1 / 40

Ultra-fast Database Search:  Super-Parallel Holography versus Quantum Computing

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.

deacon
Télécharger la présentation

Ultra-fast Database Search:  Super-Parallel Holography versus Quantum Computing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 COMPUTING POWER IS EXPONENTIAL IN NUMBER OF BITS WHY IS QUANTUM COMPUTER POWERFUL ? : ENTANGLEMENT FACTORING VERY LARGE NUMBERS EFFICIENTLY SPEEDY DATA BASE SEARCH QUANTUM MEMORY FOR QUANTUM COMMUNICATION SYSTEMS SIMULATION OF QUANTUM SYSTEMS

  3. QUANTUM COMPUTER: SIMPLE DEFINITION ……………………………………………………………………… n 1 2 3 4 |1>=|0,0,0,0,0,0,…….0,0,0> N=2n ALLOWED STATES: |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 ……………………………………………………………………… n 1 2 3 4 |1>=|0,0,0,0,0,0,…….0,0,0> |2>=|0,0,0,0,0,0,…….0,0,1> PREPARE THE SYSTEM IN AN EQUAL SUPER-POSITION OF EACH OF THE N=2n STATES, REPRESENTING THE STORED DATA BASE: |N>=|1,1,1,1,1,1,…….1,1,1> ………………………………………...... |N> |1> |2> |3>

  5. EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER ……………………………………………………………………… n 1 2 3 4 |K> 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> ………………………………………...... |N> |1> |2> |3>

  6. EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER ……………………………………………………………………… n 1 2 3 4 -|K> |K> 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> ………………………………………...... |N> |1> |2> |3>

  7. EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER ……………………………………………………………………… n 1 2 3 4 COMPUTE AVERAGE, AND FLIP EACH STATE AROUND THE AVERAGE: ………………………………………...... |N> |1> |2> |3> Vi A+(A-Vi) ………………………………………...... |N> |1> |2> |3>

  8. EFFICIENT DATA BASE SEARCH WITH A QUANTUM COMPUTER ……………………………………………………………………… n 1 2 3 4 |K> 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> ………………………………………...... |N> |1> |2> |3>

  9. 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) 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 The specific device we discussed is the Holographic Super-Correlator, which performs angularly-multiplexed correlation in a thick hologram in many spatial spots simultaneously

  10. HOLOGRAPHIC OPTICAL CORRELATOR:BASIC IDEA

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

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

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

  16. HOLOGRAPHIC MEMORY UNIT BS BE CCDA BS IFBR BE HMDX HMDX AP HR LLA HMU HR LLA SLM CCDA TARGET ID: 7968023 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

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

  18. 2D SCANNING MECHANISM HMU

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

  20. DEMONSTRATION OF HMDX

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

  22. SIMULTANEOUSCORRELATION WITH 3X3 HMDX

  23. SIMULTANEOUSCORRELATION WITH 3X3 HMDX

  24. SIMULTANEOUSCORRELATION WITH 3X3 HMDX

  25. SIMULTANEOUSCORRELATION WITH 3X3 HMDX

  26. SIMULTANEOUSCORRELATION WITH 3X3 HMDX

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

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

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

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

  31. HOLOGRAPHIC MULTIPLEXER/DEMULTIPLEXER IMAGE FLATTENING BEAM EXPANDER HOLOGRAPHIC MEMORY UNIT REDUCING TELESCOPE APERTURE REDIRECTOR REDIRECTOR LENSLET ARRAY SHUTTER IMAGING CCD 2-D BEAM DEFLECTOR TARGET ID: 7968 TARGET ID: 7968023 RETRIEVED IMAGE READ LASER PROPOSED SUPER-PARALLEL HRAM

  32. PRELIMINARY RESULTS FROM SIMPLE GEOMETRY 338 HMU HOLOGRAPHIC REDIRECTOR HMU CCD READ BEAM (1,1) (1,2) (1,3) SPLITTER READ OUT DATA (2,1) (2,2) (2,3) TELESCOPE (3,1) (3,2) (3,3) APERTURE Data Read-Out From Location 3X2

  33. HOLOGRAPHIC OPTICAL CORRELATOR:THIN MEDIUM: UAV GUIDANCE

  34. HOLOGRAPHIC OPTICAL CORRELATOR:THIN MEDIUM: UAV GUIDANCE

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

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

  37. MATERIALS FOR TWO-PHOTON MEMORY: BACTERIORHODOPSIN

  38. PROPOSED SUPER-PARALLEL ASSOCIATIVE MEMORY

  39. SOME REFERENCES FOR HIGH-SPEED HOLOGRAPHIC SEARCH 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).

  40. Aquantum computer can search through N unsorted objects in O(N1/2) steps, using only O(Log2N) quantum bits (Grover’s Algorithm: GA) 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 The specific device we discussed is the Holographic Super-Correlator, which performs angularly-multiplexed correlation in a thick hologram in many spatial spots simultaneously Using existing materials and technology, this will enable simultaneous search through ten million images, encoded using a terabyte capacity memory COMPARABLE TO QUANTUM-COMPUTER, BUT ACTUALLY EXISTS SUMMARY

More Related