A1: Not enough energy Variational calculus A2: Too much symmetry Group theory

1. Preview: How can we be sure a physical system is not running a (possibly occult) quantum computation? • A1: Not enough energy • Variational calculus • A2: Too much symmetry • Group theory • A3: Ensemble averaging • Statistical mechanics • Master equations • A4: The system is too noisy • Kraus operators (sometimes called measurement operators) • Product-sum representations (both separated and linked) • What these techniques have in common: • They reduce the system complexity class from EXP to P • Historically, they are all linked to beautiful physics and deep mathematics, • They have great utility for quantum system engineering (the focus of this talk) Quantum system engineering is stimulating new approaches in math and physics the least-studied class of quantum analysis methods

2. Emerging Techniques for Solving NP-Complete Problems in Mathematics, Biology, Engineering, … and Physics Presented by: The Quantum System Engineering Group University of Washington Seattle, Washington, USA Personnel: Joseph L. Garbini John Jacky John Sidles Doug MounceStudents: Joe Malcomb Kristi Gibbs Chris Kikuchi Tony Norman October 11, 2005UW Condensed Matter Seminar This talk is a blueprint for integrated technology development UWMICORN Collaboration: Al Hero / Michigan John Marohn / Cornell Doran Smith / ARO Dan Rugar / IBM UWMICORN++ Chris Hammel / Ohio State Raffi Budakian / Illinois Mike Roukes / CalTech Keith Schwab / Cornell White paper available at www.mrfm.org Kick-off meeting: November 13, 2005

3. The Historic Challenge of Quantum Microscopy I put this out as a challenge: Is there no way to make the electron microscope more powerful? … Make the microscope one hundred times more powerful, and many problems of biology would be made very much easier. 1959: Richard Feynman There’s Plenty of Room at the Bottom 1946: John von Neumann to Norbert Weiner Electron microscopy Crystallography 1946: Linus Pauling System biology proposal to Rockefeller Foundation Pauling, von Neumann, and Feynman shared a vision and issued a challenge; now we’re going to fulfill it There is no telling what really advanced electron microscopic techniques will do. In fact, I suspect that the main possibilities lie in that direction. It is appalling to consider how meager is our information about the composition and structure of proteins … Extremely important advances could be achieved if the effective resolving power of the electron microscope could be considerably improved.

4. FAQ: Program for Single Nuclear Spin Detection Q1: What is a reasonable technical path to single-nuclear-spin detection? Q2: What are appropriate performance metrics and technical milestones? Q3: When might this technology reasonably be ready? Q4: What tasks could this technology accomplish? Q5: Are we confident that quantum microscopy will work? Q6: How can this technology help winthe Global War on Terror (GWOT)? Q7: What is the logical next step? A1: The path is smaller, colder, quieter device development A2: The metric is bits-per-second received from each target spin A3: By 2010, if historic rates of progress are sustained A4: Comprehensive access to resources of “chemical space” A5: We’ll know soon. E2e analysis and emulation now feasible A6: New resources are a strategic requirement for GWOT victory A7: a satellite-scale integrated launch program: MOQSI This talk’s key question:will quantum microscopy work?

5. The Path to Single Nuclear Spin Detection: FAQ Q1: What is a reasonable technical path to single-nuclear-spin detection? Moore’s Law Progress in MRFM A1: The path is smaller, colder, quieter device development Moore’sLawdesignrules • smaller • colder • quieter We’re well underway, with a clear path forward • MRFM sensitivity has improved by 140 dB in twelve years • Equivalent to doubling sensitivity every 3.1 months for 46 doublings • MRFM has Moore’s Scaling: smaller, colder, quieter devices work better

6. The Path to Single Nuclear Spin Detection: FAQ Q2: What are appropriate performance metrics and technical milestones? A2: The metric is bits-per-second received from each target spin Informatic capacity is our primary metric • Jiro Horikoshi and John Boyd • Channel capacity is a good choice for an MRFM design metric because it: • Directly reflects the mission,(gain information from spins) • Provides strategic guidance for device design • Establishes fundamental physical bounds on performance Horikoshi: Eagles of Mitsubishi Boyd: US Flight Test Manual (FTM108) Good design metrics reflect the overall mission UWMICORN: Program for Achieving Single Nuclear Spin Detection

