Atomer: Fysikkens Rolling Stones

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Quantum Computing as a Collective
Effort Klaus Mølmer Aarhus, Denmark Collabor
ation with Karl Tordrup, Antonio Negretti,
Zoltan Kuzucs, Aarhus (Ulm) Rob
Schoelkopf and Dave Schuster, Yale Andrew
Briggs, Hua Wu, Arzhang Ardavan, John Morton,
and Janus Wesenberg, Oxford
(Singapore)
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Quantum computing, the usual way

• N bits in N atom product states
• Individual access? one-bit gates
• Interactions? two-bit gates

State 01 001gt
This talk Collective Encoding
Many identical quantum systems share all quantum
bits.
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uper atom



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Many-atom collective states

• Strong coupling ( vN superradiance)
• (ltb,a, .. alta,b,a .. a lta,a, b)/vN VN
  aa agt vN ltbV1agt

• Weak dependence on loss and on imperfect
  preparation
• aa .. agt agt ? (b,a, .. agta,b,a .. agt a,a,
  bgt) agtaa .. agtV agt

M random atoms
vN k1gt
M incoherent terms

• Only need Hamiltonian, invariant under
  permutations among particles

• Slow and stopped light
• Quantum state storage and teleportation with
  ensembles
• Quantum spin squeezing and entanglement
• Quantum repeaters
• Precision probing, magnetometry
• in continuous variable setting.

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uper Qubit
0gt
1gt



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Two questions1. How do we restrict the
collective excited state population to only zero
and one ?2. How do we encode more than a single
qubit ?
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• This talk
• 1 Collective excitation through a circuit cavity
  field,
• blocked by a Cooper pair box two-level
  system.
• 2 Holographic storage of qubits in
• spatially extended ensemble.

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The system Nature 431, 162 (2004) 449, 443
(2007),
cm long meandering stripline cavity confines
an RF quantum field to a few micron wide field
mode.
This work, Imamoglu
Zoller, KM,
Sørensen, Saffman,
This work,
Yale,
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The system Nature 431, 162 (2004) 449, 443
(2007),
cm long meandering stripline cavity confines
an RF quantum field to a few micron wide field
mode.
This work, Imamoglu
Zoller, KM,
Sørensen, Saffman,
This work,
Yale,
vN enhancement
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Details of our proposal Wesenberg et al., Phys.
Rev. Lett. 103, 070502 (2009) (See also, A.
Imamoglu, Phys.Rev.Lett.102, 083602, (2009)).
P in Si
NV centers in diamon
Rare earth ions

Collectively enhanced (vN) coupling to N 1010 -
1012 spins Hz ?MHz !!!
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uperqubits
Phase gradient
eif(z)



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From one bit to many holographic storage

• ggt ?gt, egt?gt
• Gradient Zeeman shift
• Phase f(z)kz
• 1000 orthogonal modes

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A quantum Turing machine
Magnetic field gradients to shift memory
Superconducting qubit processor head
Electron spin ensemble memory
By Tom DunneAmerican Scientist 2002 (With thanks
to Dave Schuster, Yale)
Cavity interface

• Key properties
• A processor head
• Processor/Memory interface
• A homogenous storage medium
• Means of winding the tape

So, how well does it work ?
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µsec
10-100 MHz
msec
2g 100 MHz
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µsec
1-10 MHz
10-100 MHz
msec-sec
msec
Schoelkopf group at Yale has seen collectively
enhanced Coupling in gt MHz range, (unpublished).
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msec-sec
1-10 MHz
µsec
1-10 MHz
10-100 MHz
msec-sec
msec

• B-gradient for winding tape
• (-B)-gradient for re-wind
• - or p-pulse same gradient!

H. Wu et al P-doped silicon arXiv0908.0101
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Going nuclear

• Electron spin coherence times few msec.
• Nuclear spin coherence times few sec.

H. Wu et al arXiv0908.0101
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• Status and outlook for collective spin ensemble
  computer
• 100-1000 qubit register with simple, fast access
• Coherence time gtgt gate time
• Collective coupling of circuit cavity field to
  macroscopic spin ensemble has been observed
  (Yale, 2008).
• Holographic storage of classical field
  amplitudes in separate modes in electron spin
  ensemble has been observed
• Seconds of storage time in nuclear spin (Oxford,
  2009).
• Theory analysis of decoherence mechanism,
  refocussing, addressing .
• Search for optimum candidate systems
• N_at_C60, P in Si,
• NV centers in diamond,
• rare-earth HF-states,