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SUMMARY:Universal Quantum Hamiltonians - Stephen Piddock\, University of B
 ristol
DTSTART:20161201T141500Z
DTEND:20161201T151500Z
UID:TALK68263@talks.cam.ac.uk
CONTACT:Steve Brierley
DESCRIPTION:In "analogue" quantum simulation\, the Hamiltonian of a quantu
 m many body system is directly encoded into the Hamiltonian of another qua
 ntum system\, without the need for a fully scalable fault tolerant quantum
  computer. In this talk\, I will rigorously justify our definition of anal
 ogue simulation\, where all the physics of a target Hamiltonian is reprodu
 ced in the low energy part of another\, up to arbitrarily small accuracy. 
 This definition is very strong and immediately leads to a number of intere
 sting consequences. For example\, the locality structure of the original H
 amiltonian is preserved\, such that local errors/observables on the simula
 tor correspond to local errors/observables on the original system\, allowi
 ng us to to take a first step in justifying why error correction may not b
 e needed in analogue simulations of this form. A family of Hamiltonians wh
 ich can simulate all other local spin hamiltonians is called "universal"\,
  and we show that this property easily implies BQP-completeness (up to a d
 epth 1 quantum circuit reduction). Finally we show that very simple spin m
 odels such as the qubit Heisenberg or XY interactions are universal in thi
 s sense\, and we are in fact able to classify all sets of two-qubit intera
 ctions into universality classes. (Based on joint work with Toby Cubitt an
 d Ashley Montanaro)
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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