Quantum Information/Computing
at DAMOP 2008
E. Gerjuoy
DAMOP 2008 QC/QI STATISTICS (I)
Invited Paper sessions
There were 28 invited paper sessions, containing 96
(typically half hour long) invited talks. Five of these
sessions had titles which pretty explicitly indicated they
would be of interest for quantum computing (qc) or
quantum information (qi), e.g., “Quantum Control of
Polar Molecules,” and “Optical Quantum Memory.”
Three other sessions, though otherwise titled, contained
one or more invited talks of qc/qi interest. All told, there
were 17 invited papers whose abstracts indicated they
would be of interest to qc/qi researchers. There were
only 5 such invited papers at DAMOP 2007.
GRADUATE STUDENT THESIS SESSION
Titles of Invited talks and Institutions
where work was performed.
1.
2.
3.
4.
“Coherent Manipulation of Single Electronic and
Nuclear Spins in Diamond.” Bates College and
Harvard University.
“Towards Hybrid Quantum Information
Processing With Polar Molecules.” University of
Innsbruck, Austria and Austrian Academy of
Science Institute for Quantum Optic and
Quantum Information.
“Solid State Analogs in Bose-Condensed Gases.”
MIT.
“Remote Entanglement and Quantum Networks
with Trapped Ions.” University of Michigan.
ABSTRACT OF GURUDEV DUTT’S INVITED PAPER
“Coupled Electronic and Nuclear Spin
Quantum Registers in Diamond.”
Building scalable quantum information systems is
a central challenge facing modern science…We
discuss experiments that demonstrate addressing,
preparation, and coherent control of individual
nuclear spin qubits in the diamond lattice at room
temperature…Our results show that coherent
operations are possible with individual solid-state
qubits whose coherence properties approach those
of isolated atoms and ions…[T]he nuclear spins serve
as a resource for quantum memory and quantum
logic operations.
Abstract of Invited Paper QC/QI “Theory”
“Toward Quantum Computing With Polar Molecules.”
David DeMille, Yale University
The unique properties of polar molecules makes them
potentially
very attractive for quantum information processing. The
rotational degree of freedom gives such molecules large
polarizability at DC and microwave frequencies, enabling
strong couplings between distant molecules… In this talk I will
discuss evolving ideas for possible architectures to take
advantage of these properties…I will also discuss our
experimental progress towards this goal.
DAMOP 2008 QC/QI STATISTICS (II)
Contributed Paper sessions
There were 36 Contributed Paper sessions, with
each session typically containing 10-12 ten minute
talks. All told, there were a total of 27 ten minute
papers on subjects of qc/qi relevance, with most of
these papers in a pair of sessions titled:
1. “Quantum Computation”
2. “Entanglement and Decoherence”
The counterpart numbers in DAMOP 2007 were a
total of 47 ten minute talks on subjects of qc/qi
relevance, with four Contributed Paper sessions
largely devoted to qc/qi.
DAMOP 2008 QC/QI STATISTICS (III)
There also were three Poster sessions, with a total of 431
posters. Two subsessions of these Poster sessions, titled
respectively “Quantum Information” and “Quantum
Computation,” contained a total of 10 posters. DAMOP 2007
did not have a “Quantum Computation” poster subsession, but
its “Quantum Information” subsession contained 25 posters.
As in DAMOP 2007, scattered through the various DAMOP
2008 Poster subsessions were other posters of qc/qi interest,
e.g., a poster titled “Experimental test of non-local realism…”
DAMOP 2008 Talks to be (Hopefully) Discussed
1.
2.
3.
“Remote Entanglement and Quantum Networks with
Trapped Atomic Ions,” DAVID MOEHRING,
University of Michigan. Invited Paper, Graduate
Student Thesis Session.
“Geometric Phases and Bloch Sphere Constructions
for SU(N), with a Complete Description of SU(4),”
DMITRY USKOV, Tulane University and RAVI
RAU, Louisiana State University. Contributed 10
minute paper.
