Quantum information with cold atoms
Zheng-Wei Zhou( 周正威)
Key Lab of Quantum Information , CAS, USTC
October, 2009 KITPC
• Backgrounds on Quantum Computation(QC)• Quantum Computation(QC) and Quantum
Simulation(QS) with Cold atoms Standard model for QC
One-Way QC
QS for highly-correlated many body models
• Quantum Communication• Summary and Outlook
Outline
Backgrounds on Quantum Computation(QC)
Father of QC ( 1981 - 1985 )
Elementary Gates for QC ( 1995 )
A. Barenco (Oxford), C. H. Bennett (IBM), R. Cleve (Calgary), D. P. DiVincenzo (IBM), N. Margolus (MIT), P. Shor (AT&T), T. Sleator (NYU), J. Smolin (UCLA), H. Weinfurter (Innsbruck)
R. Feynman D. Deutsch
C. H. Bennett
Quantum Algorithms
1994
1997
Some Methods to Overcome Decoherence
( 1 ) Quantum Error Correcting Codes( Shor , Steane , Calderbank , Laflamme , Preskill , etc. )( 1995 - 2000 )
( 2 ) Decoherence-Free Subspaces( Duan, Guo, Zanardi, Whaley , Bacon, Lidar, etc. )( 1997 - 2000 )
( 3 ) Dynamical Decoupling method( Lolyd , Viola , Duan , Guo, Zanardi , etc. ) ( 1998 - 1999 )
Standard Model for QC
Beyond Standard model (I)
• Topological Quantum Computing
A. Kitaev (1997)
Beyond Standard model (II)
• One Way Quantum Computing
R. Raussendorf H. Briegel (2000)
Beyond Standard model (III)
• Adiabatic Quantum Computation
Dorit Aharonov et. al (2004)
J. Goldstone et. al (2000)
E
t
......
Adiabatic QCStandard QC
P. Zoller
D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac and P. Zoller (1998)
Intermediate targets of QC——Simulating highly-correlated many body systems
D. Jaksch
Quantum Computer
Standard QC
model
Quantum Simulation
Adiabatic
QC
Beyond Classical Computer
Topological
QC
Deco
heren
ce, Scalab
ility, En
ergy g
ap,
etc
Once Fault-Tolerant QC can be realized…
Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms
Standard model for QC
One-Way QC
QS for highly-correlated many body models
Standard Model for QC
1. Register of 2-level systems (qubits)
The physical origin of the confinement of cold atoms with laser light is the dipole force:
Olaf Mandel, et al., Phys. Rev. Lett. 91, 010407 (2003)
2. Initialization of the qubit register
However, nonideal conditions will always result in defects in that phase (i.e., missing atoms and overloaded sites). How to suppress these defects in the lattice?
A possible approach is: the coherent filtering scheme.
P. Rabl, et al., Phys. Rev. Lett. 91,110403, (2003)
3 、 4. Tools for manipulation: 1- and 2-qubit gates and readout 1-qubit
1: Whether global operations are enough to implement universal quantum computation?
2: How to addressing single qubit in this system?
As far as ultracold atoms trapped in an optical lattice is concerned, global operations on atoms are available. However, addressing individual atom becomes very difficult. So, to implement universal quantum computation, we should answer the following questions:
OR
(S. Lloyd, Science 261, 1569 (1993); S. C. Benjamin, PRA 61, 020301R, 2000, PRL 88, 017904, 2002)
Some proposals for QC via global operations
Cellular-automata Machine
QC via translation-invariant operations
R. Raussendorf, Phys. Rev. A 72, 052301 (2005). K. G. H. Vollbrecht et al., Phys. Rev. A 73, 012324 (2006). G. Ivanyos, et al., Phys. Rev. A 72, 022339 (2005).Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).
In the above proposals, only translationally invariant global operations are required!
Redundant qubits (space and time overhead)
Initialization
Physical implementation
Shortcomings:
Bose Hubbard model
Ising Model
Type I
Type II
PRL 91,090402 (2003)
PRL 81, 3108 (1998); 90, 100401(2003); 91,090402 (2003)
Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).
(Effective periodic magnetic field induced by left and right circularly polarized light)
1D
2D
Addressing single qubit
Two-qubit operation
Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).
(Phys. Rev. A 70, 012306 (2004); Phys. Rev. Lett. 93, 220502 (2004))
Some proposals for QC via addressing single atom
Marked Qubit as Data-bus
Phys. Rev. A 70, 012306 (2004)
single-qubit rotation via multiqubit addressing
J. Joo, et al., PHYSICAL REVIEW A 74, 042344 (2006)
single-qubit rotation via Position-dependent hyperfine splittings
C. Zhang, et al., PHYSICAL REVIEW A 74, 042316 (2006)
the progress of experiments
Imaging of single atoms in an optical lattice
Nelson, K. D., Li, X. & Weiss, D. S. Nature Phys. 3, 556–560 (2007).
effective magnetic field results from the atom‘s vector light shift :
Novel quantum gates via exchange interactions
Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in anoptical lattice. Nature 448, 452–456 (2007).
Science 319, 295–299 (2008).
Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).
5. Long decoherence times
How many gate operations could be carried out within a fixed decoherence time?
“ For the atoms of ultracold gases in optical lattices, Feshbach resonances can be used to increase the collisional interactions and thereby speed up gate operations. However, the ‘unitarity limit’ in scattering theory does not allow the collisional interaction energy to be increased beyond the on-site vibrational oscillation frequency, so the lower timescale for a gate operation is typically a few tens of microseconds.”
