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# COMPUTATIONAL PHYSICS: FROM THE MECHANICAL TO THE QUANTUM COMPUTATION

SAPO Codebits 2014: Talk

These are the slides of my talk on SAPO Codebits VII at Lisbon.

For the most part of the science's history, the numerical computation was part of a large amount of ways to realize some daily forecasts and to confirm (or invalidate) many theories. But, besides the Uncertain of Physics, we are limited by our computational skills.

My biggest objective in this presentation is to bring some interesting topics derived from the computational area in Physics. It's a tremendous discipline to be treated numerically and it brings a lot of challenges.

April 12, 2014

## Transcript

2. ###  Pen and Paper  Chalk and Slate  Tables

It was mostly associeted with numbers By 2000 BC, computing started to evolve with abstract concepts Number Mathematical object Basic Arithmetic (on numbers) Unary operations (sign) Binary operations (+, -, *, /) DANIEL BENTO - 2014 COMPUTING?
3. ### ABACUS 2700 – 2300 BC – Sumerian Abacus Adopted in

many places, exemple: • Babylonia • Egypt • Persia • Greek • Roman • Chinese • Indian • Japanese • Korean • Native American • Russian DANIEL BENTO - 2014
4. ### Logarithm Properties: log(ab) = log(a) + log(b) log(a/b) = log(a)

– log(b) log(a^b) = blog(a) log(a^(1/b)) = (1/b) log(a) - Very useful during science evolution. Because… it simplifies a lot of calculations; (sum/subtractions insted of multiplications /divisions) Exemple: We want: 1670*12, so 10^log(1670*12) log(1670*12) = log(1670) + log(12) ~ 3.2227 + 1.079 = 4.3017 10^4.3017 ~ 20030.87 ~ 1670*12 = 20040 DANIEL BENTO - 2014 TABLES AND LOG TABLES Napier (1614) – Logarithm Method Euler (1730) - Natural Logarithm Kepler used it a lot for Astronomy
5. ### • Wilhelm Schickard • Blaise Pascal • Leibniz • Charles

Xavier Thomas DANIEL BENTO - 2014 Computational Machines Schickard’s calculating machine Thomas Arithmometer – First digital mechanical calculator

8. ### AND: A & B OR: A + B NOT: ~A

NAND: A|B NOR: A - B XOR: A ◦ B XOR: A • B LOGIC GATES NOT and NAND are Universal Gates DANIEL BENTO - 2014
9. ### DANIEL BENTO - 2014 TURING MACHINE AND VON NEUNMANN ARCHITECTURE

Turing Machine Implementation Von Neumann Architecture Von Neunmann Alen Turing
10. ### Electronic Numerical Integrator And Computer  Turing-Complete  Digital 

Programmable Numbers: - 17.500 Vacum tubes - 7.200 Crystal diodes - 1.500 Relays - 70.000 Resistors - 10.000 Capacitors Arithmetic counting pulses 10 by 10 digits take 2800 microseconds DANIEL BENTO - 2014 ENIAC – FIRST COMPUTER
11. ### The correlator in the ALMA Array Operations Site Technical Building

Radio Astronomy - 134 million processors - 17 quadrillion operations per second - Solid State Disks - Twice the normal airflow needed - Seismic activity in account ALL THIS TO PROCESS DATA FROM THE 66 ANTENNAS DANIEL BENTO - 2014 SCIENTIFIC COMPUTATION - ALMA
12. ### - 25 Petabytes of data proccessed per year - 40

world facilities DANIEL BENTO - 2014 SCIENTIFIC COMPUTATION - CERN Particle Physics

14. ### WAVE EQUATION – 1 DIMENSION 1 = sin() 2 =

cos() DANIEL BENTO - 2014
15. ### = (() + ) WAVE EQUATION – SUM PARTIAL I

PARTIAL II PARTIAL III PARTIAL IV SUM DANIEL BENTO - 2014

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25. ### Introducted by Yurin Manin (1980) and Feynman (1982) • Two-state

quantum system – qubits • Operate by unitary evolution (time-dependente Schrödinger equation) • Operate in qubits as bits in classical mechanics • It needs a large number of qubits for entanglement • It is extremely sensitive • Most of the problems are solved in the same time as classical computers, but: • Classical Prime Factorization ~ exp(2L^1/3 ln(L^2/3)) • Quantum Prime Factorization ~ 300L^3 where L = ln(N), N number of digits classical method is faster for L = 10, quantum method is faster for L > 200 (10^9 years to about 8 hours) QUANTUM COMPUTATION DANIEL BENTO - 2014
26. ### • In classical mechanics the initial and final states are

linked • In quantum mechanics the final state is random at one time at one direction • Atoms can bound infinite states UNITARY EVOLUTION DANIEL BENTO - 2014
27. ### BLOCH SPHERE DANIEL BENTO - 2014 Geometric representation of two-level

quantum mechanical system qubit - Hilbert space - North and South poles are chosen for the |0> and |1> (electron spin up and spin down) - It can be extended to n-level quantum space
28. ### QUANTUM LOGIC GATES Fredkin Gate: CSWAP Gate 3-bit gate Universal

for Classical Computation Toffoli Gate: CCNOT Gate 3-bit gate Universal for Classical Computation CNOT Gate 2-bit gate NOT Gate SWAP Gate Hadamard Gate Pauli-X Gate – Rotation on Bloch Sphere around X-Axis by π radians = Classic NOT GATE Pauli-Y Gate – Rotation on Bloch Sphere around Y-Axis by π radians Pauli-Z Gate – Rotation on Bloch Sphere around Z-Axis by π radians DANIEL BENTO - 2014

30. ### DANIEL BENTO - 2014 D-WAVE QUANTUM COMPUTER 128 qubit using

quantum annealing
31. ### DANIEL BENTO - 2014 NEW FORMS OF COMPUTING • Metamaterials

• DNA • Spintronics

- 2014