“Quantum Computation Schemes Based On Polar
Molecules,” ELENA KUZNETSOVA et al,
University of Connecticut and Harvard-Smithsonian
Center for Astrophysics. Contributed 10 minute
paper.
Abstract of David Moehring Talk
“The recent development of quantum information science and its potential
applications have brought many of the fundamental questions of quantum
physics to the mainstream…I discuss a system at the heart of these questions
—quantum entanglement of the spin states of two individual massive
particles at a distance…I present the theory and the experimental realization
of the entanglement of two trapped atomic ions separated by one meter.
Trapped ions are among the most attractive systems for scalable quantum
information because they can be well isolated from the environment and
manipulated easily with lasers. In particular, I discuss our results including
the first explicit demonstration of both quantum entanglement between a
single trapped ion and its single emitted photon, as well as entanglement
between two macroscopically separated quantum memories. The
entanglement protocols used in these experiments…can be used to create a
platform for a scalable quantum information network or a distributed
quantum computer…”
Outline of presentation
• Motivation
– Why ion-trap quantum computing
• Background
– Requirements for experiments with
trapped ions
– Requirements for remote entanglement of
trapped ions
• Experimental results
– Ion-photon and remote-ion entanglement
– Bell inequality violations
Quantum Computing with Ions and Photons
• Ions: quantum memory
– long-lived coherence (>10 seconds measured)
– trapping times of days
– near-perfect state initialization and detection
• Photons: quantum communication
– coherence over long distances
(kilometers)
Our Ion and Photon Qubits
• Ions: quantum memory
– Hyperfine ground states (171Yb+)
– Qubit rotations via microwaves or
Raman beams
|
|
• Photons: quantum communication
– Orthogonal polarizations/resolved frequencies
– Qubit rotations with waveplates (polarizations)
|V
|H
l/2
Ion-Photon Entanglement
171Yb+
Polarization Qubits
2P
1/2
|
|
2S
1/2
Matsukevich et al., PRL 100, 150404 (2008)
Blinov, Moehring, Duan, Monroe, Nature 428, 153 (2004)
Ion-Photon Entanglement
171Yb+
Polarization Qubits
2P
1/2
369 nm
|V
|
2S
1/2
l/4
Ion
Hyperfine ground states
| state is F=1, m=1
| state is F=1, m=-1
Photon
|H
|
Two different light
polarizations |H and |V
Ion-Photon Entanglement
|H| - |V|
Matsukevich et al., PRL 100, 150404 (2008)
Blinov, Moehring, Duan, Monroe, Nature 428, 153 (2004)
Remote Ion Entanglement
171Yb+
Polarization Qubits
Ion
Hyperfine ground states
| state is F=1, m=1
| state is F=1, m=-1
2P
1/2
369 nm
|V
|
2S
1/2
Photon
|H
|
Two different light
polarizations |H and |V
Ion-Photon Entanglement
(|H| - |V|)a  (|H| - |V|)b
Matsukevich et al., PRL 100, 150404 (2008)
Remote Ion Entanglement
Single Photon Detectors
|Y = (|Ha|a - |Va|a)
 (|Hb|b - |Vb|b)
BS
|Yi = |Hi|i - |Vi|i
2 distant ions
Remote Ion Entanglement
171Yb+
Polarization Qubits
Ion
Hyperfine ground states
| state is F=1, m=1
| state is F=1, m=-1
2P
1/2
369 nm
|V
|
Photon
|H
|
2S
1/2
Two different light
polarizations |H and |V
Ion-Photon Entanglement
(|H| - |V|)a  (|H| - |V|)b
Matsukevich et al., PRL 100, 150404
Coincidence projects ions onto:
|Y-ions = |a|b - |a|b
Remote Ion Entanglement
171Yb+
Frequency Qubits
2P
1/2
369 nm
|
2S
1/2
|
Duan et al., PRA 73, 062324 (2006)
Madsen, et al., PRL 97, 040505 (2006)
Advantages
•Can decay directly to
“clock qubit”
•Can allow for remote
quantum gates directly
Disadvantages
•Difficult to characterize
ion-photon entanglement
Remote Ion Entanglement
171Yb+
Frequency Qubits
Ion
Hyperfine ground states
| state is F=1, m=0
| state is F=0, m=0
2P
1/2
369 nm
Photon
171
Yb + ion
Two different light
frequencies |R and |B
|
2S
1/2
12.6 GHz
|
Moehring et al., Nature 449, 68 (2007)
Remote Ion Entanglement
171Yb+
Frequency Qubits
Ion
Hyperfine ground states
| state is F=1, m=0
| state is F=0, m=0
2P
1/2
Photon
369 nm
Two different light
frequencies |R and |B
|
2S
1/2
12.6 GHz
|
Moehring et al., Nature 449, 68 (2007)
Ion-Photon Entanglement
(||R - ||B)a  (||R - ||B)b
Coincidence projects ions onto:
|Y-ions = |a|b - |a|b
Entangled!
