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
Transcript
Preview: How can we be sure a physical system is not running a (possibly occult) quantum computation?
Preview: How can we be sure a physical system is not running a (possibly occult) quantum computation?
• 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
October 11, 2005UW Condensed Matter Seminar
White paper available at
www.mrfm.org
Kick-off meeting: November 13, 2005
Emerging Techniques for Solving Emerging Techniques for Solving NP-Complete Problems in NP-Complete Problems in Mathematics, Biology, Mathematics, Biology, Engineering, … and PhysicsEngineering, … and Physics
Presented by:
The Quantum System Engineering GroupUniversity of WashingtonSeattle, Washington, USA
Personnel:Personnel:
Joseph L. GarbiniJohn JackyJohn SidlesDoug Mounce
Students:Students:Joe MalcombKristi GibbsChris KikuchiTony Norman
UWMICORNUWMICORN Collaboration: Collaboration:
Al Hero / MichiganJohn Marohn / CornellDoran Smith / ARODan Rugar / IBM
This talk is a blueprint for integrated technology
development
1959: Richard FeynmanThere’s Plenty of Room at the Bottom
1946: John von Neumann to Norbert WeinerElectron microscopyCrystallography
1946: Linus PaulingSystem 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.
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.
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There is no telling what really advanced electron microscopic techniques will do. In fact, I suspect that the main possibilities lie in that direction.
There is no telling what really advanced electron microscopic techniques will do. In fact, I suspect that the main possibilities lie in that direction.
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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.
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.
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The Historic Challenge of Quantum MicroscopyThe Historic Challenge of Quantum MicroscopyThe Historic Challenge of Quantum MicroscopyThe Historic Challenge of Quantum Microscopy
Pauling, von Neumann, and Feynman shared a vision and issued a challenge;
now we’re going to fulfill it
FAQ: Program for Single Nuclear Spin DetectionFAQ: Program for Single Nuclear Spin DetectionFAQ: Program for Single Nuclear Spin DetectionFAQ: 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:A5: We’ll know soon. E2e analysis We’ll know soon. E2e analysis and emulation now feasibleand 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?
Moore’s Law Progress in MRFMMoore’s Law Progress in MRFM
• smaller• colder • quieter
• smaller• colder • quieter
Moore’sLaw
designrules
Moore’sLaw
designrules
• 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: FAQThe Path to Single Nuclear Spin Detection: FAQThe Path to Single Nuclear Spin Detection: FAQThe 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
The Path to Single Nuclear Spin Detection: FAQThe Path to Single Nuclear Spin Detection: FAQThe Path to Single Nuclear Spin Detection: FAQThe 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: Boyd: US Flight Test Manual (FTM108)US Flight Test Manual (FTM108)
UWMICORN:UWMICORN: Program for Achieving Program for Achieving Single Nuclear Spin Detection Single Nuclear Spin Detection
Informatic capacityis our primary metric
1992 20102004
Quantum biomicroscopy has plenty of SNR headroom
The Path to Single Nuclear Spin Detection: FAQThe Path to Single Nuclear Spin Detection: FAQThe Path to Single Nuclear Spin Detection: FAQThe 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
– 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
1998after 17 years’pursuit of
engineeringperfection,
Caves’ quantumlimits wereachieved
Lesson: quantum system engineering (QSE) is “The unrelenting pursuit of engineering perfection”
Approaching the quantum limits will require a sustained
technological effort
The Path to Single Nuclear Spin Detection: FAQThe Path to Single Nuclear Spin Detection: FAQThe Path to Single Nuclear Spin Detection: FAQThe 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):
NatureNature 432, p. 823 (2004) 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”
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
engineeringcomplexityclasses
• 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
The orthodoxy of “Mike and Ike”:
All quantum simulations are equivalent to …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
Chapters1,2,8,9
The analysis tools we needare already in the literature
details: quant-ph/0401165
The order and connection of ideas is the same The order and connection of ideas is the same as the order and connection of things … as the order and connection of things … SpinozaSpinoza
• 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
“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
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)
•no spatial symmetry•no spatial ordering• random dipole coupling•noisy environment
tough to simulate
QDE of spin dustwith synopticnoise tuning
QDE of spin dustwith ergodicnoise tuning
QDE of randomproduct states(analytic result)
quantum dispersion entropy (QDE)
cu
mu
lati
ve
dis
trib
uti
on
fu
nc
tio
n (
CD
F)
18-spin quantum dispersion entropy values
QDE of randomHilbert states
(analytic result)
Replacing quantum noise with covert quantum measurement yields
compressed Hilbert space trajectories
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 trajectoriescan be stored in P-space and
computed in P-time
Q5: Are we confident that quantum microscopy will work?
A5.4: Separated reps perform well even in “tough” spin systems
synopticnoise tuning
ergodicnoise tuning
rank = 1 rank = 2
rank = 5 rank = 10
rank = 20 rank = 30
number of spins
fid
eli
tyfi
de
lity
fid
eli
ty
number of spins
fidelity of separated representationsNumerical simulations ofhigh-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 temperatureand in the absence of symmetries
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”)
• 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
• 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 Territory biospace frontier
Missouri River quantum microscopy
Corps of Discovery MURI and MOQSI
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MURI/MOQSI is a 21st Century “Corps of Discovery” – opening
a new & unbounded frontier
The Path to Single Nuclear Spin Detection: FAQThe Path to Single Nuclear Spin Detection: FAQThe Path to Single Nuclear Spin Detection: FAQThe 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
Q5Q5**:: How can we eliminate terrorism’s primary resources: How can we eliminate terrorism’s primary resources: hunger, poverty, desperation, and chaos?hunger, poverty, desperation, and chaos?
A5A5**:: New resources, new projects, and new kinds of work New resources, new projects, and new kinds of work all support a pivotal strategic objective: creating all support a pivotal strategic objective: creating one billion jobs in the next twenty yearsone billion jobs in the next twenty years
We must win the GWOT; failure is not an option.
New resources are a vital need.
• 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.
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 Mathematics The Power of Knowledge
The Power of DiscoveryThe Power of Resources
“Ordinary people can make extraordinary contributions”
