ultra-fast database search: super-parallel holography versus quantum computing team: john shen...
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Ultra-fast Database Search: Super-Parallel Holography versus Quantum Computing
Team:John Shen (Graduate Student)Dr. Renu Tripathi (Post-Doc)Prashanth Ravishankar (UG)Matthew Hall (UG)
Supported By:DARPA, AFOSR
QUANTUM COMPUTER
USES INDIVIDUAL QUANTUM SYSTEMS AS BITS
APPLICATIONS
FACTORING VERY LARGE NUMBERS EFFICIENTLY
SPEEDY DATA BASE SEARCH
QUANTUM MEMORY FOR QUANTUM COMMUNICATION SYSTEMS
SIMULATION OF QUANTUM SYSTEMS
COMPUTING POWER IS EXPONENTIAL IN NUMBER OF BITS
WHY IS QUANTUM COMPUTER POWERFUL ? : ENTANGLEMENT
QUANTUM COMPUTER: SIMPLE DEFINITION
1 2 3 4 ……………………………………………………………………… n
N=2n ALLOWED STATES: |1>=|0,0,0,0,0,0,…….0,0,0>
|2>=|0,0,0,0,0,0,…….0,0,1>
|N>=|1,1,1,1,1,1,…….1,1,1>
CREATE AN OPERATOR: ji
NjNi
jijiQ
,
1,1,
ˆ
A MACHINE CAPABLE OF PRODUCING THIS OPERATOR, REPRESENTED AS AN NXNMATRIX, IS A QUANTUM COMPUTER
CAN BE REALIZED WITH SINGLE BIT OPERATION AND NEAREST-NEIGHBOR INTERACTION
EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER
1 2 3 4 ……………………………………………………………………… n
PREPARE THE SYSTEM IN AN EQUAL SUPER-POSITION OF EACH OF THE N=2n STATES, REPRESENTING THE STORED DATA BASE:
|1>=|0,0,0,0,0,0,…….0,0,0>
|2>=|0,0,0,0,0,0,…….0,0,1>
|N>=|1,1,1,1,1,1,…….1,1,1>
|1> |2> |3> ………………………………………...... |N>
EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER
1 2 3 4 ……………………………………………………………………… n
OBJECT OF SEARCH IS ONE OF THESE STATES:
|1>=|0,0,0,0,0,0,…….0,0,0>
|2>=|0,0,0,0,0,0,…….0,0,1>
|N>=|1,1,1,1,1,1,…….1,1,1>
|K>
|1> |2> |3> ………………………………………...... |N>
EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER
1 2 3 4 ……………………………………………………………………… n
QUANTUM COMPUTER USED TO FLIP THE SIGN OF THIS STATE ONLY:
|1>=|0,0,0,0,0,0,…….0,0,0>|2>=|0,0,0,0,0,0,…….0,0,1>
|N>=|1,1,1,1,1,1,…….1,1,1>
|K> -|K>
|1> |2> |3> ………………………………………...... |N>
EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER
1 2 3 4 ……………………………………………………………………… n
COMPUTE AVERAGE, AND FLIP EACH STATE AROUND THE AVERAGE:
Vi A+(A-Vi)
|1> |2> |3> ………………………………………...... |N>
|1> |2> |3> ………………………………………...... |N>
EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER
1 2 3 4 ……………………………………………………………………… n
AFTER O(N) STEPS, SYSTEM IS NEARLY IN
|1>=|0,0,0,0,0,0,…….0,0,0>
|2>=|0,0,0,0,0,0,…….0,0,1>
|N>=|1,1,1,1,1,1,…….1,1,1>
|K>
|1> |2> |3> ………………………………………...... |N>
SUMMARY SO FAR
A quantum computer can search through N unsorted objects in O(N1/2) steps, using only O(Log2N) quantum bits (Grover’s Algorithm: GA)
The specific device we discussed is the Holographic Super-Correlator, which performs angularly-multiplexed correlation in a thick hologram in many spatial spots simultaneously