Ion-Photon Bell Inequality Violation
B(qA1, qA2; qB1, qB2) =
|q(qA2, qB2) - q(qA1, qB2)| + |q(qA2, qB1) + q(qA1, qB1)|  2
qphoton
p/4
3p/4
p/4
3p/4
qion
0
0
p/2
p/2
q(qA1, qB2)
-0.57
0.66
-0.70
-0.61
B(p/4, 3p/4; 0, p/2) = 2.54 (0.02)
greater by 27
369 nm
Matsukevich et al., PRL 100, 150404 (2008)
Moehring et al., PRL 93, 090410 (2004)
Yb+
Remote Ion-Ion Bell Inequality Violation
B(qA1, qA2; qB1, qB2) =
|q(qA2, qB2) - q(qA1, qB2)| + |q(qA2, qB1) + q(qA1, qB1)|  2
qphoton
p/4
3p/4
p/4
3p/4
qion
0
0
p/2
p/2
q(qA1, qB2)
-0.58
0.57
-0.52
-0.55
B(p/4, 3p/4; 0, p/2) = 2.22 (0.07)
greater by 3
+
Yb
Matsukevich et al., PRL 100, 150404 (2008)
Yb+
References
K5.05
•
D. N. Matsukevich, P. Maunz, D. L. Moehring, S. Olmschenk and C. Monroe
Bell Inequality with Two Remote Atomic Qubits, Phys. Rev. Lett. 100, 150404 (2008).
•
D. L. Moehring, P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L.-M. Duan and C. Monroe
Entanglement of Single-Atom Quantum Bits at a Distance, Nature 449, 68-71 (2007).
•
S. Olmschenk, K. C. Younge, D. L. Moehring, D. Matsukevich, P. Maunz, and C. Monroe
Manipulation and Detection of a Trapped Yb+ Ion Hyperfine Qubit, Phys. Rev. A. 76, 052314 (2007).
•
P. Maunz, D. L. Moehring, S. Olmschenk, K. C. Younge, D. N. Matsukevich and C. Monroe
Quantum Interference of Photon Pairs from Two Remote Trapped Atomic Ions, Nature Physics 3, 538-541 (2007).
•
D. L. Moehring, M. J. Madsen, K. C. Younge, R. N. Kohn, Jr., P. Maunz, L.-M. Duan, C. Monroe, and B. B. Blinov
Quantum Networking with Photons and Trapped Atoms, J. Opt. Soc. Am. B, 24, 300-315 (2007).
•
M. J. Madsen, D. L. Moehring, P. Maunz, R. N. Kohn, Jr., L.-M. Duan, and C. Monroe
Ultrafast Coherent Coupling of Atomic Hyperfine and Photon Frequency Qubits, Phys. Rev. Lett. 97, 040505 (2006).
