Preview:How can we be sure a physical system is not running a possibly occult quantum computation

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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)

Quantum system engineering is stimulating new
approaches in math and physics
the least-studied class of quantum analysis
methods
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October 11, 2005UW Condensed Matter Seminar
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
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
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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 Theres 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 were 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.
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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 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 Well 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 talks key questionwill quantum microscopy
work?
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Were 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 Moores Scaling smaller, colder,
  quieter devices work better

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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
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Quantum biomicroscopy has plenty of SNR headroom
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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 yearspursuit of engineeringperfection
, Caves quantumlimits wereachieved
Lesson quantum system engineering (QSE) is The
unrelenting pursuit of engineering perfection
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A project far larger than the Genome Project
(from the on-line White Paper)
This technology helps provide Diracs foundation
for a Golden AgeOrdinary 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 Centurys
  greatest resource

Nature 432, p. 823 (2004)
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• 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
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The orthodoxy of Mike and IkeAll 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

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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 Kraus operators (which
  generate POVMs)

• Recognize that interferometer tuning invariance
  is just Chois Theorem

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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)

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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

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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
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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?
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)
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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

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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

MURI/MOQSI is a 21st Century Corps of
Discovery openinga new unbounded frontier
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We must win the GWOT failure is not an
option. New resources are a vital need.
Q5 How can we eliminate terrorisms 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
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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

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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 Discovery
The Power of Resources
We must win the GWOT failure is not an
option. New resources are a vital need.
Ordinary people can make   extraordinary
contributions
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