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CATEGORIES:CQIF Seminar
SUMMARY:Universal Quantum Hamiltonians - Stephen Piddock\,
University of Bristol
DTSTART;TZID=Europe/London:20161201T141500
DTEND;TZID=Europe/London:20161201T151500
UID:TALK68263AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68263
DESCRIPTION:In "analogue" quantum simulation\, the Hamiltonian
of a quantum many body system is directly encoded
into the Hamiltonian of another quantum system\,
without the need for a fully scalable fault tolera
nt quantum computer. In this talk\, I will rigorou
sly justify our definition of analogue simulation\
, where all the physics of a target Hamiltonian is
reproduced in the low energy part of another\, up
to arbitrarily small accuracy. This definition is
very strong and immediately leads to a number of
interesting consequences. For example\, the locali
ty structure of the original Hamiltonian is preser
ved\, such that local errors/observables on the si
mulator correspond to local errors/observables on
the original system\, allowing us to to take a fir
st step in justifying why error correction may not
be needed in analogue simulations of this form. A
family of Hamiltonians which can simulate all oth
er local spin hamiltonians is called "universal"\,
and we show that this property easily implies BQP
-completeness (up to a depth 1 quantum circuit red
uction). Finally we show that very simple spin mod
els such as the qubit Heisenberg or XY interaction
s are universal in this sense\, and we are in fact
able to classify all sets of two-qubit interactio
ns into universality classes. (Based on joint work
with Toby Cubitt and Ashley Montanaro)
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Steve Brierley
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