AFRL-VS-HA-TR-2006-1143 Quantum Algorithms for Computational Physics: Volume III of Lattice Gas Dynamics Jeffrey Yepez 3 January 2007 Approved for Public Release; Distribution Unlimited AIR FORCE RESEARCH LABORATORY Space Vehicles Directorate 29 Randolph Rd AIR FORCE MATERIEL COMMAND Hanscom AFB, MA 01731-3010 AFRL-VS-HA-TR-2006-1143 This technical report has been reviewed and is approved for publication. /signed/ Steven L. Clark, Acting Chief Battlespace Environment Division /signed/ /signed/ Frank H. Ruggiero Brian Griffith, Maj, USAF, Chief Battlespace Surveillance Innovation Center Battlespace Surveillance Innovation Center Using Government drawings, specifications, or other data included in this document for any purpose other than Government procurement does not in any way obligate the U.S. Government. The fact that the Government formulated or supplied the drawings, specifications, or other data does not license the holder or any other person or corporation; or convey any rights or permission to manufacture, use, or sell any patented invention that may relate to them. This report is published in the interest of scientific and technical information exchange and its publication does not constitute the Government’s approval or disapproval of its ideas or findings. This report has been reviewed by the ESC Public Affairs Office (PA) and is releasable to the National Technical Information Service (NTIS). Qualified requestors may obtain additional copies from the Defense Technical Information Center (DTIC). All other requestors should apply to the National Technical Information Service (NTIS).. If your address has changed, if you wish to be removed from the mailing list, or if the addressee is no longer employed by your organization, please notify AFRL/VSIM, 29 Randolph Rd., Hanscom AFB, MA 01731-3010. This will assist us in maintaining a current mailing list. Do not return copies of this report unless contractual obligations or notices on a specific document require that it be returned. Form Approved REPORT DOCUMENTATION PAGE OMB No. 0704-01-0188 The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden to Department of Defense, Washington Headquarters Services Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To) 16-03-2007 Scientific, Final 1 Oct 1999-15 Mar 2007 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Quantum Algorithms for Computational Physics: Volume III of Lattice Gas Dynamics 5 b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 61102F 6. AUTHORS 5d. PROJECT NUMBER Jeffrey Yepez 2304 5e. TASK NUMBER OT 5 f. WORK UNIT NUMBER B1 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Air Force Research Laboratory /VSBYA AFRL-VS-HA-TR-2006-1143 29 Randolph Road Hanscom AFB, MA 01731-3010 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) AFRL/VSBYA 11 . SPONSOR/MONITOR’S REPORT NUMBER(S) 12 . DISTRIBUTION/AVAILABILITY STATEMENT Approved for Public Release; distribution unlimited. . 13. SUPPLEMENTARY NOTES 14 . A B S T R A C T This report is divided into two tracks, an introductory track and a technical track. Ths introductory track includes a general introduction and background, introductions to two types of analog (and parallel) quantum computing, and an overview oriented conclusion. The technical track includes sections on quantum memory, conservative quantum logic, and quantum algorithm types, including quantum algorithms for the Dirac and Schroedinger quantum mechanical wave equations, the mesoscopic scale quantum Boltzmann equation, and the quantum algorithms for the diffusion equation, Burgers equation, magnetohydrodynamic Burgers equations, and the Navier-Stokes fluid equation. 15. SUBJECT TERMS Quantum computer Qubit Quantum lattice gas Quantum simulation Electron gas Decoherence Spin Full adder Fermions Physical modeling Physical quantum algorithms 16. S ECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE ABSTRACT OF Jeffrey Yepez PAGES 19B. TELEPHONE NUMBER (Include area code) UNCL UNCL UNCL Standard Form 298(Rev. 8/98) Prescribed by ANSI Std. Z39.18