Algorithms, Logic and Complexity. Quantum computation. basic explanations! &! survey of progress
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1 Algorithms, Logic and Complexity Quantum computation basic explanations! &! survey of progress
2 Index Why Quantum Computation?! Quantum mechanics! D-wave! Quantum programming
3 «If you think you understand quantum mechanics, you don't understand quantum mechanics.» Richard Feynman
4 Quantum computation Why quantum computation? 1E+30 Numbers of roads Older than universe 1600 years Some unsolvable problems:! For example the salesman problem:! What is the shortest way for visit all cities.! Complexity: factorial! With 1 GHz (10^9 operations/sec): Operations 1E sec 1E , ,5 30 Towns
5 Dynamic programming:! curse of the dimensionality! Complexity: power of two: (n^2)*(2^n)! Numbers of roads 1E+30 Quantum computation Why quantum computation? Operations 1E+15 1E , ,5 90 Towns
6 Dynamic programming:! curse of the dimensionality! Complexity: power of two: (n^2)*(2^n)! Quantum computation Why quantum computation?
7 Dynamic programming:! curse of the dimensionality! Complexity: power of two: (n^2)*(2^n)! Quantum computation Why quantum computation? Other problem:! Prime decomposition:! N=P*Q (with P and Q prime numbers)!! This N is use by the RSA crypto system :!
8 ! Prime decomposition: N=P*Q (with P and Q prime numbers)!! RSA-2048 = $ Classic computation:! General Number Field Sieve:!! t 4*10^17 seconds 13*10^9 years! The age of the universe! Quantum computation! Shor's algorithm:!! t 10 seconds
9 Quantum mechanics : Newton VS Quantum Newton mechanics (Classic Physics) Quantum Physics drive in a nail! describe sea waves! send a rocket to the Moon Classical limit:we can t use the same laws quantization of certain physical properties! wave particle duality! principle of uncertainty! quantum entanglement Position! Speed! Acceleration double-slit experiment! Photoelectric effect! black-body radiation
10 Quantum mechanics : Uncertainty principle Deterministic Domain! Probabilistic Domain Measurement problem looking the object change is state Schrödinger cat Experiment we can t look the box! (in this case we destroy the machine)
11 Quantum mechanics : Bit to Qubit Bit 0 or 1 Qubit Superposition 0 or 1 or BOTH 00! 01! 10! 11 B1 B2 =>2 coefficients 00 >! 01 >! 10 >! 11 > E1 E2 E3 E4 =>4 coefficients
12 Quantum mechanics : Bit to Qubit Bit 0 or 1 Qubit Superposition 0 or 1 or BOTH 00! 01! 10! 11 n bits => n states B1 B2 =>2 coefficients 00 >! 01 >! 10 >! 11 > N qubits => 2^N states E1 E2 E3 E4 =>4 coefficients
13 Quantum mechanics to Quantum Computers build with this strange physics a big object which we can manipulate.! Coherence! Decoherence Problem:! Cold temperature close to 0 K New language
14 A big box for 512 qubits D-Wave the world's first commercially available quantum computer
15 A big box for 512 qubits D-Wave the world's first commercially available quantum computer
16 A big box for 512 qubits D-Wave the world's first commercially available quantum computer
17 Not universal quantum computer D-Wave: quantum computing or quantum scam?! 21=3x7 with 5 qubits
18 How to program it? Shor's algorithm (prime decomposition)! Grover's algorithm (database)! quantum simulator! Universal quantum simulator <=> Quantum Turing Machine
19 others solutions? Diamond-based quantum computer! Trapped ion quantum computer! Adiabatic quantum computer Record at 20 C:! 39 minutes We don t know when but big issue!
20 Questions??????
21 (Recent article on the dwave) Videos & Papers links (dwave and more)! (google, NASA & Dwave)! (Quantum animations with cat)! (comics on Quantum computer)! (comics on quantum world)! (bit & qubit)! (turing to quantum Kaku)! (15=3*5)! ( scientific article )! (TM and Quantum)! (Quantum programming from Cornell Uni )!
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