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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) the least-studied class of quantum analysis methods Quantum system engineering is stimulating new approaches in math and physics

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October 11, 2005 UW Condensed Matter Seminar White paper available at www.mrfm.org Kick-off meeting: November 13, 2005 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, USAPersonnel: Joseph L. Garbini John Jacky John Sidles Students: Doug Mounce Students: Joe Malcomb Kristi Gibbs Chris Kikuchi Tony Norman 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 This talk is a blueprint for integrated technology development

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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 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. 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. The Historic Challenge of Quantum Microscopy Pauling, von Neumann, and Feynman shared a vision and issued a challenge; now we’re going to fulfill it

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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 win the 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?

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Moore’s Law Progress in MRFM smaller colder quieter smaller colder quieter Moore’s Law design rules 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 The Path to Single Nuclear Spin Detection: FAQ Q1:What is a reasonable technical path to single-nuclear-spin detection? A1:The path is smaller, colder, quieter device development We’re well underway, with a clear path forward

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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 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 Good design metrics reflect the overall mission Horikoshi: Eagles of Mitsubishi Boyd: US Flight Test Manual (FTM108) UWMICORN: Program for Achieving Single Nuclear Spin Detection Informatic capacity is our primary metric

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199220102004 Quantum biomicroscopy has plenty of SNR headroom

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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 Sustaining MRFM progress requires three coordinated efforts: – –Synthesizing engineering principles from 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 engineering perfection, Caves’ quantum limits were achieved Lesson: quantum system engineering (QSE) is “The unrelenting pursuit of engineering perfection” Approaching the quantum limits will require a sustained technological effort

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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): Nature 432, p. 823 (2004) Nature 432, p. 823 (2004) 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 This technology helps provide Dirac’s foundation for a Golden Age: “Ordinary people can make extraordinary contributions”

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Q5:Are we confident that quantum microscopy will work? A5:We’ll know soon. E2e analysis and emulation now feasible NP-hard EXP NP P engineering complexity classes P: derive and check using polynomial memory 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-Carlo emulation 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 techniques that reside in NP, not EXP, are a mission-critical requirement

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The orthodoxy of “Mike and Ike”: All quantum simulations are equivalent to … 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 Chapters 1,2,8,9 The analysis tools we need are already in the literature details: quant-ph/0401165

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

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

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“jump” reservoir “noise” reservoir “measurement” reservoir measured data spin dynamics 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 be efficiently simulated

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Q5:Are we confident that quantum microscopy will work? A5.2:Generalize to higher- dimensional spin systems 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) Numerical simulations of high-temperature spin dust – a deliberately tough challenge – no spatial symmetry no spatial ordering random dipole coupling noisy environment tough to simulate QDE of spin dust with synoptic noise tuning QDE of spin dust with ergodic noise tuning QDE of random product states (analytic result) quantum dispersion entropy (QDE) cumulative distribution function (CDF) 18-spin quantum dispersion entropy values QDE of random Hilbert states (analytic result) Replacing quantum noise with covert quantum measurement yields compressed Hilbert space trajectories

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Q5:Are we confident that quantum microscopy will work? A5.3:Beylkin & Mohlenkamp’s algo- rithms provide a vital tool 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 Compressed Hilbert trajectories can be stored in P-space and computed in P-time

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

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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? 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 A:Apply linked quantum representation theory (as summarized in five paragraphs … ) P-time quantum system simulation is a mission-critical capability that is now coming on-line By definition, a linked representation is a separated representation subjected to linear constraints (the “wire-ties”)

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High-level system simulation is central to modern strategic capability Q5:Are we confident that quantum microscopy will work? A5.6:Large-scale quantum system simulations will tell us 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” Open strategic advantage (OSA) strategies are easy to understand, impossible to stop, and yield global strategic advantages

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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 Q5:Are we confident that quantum microscopy will work? A5.7:As confident as Thomas Jefferson in the Army’s “Corps of Discovery” 19th Century 21st Century Louisiana Territorybiospace frontier Missouri Riverquantum microscopy Corps of DiscoveryMURI and MOQSI MURI/MOQSI is a 21st Century “Corps of Discovery” – opening a new & unbounded frontier

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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 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 We must win the GWOT ; failure is not an option. New resources are a vital need.

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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 Q7:What is the logical next step? A7:A satellite-scale integrated launch program: MOQSI If we build it, it will work.

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

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