7. 1992 2004 2010 Quantum biomicroscopy has plenty of SNR headroom

8. The Path to Single Nuclear Spin Detection: FAQ Q3: When might this technology reasonably be ready? A3: By 2010, if historic rates of progress are sustained Approaching the quantum limits will require a sustained technological effort • Sustaining MRFM progress requiresthree coordinated efforts: • Synthesizing engineering principlesfrom the emerging nanoscale physics. • Fabricating the next generation of devices: smaller, colder, and quieter, • Testing these devices in real-world imaging environments • Shigeo Shingo and Taichii Ohno 1982 1998 after 17 years’pursuit of engineeringperfection, Caves’ quantumlimits wereachieved Lesson: quantum system engineering (QSE) is “The unrelenting pursuit of engineering perfection”

9. The Path to Single Nuclear Spin Detection: FAQ Q4: What tasks could this technology accomplish? A4: Comprehensive access to resources of “chemical space” A project far larger than the Genome Project (from the on-line White Paper): This technology helps provide Dirac’s foundation for a Golden Age:“Ordinary people can make   extraordinary contributions” • Every cell contains as 100X as many atoms as there are stars in the galaxy. • Surveying this nearly-infinite domain will be the largest scientific project that humanity has ever undertaken. • The knowledge gained will be the 21st Century’s greatest resource Nature 432, p. 823 (2004)

10. Q5: Are we confident that quantum microscopy will work? A5: We’ll know soon. E2e analysis and emulation now feasible • P: derive and check using polynomialmemory and time resources • E.g., compute a transfer function • NP: via a decision “certificate”, verify with polynomial resources • E.g, does a stable controller exist? • NP-hard: typically, the optimization or interval version of an NP problem • E.g., does a stable controller exist over an interval of model parameters? • In practice, “solved” by robust design heuristics, backed by Monte-Carloemulation and instance certificates • EXP: emulation requires exponential resources, and no certificates known • problems in EXP are inaccessible • Quantum system engineering must move from EXP to P Quantum analysis techniquesthat reside in NP, not EXP, are a mission-critical requirement engineering complexity classes P NP NP-hard EXP

11. The orthodoxy of “Mike and Ike”:All quantum simulations are equivalent to … Chapters1,2,8,9 The analysis tools we needare already in the literature details: quant-ph/0401165 • Objective: compute the wave function in P-time and store it in P-space • Strategic insight: tune the noise to “compress” the Hilbert space trajectory • First requirement: the compressed trajectory must fit in P-space • Second requirement: the compression algorithm must run in P-time

12. The order and connection of ideas is the same as the order and connection of things … Spinoza Kraus operators map one-to-one onto standard engineering hardware; this motivates novel applications • Construct A and B operators from optical transfer matrices • Recognize that A and B are Krausoperators (which generate POVMs) • Recognize that interferometer “tuning invariance” is just Choi’s Theorem

13. measured data spin dynamics “jump”reservoir “noise”reservoir “measurement”reservoir

14. Q5: Are we confident that quantum microscopy will work? A5.1: Quantum emulation of the IBM single-spin experiment IBM’s 13-hour single-spin experiment can beefficiently simulated measured data spin dynamics “jump”reservoir “noise”reservoir “measurement”reservoir

15. Numerical simulations ofhigh-temperature spin dust– a deliberately tough challenge – • no spatial symmetry • no spatial ordering • random dipole coupling • noisy environment tough to simulate Q5: Are we confident that quantum microscopy will work? A5.2: Generalize to higher-dimensional spin systems 18-spin quantum dispersion entropy values QDE of spin dustwith synoptic noise tuning Replacing quantum noise with covert quantum measurement yieldscompressed Hilbert space trajectories QDE of randomproduct states(analytic result) cumulative distribution function (CDF) QDE of spin dustwith ergodic noise tuning QDE of random Hilbert states(analytic result) quantum dispersion entropy (QDE) • Exact 18-spin quantum trajectories yield QDE CDFs that are restricted to an exponentially small fraction of Hilbert space • This is good news, because such low entropy values assure us that a compression algorithm must exist (but do not provide an explicit example) • Now we are motivated to search for an explicit algorithm that consumes only P-space and P-time resources (see next three slides)

16. Q5: Are we confident that quantum microscopy will work? A5.3: Beylkin & Mohlenkamp’s algo-rithms provide a vital tool Compressed Hilbert trajectoriescan be stored in P-space andcomputed in P-time • Separated representations provide a “JPEG format” for compressing quantum state trajectories • They efficiently compress all Hilbert states except the high-rank states employed in quantum computation • They are well-suited to quantum system engineering