•
L.-M. Duan, M. J. Madsen, D. L. Moehring, P. Maunz, R. N. Kohn, Jr., and C. Monroe
Probabilistic Quantum Gates between Remote Atoms through Interference of Optical Frequency Qubits, Phys. Rev. A
73, 062324 (2006).
•
D.L. Moehring, M. J. Madsen, B.B. Blinov, and C. Monroe
Experimental Bell Inequality Violation with an Atom and a Photon, Phys. Rev. Lett. 93, 090410 (2004).
•
L.-M. Duan, B. B. Blinov, D. L. Moehring, and C. Monroe
Scalable Trapped Ion Quantum Computation with a Probabilistic Ion-Photon Mapping, Quant. Inf. Comp. 4, 165-173
(2004).
•
B.B. Blinov, D.L. Moehring, L.-M. Duan, and C. Monroe
Observation of entanglement between a single trapped atom and a single photon, Nature 428, 153-157 (2004).
C6.09
Abstract of Dmitry Uskov Talk
Geometric Phases and Bloch Sphere Constructions
for SU(N), with a Complete Description of SU(4).
A two-sphere (“Bloch” or “Poincare”) is familiar for
describing the dynamics of a spin-1/2 particle or light
polarization. Analogous objects are derived for unitary
groups larger than SU(2). We focus, in particular, on
the SU(4) of two qubits which describe all possible logic
gates in quantum computation. For a general
Hamiltonian of SU(4) with 15 parameters we derive
Bloch-like rotation of unit vectors analogous to the one
familiar for a single spin in a magnetic field.
See: Quant-ph 0801.2091.
15 generators of the SU(4) group
Hamiltonian   ˆ n xn (t ), ˆ n are generators of SU (4)
 x (1) ,  y (1) ,  z (1)
spin 1 / 2 Local rotations SU (2) group
 x (2) ,  y (2) ,  z (2)
spin 1 / 2 Local rotations SU ( 2) group
 x (1) z (2) ,  x (1) y (2) ,  x (1) x (2) 
y z , y  y ,  y x
(1)
(2)
(1)
(2)
(1)
(2)
 z (1) z (2) ,  z (1) y (2) ,  z (1) x (2)

 spin  spin coupling


We suggest an algebraic descriptions of dynamics of 2dimentional subspaces of 4-leves systems in a form quite
similar to the Bloch-vector description of 2-level density matrices,
using transformed
Plucker Coordinates on Grassmanian
manifolds G(2,4,C)
Six Plucker Coordinates are 6 minors of 2×4 matrix
P1,2..6  P1,2 ,  P1,3 , P1,4 , P2,3 , P2,4 , P3,4 
for example,
 u11 u12 
P1,2  det 

u
u
 21 22 
 u11 u12 
u u 
 11 22 
 u11 u32 


u
u
 11 42 
To illustrate how the method may lead to some
physical insights in a complicated non-stationary quantum
problem consider two interacting qubits – the cornerstone
problem in quantum information theory.
The full dynamic group is 15-dimentional SU(4) group of unitary
transformations. Present method allows to obtain semi-analytic solution
for the Spin(5) 10-dimentional subgroup of the SU(4).
The Hamiltonian of the problem has the form of a linear
combination of ten generators with time-dependent coefficients. We
group the latter in a form of 5×5 antisymmetric real matrix (for the
purpose which will be clear shortly). Using common representation of
su(4) generators as tensor products of standard Pauli matrices we write
the Hamiltonian as
H = F2,1 3 2  F3,1  2 2  F3,2 1 2  F4,i  31 i 2  F5,i 11 i 2  F5,4  21
Abstract of Elena Kuznetsova Talk
Polar molecules have recently attracted significant interest as a
viable platform for quantum computing. They combine the
advantages of neutral atoms and trapped ions, making them
compatible with various architectures, e.g., optical lattices and
solid-state systems. Molecules with large permanent dipole
moments can display strong dipole-dipole interactions, allowing for
the realization of fast conditional two-qubit gates. In recent work
we proposed a model of controllable dipole-dipole interactions in
which laser excitation from a ground electronic state with negligible
dipole moment to an excited state with a large dipole moment
allows one to “switch on” the interaction…We study the robustness
of such a phase gate and analyze the experimental feasibility of the
approach, using the CO molecule as a specific example. We are
continuing to investigate several other schemes involving polar
molecules and novel architectures such as a solid-state approach
with polar molecules doped into rare-gas matrices.
