Transcript Preview: How can we be sure a physical system is not running a (possibly occult) quantum computation? • A1: Not enough energy –

Preview: How can we be sure a physical system is not running
a (possibly occult) quantum computation?
• A1: Not enough energy
– Variational calculus
• A2:Quantum
Too much symmetry
system
engineering
stimulating
• A3:is
Ensemble
averaging new approaches
– Statistical mechanics
in math and physics
– Master equations
– Group theory
• 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:
the least-studied class of
quantum analysis methods
– 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)
October 11, 2005
UW Condensed Matter Seminar
Emerging Techniques for Solving
NP-Complete Problems in
Mathematics, Biology,
Engineering, … and Physics
This talk is a blueprint
for integrated technology
The Quantum System Engineering Group
University of Washington
Seattle, Washington, USAdevelopment
Presented by:
Personnel:
UWMICORN Collaboration:
Joseph L. Garbini
John Jacky
John Sidles
Doug Mounce
Al Hero / Michigan
John Marohn / Cornell
Doran Smith / ARO
Dan Rugar / IBM
Students:
Joe Malcomb
Kristi Gibbs
Chris Kikuchi
Tony Norman
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
The Historic Challenge of Quantum Microscopy
1959: Richard Feynman
There’s Plenty of Room
at the Bottom
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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1946: John von Neumann to Norbert Weiner
Pauling, von Neumann, and Feynman
There is no telling what really advanced
shared a vision
issued
a do.
challenge;
electronand
microscopic
techniques will
In fact, I suspect that the main
now we’re
to fulfill it
possibilitiesgoing
lie in that direction.
Electron microscopy
Crystallography
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1946: Linus Pauling
System biology
proposal to
Rockefeller
Foundation
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 A1: The path is smaller, colder,
to single-nuclear-spin detection?
quieter device development
Q2: What are appropriate performance
metrics and technical milestones?
A2: The metric is bits-per-second
received from each target spin
Q3: When might this technology
reasonably be ready?
A3: By 2010, if historic rates
of progress are sustained
Q5: Are we confident that quantum
microscopy will work?
A5: We’ll know soon. E2e analysis
and emulation now feasible
Q6: How can this technology help win
the Global War on Terror (GWOT)?
A6: New resources are a strategic
requirement for GWOT victory
Q7: What is the logical next step?
A7: a satellite-scale integrated
launch program: MOQSI
This talk’s key question:
Q4: What tasks could this technology
A4: Comprehensive access to
will
quantum
microscopy
work?
accomplish?
resources of “chemical space”
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
Moore’s Law Progress in MRFM
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
Moore’s
Law
design
rules
• smaller
• colder
• quieter
The Path to Single Nuclear Spin Detection: FAQ
Q2: What are appropriate performance
metrics and technical milestones?
• Jiro Horikoshi and John Boyd
A2: The metric is bits-per-second
received from each target spin
Informatic capacity
is our primary metric
Horikoshi: Eagles of Mitsubishi
Boyd: US Flight Test Manual (FTM108)
Good design metrics
reflect the overall mission
• 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
UWMICORN: Program for Achieving
Single Nuclear Spin Detection
Quantum biomicroscopy
has plenty of SNR headroom
1992
2004 2010
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
Approaching the quantum
limits will require1982
a sustained
technological effort
1998
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
after 17 years’
pursuit of
engineering
perfection,
Caves’ quantum
limits were
achieved
Lesson: quantum system engineering (QSE) is
“The unrelenting pursuit of engineering perfection”
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
Nature 432, p. 823 (2004)
21st Century’s greatest resource
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 polynomial
memory and
time resources
Quantum analysis
techniques
engineering
– E.g., compute a transfer function
complexity
that reside •inNP:NP,
not EXP,
classes
via a decision “certificate”,
verify with polynomial resources
are a mission-critical
requirement
– E.g, does a stable controller exist?