17. Numerical simulations ofhigh-temperature spin dust– a deliberately tough challenge – • no spatial symmetry • no spatial ordering • random dipole coupling • noisy environment tough to simulate Q5: Are we confident that quantum microscopy will work? A5.4: Separated reps perform well even in “tough” spin systems fidelity of separated representations fidelity These techniques are robust: they work even at high temperatureand in the absence of symmetries rank = 1 rank = 2 fidelity rank = 5 rank = 10 synoptic noise tuning ergodic noise tuning fidelity rank = 20 rank = 30 number of spins number of spins

18. Q5: Are we confident that quantum microscopy will work? A5.5: Now, large-scale quantum spin systems can be analyzed in P-time Q: How can we emulate thousands of quantum spins with polynomial space and time resources? A: Apply linked quantum representation theory(as summarized in five paragraphs … ) P-time quantum system simulation is a mission-critical capabilitythat is now coming on-line • The mission-critical MURI/MOQSI objectives: • Reliably predict strong-gradient quantum spin physics • Maximize system performance metrics • Build confidence that MURI/MOQSI will go all the way By definition, a linked representation is a separated representation subjected to linear constraints (the “wire-ties”)

19. Q5: Are we confident that quantum microscopy will work? A5.6: Large-scale quantum system simulations will tell us • High-level system simulation is central to modern strategic capability Open strategic advantage (OSA) strategies are easy to understand, impossible to stop, and yield global strategic advantages • Open high-level simulations build open strategic advantage (OSA) • Builds technical confidence: “If we build it, it will work” • Creates trans-national business alliances: “We want to be part of your strategy” • Establishes open strategic advantage: “Deceive the sky to cross the ocean”

20. Q5: Are we confident that quantum microscopy will work? A5.7: As confident as Thomas Jefferson in the Army’s “Corps of Discovery” • Strategically, MURI/MOQSI is a 21st Century “Corps of Discovery” • Deploy our new quantum system engineering simulation tools • Build technical confidence and catalyze alliances: “If we build it, we it will work” • Embrace and extend the open strategic advantage of biospace • Maximize job creation and entrepreneurial opportunity • For strong impact: deploy 5K imaging devices at $1M each • For maximal impact: deploy 1M devices at $5K each; • The informatic harvest is ~3 petacoordinates per year • This yields the “Chris Kikuchi Open Strategic Advantage” • Achieve all that our forebears challenged us to accomplish MURI/MOQSI is a 21st Century “Corps of Discovery” – openinga new & unbounded frontier

21. The Path to Single Nuclear Spin Detection: FAQ Q6: How can this technology help win the Global War on Terrorism (GWOT)? A6: New resources are a strategic requirement for GWOT victory We must win the GWOT; failure is not an option. New resources are a vital need. Q5*: How can we eliminate terrorism’s primary resources: hunger, poverty, desperation, and chaos? A5*: New resources, new projects, and new kinds of work all support a pivotal strategic objective: creating one billion jobs in the next twenty years

22. Q7: What is the logical next step? A7: A satellite-scale integrated launch program: MOQSI If we build it, it will work. • Year 1: Demonstrate technology and build community • Milestone I: Close-approach electric noise in wet, salty samples • Milestone II: 3D bioimages with viral-scale resolution • Milestone III: E2e quantum system design via P-time algorithms • Primary objective I: technical and strategic consensus • Primary objective II: a team to take it all the way. • Year 2: Launch MOQSI (draft white paper: Nov. 2005) • Mechatronic and Optical Quantum Sensing Initiative • Five-year at $10M/year in support of five MOQSI Groups • Year 3: Commercial development platforms • JEOL, Oxford, Digital Instruments • Year 4: Pursuit of “smaller, sharper, colder, cleaner” • With confidence that “If we build it, it will work”. • Year 5: Single-proton resolution in a bioimaging context

23. Walter Reed Caroline Herschel Linus Pauling BarbaraMcClintock Baruch Spinoza Richard Feynman Lynn Margulis Anton van Leeuwenhoek John vonNeumann Jane Goodall RobertHooke “Power, before it comes from arms or wealth, emanates from ideas” K. N. Cukier The Power of Mathematics The Power of Knowledge The Power of Resources The Power of Discovery We must win the GWOT; failure is not an option. New resources are a vital need. “Ordinary people can make   extraordinary contributions”

24. Thank you