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CATEGORIES:Wednesday Seminars - Department of Computer Scienc
e and Technology
SUMMARY:In the beginning God created tensor\, ... then mat
ter\, ... then speech - Bob Coecke\, Oxford Univer
sity Computing Laboratory
DTSTART;TZID=Europe/London:20110209T141500
DTEND;TZID=Europe/London:20110209T151500
UID:TALK28689AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28689
DESCRIPTION:This is a tale about quantum computing and a bit o
f natural language\nprocessing\, ... all in pictur
es!\n\nIt is now exactly 75 years ago that John vo
n Neumann denounced his own\nHilbert space formali
sm: ``I would like to make a confession which may\
nseem immoral: I do not believe absolutely in Hilb
ert space no more.''\n(sic) [1] His reason was tha
t Hilbert space does not elucidate in any\ndirect
manner the key quantum behaviors. Together with B
irkhoff he\ncrafted `quantum logic'\, ... a failed
research program.\n\nSo what are these key quantu
m behaviors then? [2\, 3] For Schrodinger\nthis
is the behavior of compound quantum systems\, desc
ribed by the tensor\nproduct [4\, again 75 years a
go]. While the quantum information endeavor\nis t
o a great extend the result of exploiting this imp
ortant insight\, the\nlanguage of the field is sti
ll very much that of strings of complex\nnumbers\,
which is akin to the strings of 0's and 1's in th
e early days of\ncomputer programming. If the man
ner in which we describe compound quantum\nsystems
captures so much of the essence of quantum theory
\, then it should\nbe at the forefront of the pres
entation of the theory\, and not preceded by\ncont
inuum structure\, field of complex numbers\, vecto
r space over the\nlatter\, etc\, to only then pop
up as some secondary construct.\n\nOver the past c
ouple of years we have played the following game:
how much\nquantum phenomena can be derived from `c
ompoundness + epsilon'. It turned\nout that epsilo
n can be taken to be `very little'\, surely not in
volving\nanything like continuum\, fields\, vector
spaces\, but merely a\n`two-dimensional space' of
temporal composition (cf `and then') and\ncompoun
dness (cf `while')\, together with some very natur
al purely\noperational assertion\, including one w
hich in a constructive manner\nasserts entanglemen
t\; among many other things\, trace structure (cf
von\nNeumann above) then follow [5\, survey]. Thi
s `categorical quantum\nmechanics' research progra
m started with [6].\n\nIn a very short time\, this
radically different approach has produced a\nuniv
ersal graphical language for quantum theory which
helped to resolve\nsome open problems [7\,8\,9]\,
in quantum foundations\, measurement based\nquantu
m computing\, and on the structure of multi-partit
e entanglement. It\ngives a particularly elegant a
ccount on complementarity and the quantum\nclassic
al interaction [10\, 11]. It also paved the way to
automate quantum\nreasoning\, by means of the Qua
ntomatic software [12].\n\nThe approach has even h
elped to solve problems outside physics\, most\nno
tably in modeling meaning for natural languages wh
ich was the first\nelegant mathematical solution
to this problem [13\, 14]. Both the\nautomation a
nd the support of structures in natural language j
ustifies the\nlabel of "Logic" (as opposed to Birk
hoff and von Neumann's quantum logic).\n\n[1] M Re
dei (1997) Why John von Neumann did not like the H
ilbert space\nformalism of quantum mechanics (and
what he liked instead). Stud Hist\nPhil Mod Phys
27\, 493-510.\n\n[2] For von Neumann\, initially t
hese were the propositions that one could\nmeasure
with certainty\, an idea that he later abandoned
in favor of the\ntrace structure\, which generates
probability [1].\n\n[3] Still\, today for most ph
ysicists `quantum' is synonym for `Hilbert\nspace'
\, which of course is not unrelated to the dominan
t ``shut up and\ncalculate''-interpretation of qua
ntum theory.\n\n[4] E Schroedinger\, (1935) Discus
sion of probability relations between\nseparated s
ystems. Proc Camb Phil Soc 31\, 555-563\; (1936)
32\, 446-451.\n\n[5] B Coecke (2010) Quantum pictu
ralism. Cont Phys 51\, 59-83.\narXiv:0908.1787\n\n
[6] S Abramsky & B Coecke (2004) A categorical sem
antics of quantum\nprotocols. LiCS '04. arXiv:0808
.1023\n\n[7] B Coecke\, B Edwards and RW Spekkens
(2010) Phase groups and the origin\nof non-localit
y for qubits. ENTCS\, to appear. arXiv:1003.5005\
n\n[8] R Duncan and S Perdrix (2010) Rewriting mea
surement-based quantum\ncomputations with generali
sed flow. ICALP'10.\n\n[9] B Coecke and A Kissinge
r (2010) The compositional structure of\nmultipart
ite quantum entanglement. ICALP'10. arXiv:1002.254
0\n\n[10] B Coecke and R Duncan (2008) Interacting
quantum observables.\nICALP'08. arXiv:0906.4725\n
\n[11] B Coecke and S Perdrix (2010) Environment a
nd classical channels in\ncategorical quantum mech
anics. CSL'10. arXiv:1004.1598\n\n[12] L Dixon\, R
Duncan & A Kissinger.\ndream.inf.ed.ac.uk/project
s/quantomatic/\n\n[13] B Coecke\, S Clark & M Sadr
zadeh (2010) Ling Anal 36. Mathematical\nfoundatio
ns for a compositional distributional model of mea
ning.\narXiv:1003.4394\n\n[14] New Scientist: Quan
tum links let computers understand language\, 8\nD
ecember 2010.\n\n
LOCATION:Lecture Theatre 1\, Computer Laboratory
CONTACT:Stephen Clark
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