quantum computing bcs belgium branch. quantum computing basic quantum mechanics quantum algorithms...
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Quantum Computing
BCS Belgium Branch
Quantum Computing
• Basic Quantum Mechanics
• Quantum Algorithms
• Quantum Computer Hardware
Basic Quantum Mechanics
• Wave particle duality• Coherence• Interference• Young’s slits• Entanglement
• Observer matters
• Classical physics• Exact knowledge• Deterministic
Beam Splitter
• Split light beam with semi silvered mirror
A
B
Interference
• Split and recombine light beams
A
B
Interference
• Split and recombine light beams
A
B
Young’s slits
Diffraction patterns
Wave Interference
+ +
= =
EPR Paradox
• Quantum Teleportation made real
Teleportation diagrams Courtesy of IBM, Copyright, IBM Corp, 1995
Quantum Interference
• Superpositions of quantum states
• Wavefunctions are complex
• Modulus has a physical interpretation
Classical Bits are 0 or 1
• Classical CPUs use binary representation
• Only 0 or 1 is defined
• N-bit register contains one number from 2N
1
0
Qubits are the key
• Quantum CPU works on Qubits
• Represent 0 and 1• Or any mixture
• N-bit register may contain any subset of numbers from 2N
|1>
|0>
-|1>
-|0>
Hadamard Transform
• Controlled mixing• Given a system with
eigenstates |0> |1>• Forms
|0> + |1>
|0> - |1>
• Self inverse
1 11 -1
1 1 1 1 1 -1 1 -11 1 -1 -11 -1 -1 1
Quantum registers
• |0> + |1> is 0 and 1• Entangle 3 qubits• And you get
• |000> + |001> + |010> +|011> + |100> + |101> + |110> + |111>
• L operations• 2L different numbers
|0>+|1> |0>+|1>|0>+|1>
|0>+|1>|0>+|1>|0>+|1>
Deutsch ’85 Problem
• Given f(x) , x = {0,1}• Compute once• Decide if f(0)=f(1)• Impossible for classical CPU
H Uf H|0>
|0> - |1> |0> - |1>
answer
Conditional Test
• Classical
• Quantum
if (x)
if (qb)
False True
|1>
|0>
-|0>
-|1>
Simon’s Algorithm ‘93
• Given a periodic function of period r
• f(x)=f(x+r)
• Find period r in polynomial time
• Single step finds all possible values of r
• Bad news r, 2r, 3r,… Nr all solutions too!
• Good news GCD is easy on classical CPU
Factoring Composites
• Factoring is slow for conventional CPUs
• Simple example – factorise
• 35 = ? x ?
• 221 = ? ? x ? ?
• 29083 = ? ? ? x ? ? ?
• Multiplying is much easier
• 123 x 456 = ? ? ? ? ?
Factoring Composites 2
• Factoring is slow for conventional CPUs
• Simple example – factorise
• 35 = 5 x 7
• 221 = 13 x 17
• 29083 = 127 x 229
• Multiplying is much easier
• 123 x 456 = 56088
Periodicity Factorisation
• a < N chosen at random
• Prob( GCD(a, N) = 1 ) > 1 / log N
• GCD (a, N) = 1
• f(x) = a x mod N
• Find period r using quantum machine
• Factors are GCD ( a r/2 mod N + 1, N )
• Fast periodicity determination => Factors
Shamir’s Twinkle
• Hardware accelerator for classical CPUs
• Optoelectronic device ~1000x faster
• 512bit RSA keys vulnerable
• Past dedicated hardware triumphs include
• WWII Colossus just beats a Pentium
• Turing’s Bombe still 60x better
Grover’s Algorithm ‘96
• Find a match in N unsorted records
• Classical brute force time ~ N/2
• Quantum algorithm time ~ N1/2
Alice|0> := -|0>
Bob|k> := -|k>H
H
Searching
• Grovers algorithm using Q comparisons
• N1/2 = 1 / sin ( / 2(2Q+1))
• N ~ 4 (2Q+1)2 / 2
Q N
1 4
2 10
3 20
4 33
Is Life a Quantum Computer?
• Q=1, N=4 DNA uses a 4 base code• UCAG
• Q=3, N=20 Life uses ~20 amino acids
• Genetic code has supersymmetry• Weird coincidence or deep link to QM ??• Decoherence time seems too short
DNA Code of Life
DNA Computing
• Adleman - Travelling salesman problem
• Fast combinatorial solutions
• Hard to set up
• Answer fast
• Interpretation slow
DNA Turing Machine
• Universal computing machine
• Molecular computing
• DNA is program tape
• Enzymes are hardware
• Nature 22 Nov 2001
Quantum Computer Hardware
• Toy versions exist, algorithms work
• 2 qubit Chloroform CHCl3
• 3 qubit Trichlorethylene CHCl=CCl2
• Other possibilities– Josephson Junctions– Ion traps, BECs
Chloroform 2 Qubits
• Nuclear spin resonance
• 1H – hydrogen
• 13C – carbon
• Complex chemical analysis
• Simple molecules
• Program by RF pulses
Programming
• Hardware dependent
• RF pulses
• Tuned lasers
• Read back output
• NMR spectrum
NMR Animation, Courtesy of IBM, Copyright, IBM Corp, 1995
The Race for More Qubits
Date Group Compound Qubits
1998 IBM Chloroform 2
1998 IBM/MIT Trichloroethylene 3
Mar 2000 LANL Crotonic acid 7
Aug 2000 MIT Fluorine 5
References
There is a lot of information available on the web from the various research groups that have specialised in quantum algorithm development and design of hardware for quantum computers.
I created this talk from a number of sources, but the ones below and their links contain additional material at a range of different levels from the basics up to and including the latest work.
Weblinks
• General reviews at many levels
http://www.qubit.org/Intros_Tuts.html
http://www.qubit.org/people/wim/quantum.html
http://www.howstuffworks.com/quantum-computer2.htm
• Scientific American review article http://www.sciam.com/1998/0698issue/0698gershenfeld.html
http://www.sciam.com/explorations/091696explorations.html
• Physics and computer science http://theory.caltech.edu/people/preskill/ph229/#reference
• University level algorithms http://www.hpl.hp.co.uk/brims/websems/quantum/ekert/sem.html
http://www.dagstuhl.de/DATA/Reports/98191/report_html.html
Weblinks
• Practical Hardware Developments
Quantum Experimental Kit http://stardec.hpcc.neu.edu/~bba/RES/QCOMP/QCOMP.html
NMR Quantum Computershttp://www.almaden.ibm.com/st/projects/quantum/nmr/
LANL 7 Qubit Machinehttp://www.lanl.gov/worldview/news/releases/archive/00-041.shtml
Quantum Teleportationhttp://www.research.ibm.com/quantuminfo/teleportation/
Weblinks • Other Related Articles
• EU Quantum Projectshttp://www.cwi.nl/projects/QAIP/
• Shamir’s Twinkle
http://www.simovits.com/archive/twinkle.pdf • DNA Computing
http://www.csd.uwo.ca/~morey/dnatalk/kevin/dna/dnaerror.html • DNA Turing Machine
http://www.nature.com/nature/links/011122/011122-2.html • Speculative
http://www.consciousness.arizona.edu/hameroff/Davies-Physics-and-life.htm