1. 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

2. 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

3. QUANTUM COMPUTER: SIMPLE DEFINITION 1234 ……………………………………………………………………… n N=2 n 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: A MACHINE CAPABLE OF PRODUCING THIS OPERATOR, REPRESENTED AS AN NXN MATRIX, IS A QUANTUM COMPUTER CAN BE REALIZED WITH SINGLE BIT OPERATION AND NEAREST-NEIGHBOR INTERACTION

4. EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER 1234 ……………………………………………………………………… n PREPARE THE SYSTEM IN AN EQUAL SUPER-POSITION OF EACH OF THE N=2 n 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>|1>|2>|2>|3>|3> ………………………………………...... |N>|N>

5. EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER 1234 ……………………………………………………………………… 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>|K> |1>|1>|2>|2>|3>|3> ………………………………………...... |N>|N>

6. EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER 1234 ……………………………………………………………………… 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> -|  K > |1>|1>|2>|2>|3>|3> ………………………………………...... |N>|N>

7. EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER 1234 ……………………………………………………………………… n COMPUTE AVERAGE, AND FLIP EACH STATE AROUND THE AVERAGE: ViVi A+(A-V i ) |1>|1>|2>|2>|3>|3> ………………………………………...... |N>|N> |1>|1>|2>|2>|3>|3> |N>|N>

8. EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER 1234 ……………………………………………………………………… 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>|K> |1>|1>|2>|2>|3>|3> ………………………………………...... |N>|N>

9. SUMMARY SO FAR A quantum computer can search through N unsorted objects in O(N 1/2 ) steps, using only O(Log 2 N) 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(N 1/2 ) steps Here we show a practical search engine that takes only O(N 1/2 ) steps It requires O(N) resources for memory, and O(N 1/2 ) resources for search

10. HOLOGRAPHIC OPTICAL CORRELATOR: BASIC IDEA

12. PROBLEMS: (A) SPATIAL MULTIPLEXING IS POTENTIALLY SLOW (B) CAN NOT COMPARE ALL OF THEM SIMULATANEOUSLY

13. HOLOGRAPHIC SUPER CORRELATOR : BASIC CONCEPT LASER DIGITAL LOGIC FOR THRESHOLDING AND DECODING TARGET ID: 7968023 SLM BE LASER READ LASER DIGITAL LOGIC FOR THRESHOLDING AND DECODING TARGET ID: 7968023 SLM BEAM EXPANDER HOLOGRAPHIC MEMORY TARGET IMAGE LENSLET ARRAY HOLOGRAPHIC REDIRECTOR HOLOGRAPHIC MUX/DEMUX IMAGE FLATTENING BEAM REDUCER BEAM EXPANDER LENSLET ARRAY CCD ARRAY BEAM SPLITTER APERTURE

14. HOLOGRAPHIC MULTIPLEXER/DEMULTIPLEXER WRITING A 1X3 HMD INDIVIDUAL READING SIMULTANEOUS READING TARGET ID: 7968023 SLM CCDA BS HMDX HR HMU LLA HR BE IFBR AP LLA CCDA M/# Needed:  N

15. HOLOGRAPHIC REDIRECTOR WRITING A 3 ELEMENT HRO READING A 3 ELEMENT HRO TARGET ID: 7968023 SLM CCDA BS HMDX HR HMU LLA HR BE IFBR AP LLA CCDA M/# Needed: 1

16. HOLOGRAPHIC MEMORY UNIT TARGET ID: 7968023 SLM CCDA BS HMDX HR HMU LLA HR BE IFBR AP LLA CCDA Substrate: PDA/Memplex TM 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

17. MEMORY WRITING SETUP 16-BIT BUS GALVO DRIVER TEL 1 TEL 3 TEL 2 PBS 50/50 BS GM1 M2 LASER M1 SHUTTER HMU SLM 2D STAGE DRIVER 2D STAGE COMPUTER DVD SLM DRIVER CONTROL PANEL DATA PAGE  2 PLATE N COMB. LOGIC GM2

18. 2D SCANNING MECHANISM HMU

19. LENSLET ARRAY TARGET ID: 7968023 SLM CCDA BS HMDX HR HMU LLA HR BE IFBR AP LLA CCDA SCHEMATIC REAL

20. DEMONSTRATION OF HMDX

21. CORRELATION WITH DIRECT IMAGE FROM SLM Recorded Holographic Images Image Correlation Diffraction SpotsDiffraction Intensity

22. SIMULTANEOUS CORRELATION WITH 3X3 HMDX

27. SIMULTANEOUS CORRELATION WITH 3X3 HMDX: 3X8 IMAGES IN EACH LOCATION

28. SIMULTANEOUS CORRELATION WITH 3X3 HMDX: 3X8 IMAGES IN EACH LOCATION

29. SIMULTANEOUS CORRELATION WITH 3X3 HMDX: 3X8 IMAGES IN EACH LOCATION

30. COMPARISON WITH QUANTUM DATABASE SEARCH LASER SLM CCDA BS HMDX HR HMU LLA HR BE IFBR AP LLA CCDA IF  N Spatial Locations  N Images Per Location O(  N) Steps Needed to Search Through N Unsorted Objects Same Speed-Up As Offered By Grover’s Algorithm for Quantum Database Search

31. PROPOSED SUPER-PARALLEL HRAM

32. APERTURE CCD HMU TELESCOPE HOLOGRAPHIC REDIRECTOR READ OUT DATA READ BEAM 3  3  8 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

33. HOLOGRAPHIC OPTICAL CORRELATOR: THIN MEDIUM: UAV GUIDANCE

35. HOLOGRAPHIC OPTICAL CORRELATOR: ASSOCIATIVE MEMORY READ/WRITE LASER (690 NM) SLM MIRROR MEMORY CUBE: BR FT LENS BS AMPLIFY & THRESHOLD ACTIVATION LASER (635 NM) TRANSLATION STAGE SHIFT-INVARIANT ASSOCIATIVE MEMORY CCD

36. HOLOGRAPHIC OPTICAL CORRELATOR: ASSOCIATIVE MEMORY INPUT IMAGE THRESHOLDED CORRELATION PEAKS PAGE 1PAGE 2 PAGE 3 IMAGE ID’D & RECALLED

37. MATERIALS FOR TWO-PHOTON MEMORY: BACTERIORHODOPSIN

38. PROPOSED SUPER-PARALLEL ASSOCIATIVE MEMORY

39. 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

40. SUMMARY Aquantum computer can search through N unsorted objects in O(N 1/2 ) steps, using only O(Log 2 N) 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(N 1/2 ) steps Here we show a practical search engine that takes only O(N 1/2 ) steps It requires O(N) resources for memory, and O(N 1/2 ) resources for search