatesarereversible

quantum gates2
Quantum Gates

Example:

Findthecorrespondingmatrix of a quantumgateX.

Example:

Find the output of a Hadamard gate. Proove that it is reversible.

quantum gates3
Quantum Gates
  • Can thefollowingmatrix be a Q-gatematrix?
  • Whataretheproperties of Q-gatematrices?
  • Whataretheothergatetypesforsinglequbits?
  • Howaboutthegatesformultiplequbits.
  • Is there a universalquantumgate?
dna computing
DNA Computing
  • Parallelcomputing
    • For certain problems, DNA computers are faster and smaller than any other computer built so far.
    • A test tube of DNA can contain trillions of strands.
  • Computingwith DNA strands
    • Depending on absenceand presence of DNA molecules.
    • Strandshavedirections.
    • How do strandssticktogether?
dna computing for tsp
DNA Computingfor TSP

Adleman’smotivatingexperiment,1994

Modified travellingsalesmanproblem (TSP): Given 7 towns, is there a routefromtown0totown6withvisitingeachtownexactlyonce?

dna computing for tsp1
DNA Computingfor TSP
  • Step-1: Constructstrands foreach link (road) consideringdirections
  • Step-2: Makethestrands joinwheretheyhavematchingnumbers.
  • Step-3: Eliminateallthestrandsotherthan 0-to-6 ones.
  • Step-4: Eliminatestrandsotherthantheoneshaving 6 strands.
  • Step-5: Lookfor1, 2,3,4, and 5 strandsone-by-one.
dna computing for tsp2
DNA Computingfor TSP
  • Computationalcomplexity?
dna computing1
DNA Computing
  • Main advantages
    • Parallel
    • Dense, small area
    • Can solve untractable problems
  • Disadvantages
    • Slow
    • Fragile
    • Unreliable, randomness
computing with nano arrays
ComputingwithNanoArrays
  • Computingmodelsfornanoarrays
    • Two-terminal switch-based
      • Diode-based
      • Transistor-based
    • Four-terminal switch-based

Self-assemblednanoarrays

two terminal switch based model1
Two-terminal Switch-based Model
  • Implementthecircuitbelowwithdiode-basednanoarrays.
four terminal switch based model1
Four-terminal Switch-based Model
  • What are the Boolean functions implemented in (a) ad (b)?
computing with s eperate d evices
Computing with SeperateDevices
  • Direct replacement of CMOS transistors
  • Some advantages over CMOS
  • Interconnection problems
  • Lack of integration

Single electron transistor

Nanowire transistor

suggested readings videos
Suggested Readings/Videos
  • Erik Lucero’ s quantum computing (2012): http://www.youtube.com/watch?v=Yl3o236gdp8
  • DNA computing: Computing with soup (2012), Article in The Economics, http://www.economist.com/node/21548488
  • Haselman, M., & Hauck, S. (2010). The future of integrated circuits: A survey of nanoelectronics. Proceedings of the IEEE, 98(1), 11-38.
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