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 1 Classical CPUs use binary representation Only 0 or 1 is defined N-bit register contains one number from 2N

Qubits are the key |1> |0> -|0> -|1> Quantum CPU works on Qubits Represent 0 and 1 Or any mixture N-bit register may contain any subset of numbers from 2N -|0> |0> -|1>

Hadamard Transform 1 1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 1 Controlled mixing Given a system with eigenstates |0> |1> Forms |0> + |1> |0> - |1> Self inverse 1 1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -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 H Uf H |0> answer |0> - |1> Given f(x) , x = {0,1} Compute once Decide if f(0)=f(1) Impossible for classical CPU

Conditional Test Classical Quantum if (x) if (qb) False True -|0> |1> -|1> |0>

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 H Alice |0> := -|0> Bob |k> := -|k> Find a match in N unsorted records Classical brute force time ~ N/2 Quantum algorithm time ~ N1/2

Searching Grovers algorithm using Q comparisons N1/2 = 1 / sin ( p / 2(2Q+1)) N ~ 4 (2Q+1)2 / p2 Q N 4 10 20 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 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 Computers http://www.almaden.ibm.com/st/projects/quantum/nmr/ LANL 7 Qubit Machine http://www.lanl.gov/worldview/news/releases/archive/00-041.shtml  Quantum Teleportation http://www.research.ibm.com/quantuminfo/teleportation/

Weblinks Other Related Articles EU Quantum Projects    Other Related Articles EU Quantum Projects http://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