P
• NP-hard: typically, the optimization
or interval version of an NP problem
NP
NP-hard
– 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
EXP
– problems in EXP are inaccessible
– Quantum system engineering
must move from EXP to P
The orthodoxy of “Mike and Ike”:
All quantum simulations are equivalent to …
Chapters
1,2,8,9
The analysis tools we need
are 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
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 Choi’s Theorem
measured data
spin dynamics
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“jump”
reservoir
“noise”
reservoir
“measurement”
reservoir
Q5: Are we confident that quantum
microscopy will work?
measured data
spin dynamics
“jump”
reservoir
A5.1: Quantum emulation of the
IBM single-spin experiment
IBM’s 13-hour single-spin
experiment can be
efficiently simulated
“noise”
reservoir
“measurement”
reservoir
Q5: Are we confident that quantum
microscopy will work?
Numerical simulations of
high-temperature spin dust
A5.2: Generalize to higherdimensional spin systems
cumulative distribution function (CDF)
18-spin quantum dispersion entropy values
– a deliberately tough challenge –
QDE of spin dust
with synoptic
noise tuning
Replacing quantum noise with
covert quantum measurement yields
compressed Hilbert space trajectories
QDE of random
product states
(analytic result)
QDE of spin dust
with ergodic
noise tuning
QDE of random
Hilbert states
(analytic result)
quantum dispersion entropy (QDE)
• no spatial symmetry
• no spatial ordering
• random dipole coupling
• noisy environment
tough to simulate
•
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)
Q5: Are we confident that quantum
microscopy will work?
A5.3: Beylkin & Mohlenkamp’s algorithms provide a vital tool
Compressed Hilbert trajectories
can be stored in P-space and
computed 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
Q5: Are we confident that quantum
microscopy will work?
Numerical simulations of
high-temperature spin dust
A5.4: Separated reps perform well
even in “tough” spin systems
fidelity of separated representations
fidelity
– a deliberately tough challenge –
These techniques are robust:
they work even at high temperature
and in the absence of symmetries
rank = 2
fidelity
rank = 1
rank = 5
rank = 10
synoptic
noise tuning
fidelity
ergodic
noise tuning
• no spatial symmetry
• no spatial ordering
• random dipole coupling
• noisy environment
tough to simulate
rank = 20
number of spins
rank = 30
number of spins
Q5: Are we confident that quantum A5.5: Now, large-scale quantum spin
microscopy will work?
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 capability
that is now coming on-line
• The mission-critical MURI/MOQSI objectives:
By definition, a linked representation is a separated
representation subjected to linear constraints (the “wire-ties”)
– Reliably predict strong-gradient quantum spin physics
– Maximize system performance metrics
– Build confidence that MURI/MOQSI will go all the way
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”
Q5: Are we confident that quantum A5.7: As confident as Thomas Jefferson
microscopy will work?
in the Army’s “Corps of Discovery”
• Strategically, MURI/MOQSI is a 21st Century “Corps of Discovery”
19th Century
21st Century
MURI/MOQSI
is a 21st Century
Louisiana Territory biospace frontier
“Corps
ofquantum
Discovery”
– opening
Missouri River
microscopy
Corps of Discovery MURI and MOQSI
a new & unbounded frontier
• 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”
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• Achieve all that our forebears challenged us to accomplish
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The Path to Single Nuclear Spin Detection: FAQ
Q6: How can this technology help win
A6: New resources are a strategic
the Global War on Terrorism (GWOT)?
requirement for GWOT victory
We must win the GWOT;
failure is not an option.
A5*: New resources, new projects, and new kinds of work
all support a pivotal strategic objective: creating
oneNew
billion jobsresources
in the next twenty yearsare
a vital need.
Q5*: How can we eliminate terrorism’s primary resources:
hunger, poverty, desperation, and chaos?
Q7: What is the logical next step?
A7: A satellite-scale integrated
launch program: MOQSI
• 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.
If we build it,
it will work.
• 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
“Power, before it comes from arms or wealth, emanates from ideas”
K. N. Cukier
The Power of Mathematics
The Power of Knowledge
Walter Reed
Caroline
Herschel
Linus
Pauling
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Barbara
McClintock
Baruch
Spinoza
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Richard Feynman
Lynn Margulis
Anton van
Leeuwenhoek
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John von
Neumann
Robert
Hooke
The Power of Resources
We must win the GWOT;
failure is not an option.
New resources are
a vital need.
Jane Goodall
The Power of Discovery
“Ordinary people can make
extraordinary contributions”
Thank you