However, given the necessity to store the database for a long time, it is likely that the user would need O(N) classical resources anyway
As such, the real significance of GA is that the search requires O(N1/2) steps
Here we show a practical search engine that takes only O(N1/2) steps
It requires O(N) resources for memory, and O(N1/2) resources for search
HOLOGRAPHIC OPTICAL CORRELATOR: BASIC IDEA
HOLOGRAPHIC OPTICAL CORRELATOR: BASIC IDEA
PROBLEMS: (A) SPATIAL MULTIPLEXING IS POTENTIALLY SLOW (B) CAN NOT COMPARE ALL OF THEM SIMULATANEOUSLY
HOLOGRAPHIC SUPER CORRELATOR : BASIC CONCEPT
LA
SER
DIGITAL LOGIC
FOR
THRESHOLDING
AND
DECODING
TARGET ID: 7968023
SLM
BE
LA
SER
LA
SER
RE
AD
LA
SER
DIGITAL LOGIC
FOR
THRESHOLDING
AND
DECODING
TARGET ID: 7968023
SLM
BEAM EXPANDER
HOLOGRAPHIC MEMORY
TARGET IMAGE
LENSLET ARRAY
HOLOGRAPHIC REDIRECTOR
HOLOGRAPHIC MUX/DEMUX
IMAGE FLATTENINGBEAM REDUCER BEAM
EXPANDER
LENSLET ARRAY
CCD ARRAY
CC
D A
RR
AY
BEAM SPLITTER
APERTURE
HOLOGRAPHIC MULTIPLEXER/DEMULTIPLEXER
WRITINGA 1X3 HMD
INDIVIDUALREADING
SIMULTANEOUSREADING
TARGET ID: 7968023
SLM
CC
DA
BS
BS
HMDX HMDXHR HMULLA HR
BE
BEIFBR
AP
LLA
CCDA
M/# Needed: N
HOLOGRAPHIC REDIRECTOR
WRITINGA 3 ELEMENTHRO
READINGA 3 ELEMENTHRO
TARGET ID: 7968023
SLM
CC
DA
BS
BS
HMDX HMDXHR HMULLA HR
BE
BEIFBR
AP
LLA
CCDA
M/# Needed: 1
HOLOGRAPHIC MEMORY UNIT
TARGET ID: 7968023
SLM
CC
DA
BS
BS
HMDX HMDXHR HMULLA HR
BE
BEIFBR
AP
LLA
CCDA
Substrate: PDA/MemplexTM
Size: 15 cm X 15 cm X 5 mm
Number of Cells: 1600
Images in each cell: 1000X8
Bits per image: 1028X1028
Capacity: 13 mil images/1.6 TB
MEMORY WRITING SETUP
16-BIT BUS
16-BIT BUS
GALVODRIVER
TEL 1
TEL 3
TE
L 2
PBS50/50 BS
GM1
M2
LA
SE
R
M1
SH
UT
TE
R
HMU
SLM
2D STAGEDRIVER
2D
STA
GE
COMPUTER
DVD
SLM DRIVER
CONTROLPANEL DATA PAGE
2 PLATE
NCO
MB
. LO
GIC GM2
2D SCANNING MECHANISM
Diode LaserDetector
BS
ReflectiveScreen withHole s
CP-X
CP-Y
FP(dx,dy)
MMU
Feedback
X
Y
CONTROLBOX
CP Scanning Mechanism
HMU
LENSLET ARRAY
TARGET ID: 7968023
SLM
CC
DA
BS
BS
HMDX HMDXHR HMULLA HR
BE
BEIFBR
AP
LLA
CCDA
SCHEMATIC REAL
DEMONSTRATION OF HMDX
CORRELATION WITH DIRECT IMAGE FROM SLM
Recorded Holographic Images Image Correlation Diffraction Spots Diffraction Intensity
SIMULTANEOUS CORRELATION WITH 3X3 HMDX
1x9 SPLITTER
3x3 REDIRECTOR
3X3 HMU
8 POSSIBLE DIFFRACTION BEAMSFROM EACH MEMORY CELL
1x9 SPLITTER
3x3 REDIRECTOR
3X3 HMU
8 POSSIBLE DIFFRACTION BEAMSFROM EACH MEMORY CELL
SIMULTANEOUS CORRELATION WITH 3X3 HMDX
12
3
S1
S2
S30
2
4
6
8
10
12
Efficiency
Column
Row
Splitter Diffraction Efficiency
12
3
S1
S2
S30
2
4
6
8
10
12
Efficiency
Column
Row
Splitter Diffraction Efficiency
a.
b.
c.
d.
a.
b.
c.
d.
SIMULTANEOUS CORRELATION WITH 3X3 HMDX
1
2
3S1
S2
S3 0
10
20
30
40
50
60
70
80
Efficiency
Column
Row
Redirector Diffraction Efficiency
SIMULTANEOUS CORRELATION WITH 3X3 HMDX
3.81 cm.