Kuznetsova, et al, Phys. Rev. A 78, 012313 (July 2008).
Why polar molecules?
D. DeMille, Phys. Rev. Lett. 88, 067901 (2002)
Combine advantages of neutral atoms and trapped ions
•
Rich level structure: electronic, vibrational, rotational states + electronic and
nuclear spin states
•
Long coherence times
•
1
~
Permanent electric dipole moment: strong dipole-dipole interactions 3
R
•
Manipulation with AC and DC electric fields
•
Compatibility with various architectures, integration into solid-state systems
•
Scalability to large number of qubits
superconducting stripline resonators +
optical lattices
electrostatic traps
Two-qubit phase gate with “switchable”
| e
| e
dipoles
|00› → |00› → |00› → |00›,
large dipole
moment state
π pulses
|01› → i|0e› →
zero dipole
moment state
| 1
| 1
| 0
| 0
π pulses
i|0e› → -|01›,
|10› → i|e0› → i|e0› → -|10›,
|11› → -|ee› → -eiφ|ee› → |11› if φ=π
direct scheme
zero
dipole
moment
state
large
dipole
moment
state
| e
| e
π pulses
π pulses
|00› → |00› → eiφ|00› → -|00›, if φ=π
| 1
| 1
| 0
| 0
inverted
scheme
|01› → i|0e› → i|0e› → -|01›,
|10› → i|e0› → i|e0› → -|10›,
|11› → -|ee› → -|ee› →
|11›
Molecular system for direct phase
gate - 13CO (carbon monoxide)
• Small μ state: ground X 1Σ+ state (μ=0.1 D)
• Large μ state: metastable a 3Π0 state (μ=1.4 D)
• Qubit states: nuclear spin states of 13C (I=1/2) in X 1Σ+
| Y1, 2 
•
state: entangled hyperfine sublevels of J=0 and J=1 of a
3Π state
0
F=3/2
+3/2
+1/2
-1/2
96 GHz
-1/2
-3/2
-1/2
F=1/2
+1/2
+1/2
-1/2
+1/2
J=0
+3/2 +1/2
J=1
~ 100 MHz
J=1
a 30
F=3/2
-3/2
F=1/2
| 0
|1
J1FX
31
==+
11/
10C
2
//
2
O
2
+
J=0
F=1/2
-1/2
Decoherence mechanisms
•
Storage and switching states
-
Hyperfine states - lifetimes ~ hours
-
Metastable switching states - lifetimes ~ sec;
phase gate times ~10-100 μs - spontaneous emission is small
-
Dipole-dipole interaction – excitation of translational states of lattice potential – phase error;
adiabatic excitation to large dipole moment states or use dipole blockade

-
Optical π and 2π pulses
Spatially varying Rabi frequency – imperfect pulse area
load molecules to translational ground state

Optical lattice
-
Scattering of lattice photons - loss of molecules
-
Lifetimes in far-detuned lattices ~0.1 -1 s

Gate times ~100 μs, coherence times ~1 s – number of operations ~ 104
major decoherence
source
Conclusions
• Polar molecules in an optical lattice represent an attractive platform for
quantum computation
• Polar molecules with “switchable” dipole moments allow one to realize a
universal set of quantum gates
• Direct phase gate can be realized with molecules similar to CO, inverted
scheme – with mixed alkali dimers
• Direct vs. inverted scheme:
Direct scheme can be electric-field free – more robust for decoherence
But:
cooling and trapping techniques are not available for general polar
molecules
Inverted scheme:
most polar molecules have large dipole moment in the ground state –
easier to find a candidate