“ Much larger interaction energies, and hence faster gate times, could be achieved by using the electric dipole–dipole interactions between polar molecules, for example, or Rydberg atoms; in the latter case, gate times well below the microsecond range are possible.”
I. Bloch, NATURE|Vol 453|19 June 2008|doi:10.1038.
Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms
Standard model for QC
One-Way QC
QS for highly-correlated many body models
R. Raussendorf H. Briegel
R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188, (2001)
Graph states
Graph States
Stabilizer code
For Example:1 32
1 2X Z
1 2 3Z X Z
2 3X Z
( 000 001 010 011 100 101 110 111 )L
Given a graph , the corresponding graph state is
Given a graph , the corresponding graph state is
A Controlled Phase Gate
D. Jaksch, et. al., Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett. 82, 1975 (1999).
Nature 425, 937 (2003)
Nature 425, 937 (2003)
New Journal of Physics 10 (2008) 023005
New Journal of Physics 10 (2008) 023005
Preparation of decoherence-free cluster states with optical superlattices
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kyVkyVxV
kxVkxVxV
yVxVV
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Liang Jiang, et. Al., Phys. Rev. A 79, 022309 (2009)
Logical qubit in decoherence-free subspace
1,2 3,4
2,3 4,1
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V
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S S
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Logical qubit:
Implementing a C-Phase Gate
Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms
Standard model for QC
One-Way QC
QS for highly-correlated many body models
Cold Atoms Trapped in Optical Lattices to Simulate condensed matter physics
D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac and P. Zoller (1998)
Advantages as one of promising candidates of quantum simulations
Neutral atoms couple only weakly to the environment, allowing long storage and coherence times.
So far, cold atoms trapped in optical lattices is the only system in which a large number of particles can be initialized simultaneously.
Highly controllabilityControl of interaction strength with magnetic field (Feshbach Resonance)Various geometry of optical latticesControllable tunneling ratesBosons, Fermions, or mixture
Bose-Hubbard Model
Effective highly-correlated many body models
Two-component Bose-Hubbard Model
Feshbach resonance -- magnitudeOptical lattice -- diversity Experiments: Ketterle, Esslinger etc.
• Weakly interacting fermions in an optical lattice
-- single-band Hubbard model (Hofstetter et al, PRL 2003)
i
iiiijji
iweak aaaauaatH ,
• Strongly (resonantly) interacting fermions in optical lattice
-- Boson-fermion Hubbard model ??
i
iiii
iionweakstrong bbaabgHH
Stoof, Holland, Zhou, etc., 2005 Inadequate!
Fermions in an Optical Lattice
• Multi-band populations (T.-L. Ho, cond-mat/0507253; 0507255, PRL 2006)
i
iiii
iionweakstrong bbaabgHH
Why is it inadequate?
~bgon Eg
Band gapOn-site coupling rate
tgoff • Off-site collision couplings (L.-M. Duan, PRL 95, 243202,2005)
Off-site coupling rate
Tunneling rate
Off-site coupling
toffg
ir
pqriiqippqr aabg
;Different bands
Strong interaction effects
• Starting point: the field Hamiltonian
•Keep all the bands
•Keep the off-site couplings
L.-M. Duan, PRL 95, 243202,2005
• Limiting case2: molecule limit
• Limiting case 1: atom limit
Quantum simulation with polar molecules
A. Micheli, G. K. Brennen and P. Zoller, A toolbox for lattice-spinmodels with polar molecules, Nature Physics, 2, 341 (2006)
• Time-of-flight imaging
expansion
tt rr density
mktrrt /0
condensate
Diagonal correlation in momentum space
kk
Detection of ultracold atoms
One can also utilize density-density correlations in the image of an expanding gas cloud to probe complex many-body states.
Nature Physics, 4, 50 (2008)
Nature Physics, 4, 50 (2008)
Quantum Simulation
Quantum Computer
Limits from classical world
Starting point
Quantum Communication Why long-distance quantum communication is so difficult?
Transmission loss/fidelity of entanglement—decreasing exponentially with the length of the connecting channel
Solution: Quantum repeater combining entanglement swapping and purification [H. Briegel et al., Phys. Rev. Lett. 81, 5932 (1998)]
Atomic-ensemble-based quantum memory is used to transfer the photonic states to the excitation in atomic internal states so that it can be stored, and after the storage of a programmable time, it should be possible to read out the excitation to photons without change of its quantum state.
M.D. Lukin et al., Phys. Rev. Lett. 84, 4232 (2000); M. Fleischhauer and M.D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
Atomic-ensemble-based quantum memory
Physical implementation of Quantum Repeater:
A Scheme based on atomic ensembles, the DLCZ scheme
[L.-M. Duan et al., Nature 414, 413 (2001)]
The phase stability problem in the DLCZ scheme
In the DLCZ protocol, two entangled pairs are generated in parallel. The relative phase between the two entangled states has to be stabilized during the entanglement generation process.
As entanglement generation process is probabilistic. The experiment has to be repeated many times to ensure that there is a click at the detectors. The two phases achieved at different runs of the experiments are usually different due to the path length fluctuations in this time interval.
A robust, fault-tolerant quantum repeater
•a) Local preparation of entanglement (at adjacent nodes) by a linear-optical polarization entangler and then entanglement swapping
•(b) Entanglement connection
•(c) Linear-optical entanglement purificationB. Zhao, Z.-B.Chen. et al., Phys. Rev. Lett, 98, 240502 (2007); Z.-B.Chen. et al., Phys. Rev. A 76, 022329 (2007).
Summary and Outlook
Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms
Standard model for QC
One-Way QC
QS for highly-correlated many body models
Quantum Communication
Lowering the temperatureAchieving single-site addressing