3.81
cm
.
1 2 3
4
7
5 6
8 9
3.84 mm.
3.84
mm
.
2.0 mm.
a.
SPA
TIA
L P
OSI
TIO
N
1
2
3
4
5
6
7
8
9
A B C D E F G H
STORAGE ANGLEb.
SPA
TIA
L P
OSI
TIO
N
1
2
3
4
5
6
7
8
9
A B C D E F G H
STORAGE ANGLEb.
SIMULTANEOUS CORRELATION WITH 3X3 HMDX
1 2 3 4
5 6 7 8 9
c.3.81 cm.
3.81
cm
.1 2 3
4
7
5 6
8 9
3.84 mm.
3.84
mm
.
2.0 mm.
a.
a.
b.
SIMULTANEOUS CORRELATION WITH 3X3 HMDX:3X8 IMAGES IN EACH LOCATION
1x9 SPLITTER
3x3 REDIRECTOR
3X3 HMU
3x8 POSSIBLE DIFFRACTION BEAMSFROM EACH MEMORY CELL
1x9 SPLITTER
3x3 REDIRECTOR
3X3 HMU
3x8 POSSIBLE DIFFRACTION BEAMSFROM EACH MEMORY CELL
SIMULTANEOUS CORRELATION WITH 3X3 HMDX:3X8 IMAGES IN EACH LOCATION
0.95 0
0.79 0
a.
+0.95° Vertical Angle Set
0° Vertical Angle Set
-0.71° Vertical Angle Set
b.
SIMULTANEOUS CORRELATION WITH 3X3 HMDX:3X8 IMAGES IN EACH LOCATION
Correlation for images 1 to 8
(First Row).
Correlation for images 9 to 16
(Second Row).
Correlation for images 17 to 24
(Third Row).
Correlation for images 1 to 8
(First Row).
Correlation for images 9 to 16
(Second Row).
Correlation for images 17 to 24
(Third Row).
0.95 0
0.79 0
a.
+0.95° Vertical Angle Set
0° Vertical Angle Set
-0.71° Vertical Angle Set
b.
COMPARISON WITH QUANTUM DATABASE SEARCHL
ASE
R
SLM
CC
DA
BS
BS
HMDXHMDXHR HMU LLA HR
BE
BEIFBR
AP
LLA
CCDA
IF
N Spatial Locations
N Im
ages Per L
ocation
O(N) Steps Needed to Search Through N Unsorted Objects
Same Speed-Up As Offered By Grover’s Algorithm for Quantum Database Search
PROPOSED SUPER-PARALLEL HRAM
IMAGING CCD
RETRIEVED IMAGE
IMAGE FLATTENING
BEAM EXPANDER
APERTURE
2-D BEAM DEFLECTOR
REDIRECTOR
SHUTTER LENSLET ARRAY
HOLOGRAPHIC MULTIPLEXER/DEMULTIPLEXER
HOLOGRAPHIC MEMORY UNIT REDUCING
TELESCOPE
READ LASER
TARGET ID: 7968023TARGET ID: 7968
REDIRECTOR
APERTURE
CCDHMU
TELESCOPE
HOLOGRAPHIC REDIRECTOR
READ OUT DATA
READ BEAM
338 HMU
(1,1) (1,2) (1,3)
(2,1) (2,2) (2,3)
(3,1) (3,2) (3,3)
SPLITTER
Data Read-Out From Location 3X2
PRELIMINARY RESULTS FROM SIMPLE GEOMETRY
HOLOGRAPHIC OPTICAL CORRELATOR: THIN MEDIUM: UAV GUIDANCE
HOLOGRAPHIC OPTICAL CORRELATOR: THIN MEDIUM: UAV GUIDANCE
HOLOGRAPHIC OPTICAL CORRELATOR: ASSOCIATIVE MEMORY
READ/WRITELASER(690 NM)
SLMMIRROR
MEMORYCUBE: BR
FT LENS FT LENSBS BS
AMPLIFY &THRESHOLD ACTIVATION
LASER(635 NM)
TRANSLATION STAGE
SHIFT-INVARIANTASSOCIATIVEMEMORY
CCD
HOLOGRAPHIC OPTICAL CORRELATOR: ASSOCIATIVE MEMORY
INPUTIMAGE
THRESHOLDED CORRELATION PEAKS
PAGE 1 PAGE 2 PAGE 3
IMAGE ID’D & RECALLED
MATERIALS FOR TWO-PHOTON MEMORY: BACTERIORHODOPSIN
PROPOSED SUPER-PARALLEL ASSOCIATIVE MEMORY
Holographic MemoryLenslet ArrayHolographic
Redirector
Holographic Mux/Demux
TARGET ID: 7968023TARGET ID: 7968023
Aperture
CCD
AC
TIV
AT
ION
LA
SE
R
RE
AD
LA
SE
R
Aperture
SLM
inpu
t
TRAN STAGELENSLET ARRAY
DET ARRAY
Holographic Redirector
MIRROR
FLC SHUTTERARRAY
Holographic MemoryLenslet ArrayHolographic
Redirector
Holographic Mux/Demux
TARGET ID: 7968023TARGET ID: 7968023
Aperture
CCD
AC
TIV
AT
ION
LA
SE
R
RE
AD
LA
SE
R
Aperture
SLM
inpu
t
TRAN STAGELENSLET ARRAY
DET ARRAY
Holographic Redirector
MIRROR
FLC SHUTTERARRAY
Holographic MemoryLenslet ArrayHolographic
Redirector
Holographic Mux/Demux
TARGET ID: 7968023TARGET ID: 7968023TARGET ID: 7968023TARGET ID: 7968023
Aperture
CCD
AC
TIV
AT
ION
LA
SE
RA
CT
IVA
TIO
NL
AS
ER
RE
AD
LA
SE
R
ApertureAperture
SLM
inpu
t
TRAN STAGETRAN STAGETRAN STAGELENSLET ARRAY
DET ARRAY
Holographic Redirector
MIRROR
FLC SHUTTERARRAY
1. M.S. Shahriar, R. Tripathi, M. Kleinschmit, J. Donoghue, W. Weathers, M. Huq, J.T. Shen, "Super-Parallel Holographic Optical Correlator for Ultrafast Database Search", Opt. Letts. 28, pp. 525-527 (2003)2. M.S. Shahriar, J. Riccobono, M. Kleinschmit, and J. Shen " Coherent and Incoherent Beam Combination Using Thick Holographic Substrates" to appear in Opt. Commun. (2003).3. L. Wong, M. Bock, B. Ham, M.S. Shahriar, and P. Hemmer, “Ultra-High Density Optical Data Storage,” in Symposium on Electro-Optics: Present and Future, Optical Society of America book series on Trends in Optics and Photonics (1998).4. P. Hemmer, M.S. Shahriar, J. Ludman, H.J. Caulfield, "Holographic Optical Memories," in Holography for the New Millenium, J. Ludman, H.J Caulfield, J. Riccobono, eds. (Springer- Verlag, New York, 2002), pp. 179-189. 5. Hassaun A. Jones-Bey, "Holographic Correlation Improves on DSP by Six Orders of Magnitude," The Laser Focus World, July 2002.6. A. Adibi, K. Buse, D. Psaltis: ""Non-volatile holographic recording in doubly-doped lithium niobate,"" Nature, vol. 393, pp. 665-668, 1998.7. Robert R. Birge, Nathan B. Gillespie, Enrique W. Izaguirre, Anakarin Kusnetzow, Albert F. Lawrence, Deepak Singh, Q. Wang Song, Edward Schmidt, Jeffrey A. Stuart, Sukeerthi Seetharaman, and Kevin J. Wise, " Biomolecular Electronics: Protein-Based Associative Processors and Volumetric Memories,"J. Phys. Chem. B, 103, 10746-10766 (1999).
SOME REFERENCES FOR HIGH-SPEED HOLOGRAPHIC SEARCH
SUMMARY
Aquantum computer can search through N unsorted objects in O(N1/2) steps, using only O(Log2N) quantum bits (Grover’s Algorithm: GA)
Using existing materials and technology, this will enable simultaneous search through ten million images, encoded using a terabyte capacity memory
The specific device we discussed is the Holographic Super-Correlator, which performs angularly-multiplexed correlation in a thick hologram in many spatial spots simultaneously
COMPARABLE TO QUANTUM-COMPUTER, BUT ACTUALLY EXISTS
However, given the necessity to store the database for a long time, it is likely that the user would need O(N) classical resources anyway
As such, the real significance of GA is that the search requires O(N1/2) steps
Here we show a practical search engine that takes only O(N1/2) steps
It requires O(N) resources for memory, and O(N1/2) resources for search