What's New
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Friday, October 10, 2008Next Thursday's (October 16) UW Numerical Analysis Research Club (NARC) lecture (click here for time and place) will mainly cover the material in a (brief) manuscript Five promises from geometric quantum mechanics for efficient quantum simulations.
Beginning students (and the general public) are welcome and may find this Feynman-related background material useful.
The recent SIAM/SIMAX Special issue on tensor decompositions and applications has taught our UW QSE Group that the state-spaces that we quantum system engineers call (informally) gabions, and which we regard as being (essentially) Kählerian geometric objects whose shape is dynamically determined by quantum informatic flow, are known to numericists as tensor networks, which are (essentially) algebraic/combinatorial objects exhibiting Kronecker-product structure.
Here is some background reading regarding the tensor network point of view:
The lecture will develop the point-of-view that the state-spaces most useful in quantum system engineering are most naturally regarded as being both geometric objects of "gabionic" type and algebraic objects of "tensor network" type, and that unifying these geometric and algebraic points of view is a promising avenue for further progress in quantum system engineering and applied mathematics.
We hope for a lively discussion, as there is plenty of work to do!
Tuesday, October 7, 2008We will be discussing our research at the UW Numerical Analysis Research Club (NARC) next week:
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Students especially are welcome, and may find this background material useful.
Monday, October 6, 2008The UW QSE Group is very excited (and impressed) by the articles and commentary in the October 2 Nature:
One reason this work is exciting is that it enormously extends the design space of quantum spin microscopy, which now ranges from sensors with j=1/2 (diamond center sensing) to j=109 (ferromagnetic MRFM tips).
To cover this design space, we are expanding our essay-in-progress What is a quantum operation gauge? into an analysis whose focus is the general role of quantum informatic gauge-invariance in large-scale simulations of quantum spin microscopy.
The broader goal of this Operation Gauge analysis is to provide mathematical foundations for QSEPACK 2.0 that can support the dovetailed needs and aims of the quantum spin microscopy community and the quantum system engineering community.
Also (needless to say) we have added a reference to the outstanding diamond-center work to the in-review Five promises from geometric quantum mechanics for efficient quantum simulation (now in version 1.0e).
Students may wonder: why is everyone so excited about these new approaches to atomic-resolution microscopy?
The reason is that comprehensive biological microscopy, in 3D, with atomic resolution, is one of the oldest dreams of science. The excitement comes because we are now approaching the fulfillment of that dream.
Richard Feynman famously described the challenge of atomic-resolution microscopy in a 1959 lecture titled There's Plenty of Room at the Bottom:
What you [physicists] should do in order for us [biologists] to make more rapid progress is to make the electron microscope 100 times better. ...
[Then it would be] very easy to answer many of these fundamental biological questions; you just look at the thing! You will see the order of bases in the chain; you will see the structure of the microsome.
Unfortunately, the present microscope sees at a scale which is just a bit too crude. 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?
Every advance in experimental capability creates (of course) a concomitant challenge to similarly advance simulation capability. The reason is simple: atomic-resolution microscopy isn't easy: to obtain images, roughly a dozen systems have to work fairly near the quantum limits, the thermodynamic limits, and the informatic limits of efficiency.
If we take a quantum system engineering point of view—meaning, if we focus upon "the design of the (quantum) whole as distinguished from the design of the (quantum) parts"—then the atomic-resolution quantum spin microscopy of a protein molecule (for example) requires, first, a predictive understanding of the dynamical behavior of systems of several hundred interacting quantum spins. Then this quantum-level understanding needs to be integrated with the practical engineering realities of system-level design (cryogenics, optics, radio-frequency modulation, sample scanning).
In another famous lecture, Richard Feynman identified the problem of efficient quantum simulation as a fundamental scientific challenge. The concluding sentence to Feynman's 1982 lecture Simulating Physics With Computers sums up this second Feynman challenge as follows:
"If you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy!"
The good news for young scientists, mathematicians, and engineers is that tremendous progress is now being made on both of Feynman's two challenges: the challenge of atomic-resolution microscopy and the challenge of large-scale quantum simulation. And the even better news (for mathematicians, scientists, and engineers of every age) is that there is still a tremendous amount of work to be done.
It is remarkable—but in retrospect, perhaps it was to be expected—that each of Feynman's two challenges is helping us to meet the other challenge.
The challenge of molecular microscopy has focussed our attention upon what at first appears to be an unpromising arena for quantum simulation: large-scale, asymmetric, high-temperature, noisy quantum systems. But counter-intuitively, such systems turn out to be among the best-suited for quantum simulation, in the sense that noise makes quantum simulation easier.
Reciprocally, the rapidly accelerating capabilities for large-scale quantum simulation are helping us to retire the risk and speed the pace of developing quantum spin microscope technologies.
The scale of atomic-scale biological structures waiting for us to explore is almost inconceivably vast: there are about as many atoms in a child's little finger than there are stars in the entire visible universe.
That is why students today are lucky to be alive at the beginning of a century in which both of Feynman's challenges are likely to be met, and the unveiling of these tremendous new resources can begin.
We are continuing to add links and refinements to the essay-in-progress ...
We may start a blog on this topic, and we're wondering who among our colleagues might be interested to read it. So we'd like to hear what aspects of this general topic would be of most interest to you.
Algebraic geometry? PDEs? Quantum information science? Geometric quantum mechanics? Quantum chemistry? Condensed matter physics? Enterprise engineering? Model order reduction? Compressive sampling? Sparse reconstruction? Petascale numerics? Atomic-resolution bioimaging?
That these fields are intimately entangled is becoming apparent.
This entry was inspired by Terence Tao's lucid essay What is a gauge?
These QSEPACK discussions have been augmented:
As before, the QSEPACK 1.0 release page is here.
The UW QSE Group, in collaboration with the Institute for Soldier Healing (IHS), has released QSEPACK 1.0 to beta testing.
The numerically efficient algorithms of QSEPACK 1.0 bring the quantum simulation capabilities of cluster-scale computing resources to the desktop.
We are now recruiting beta-testers for QSEPACK 1.0.
Access is through the QSEPACK 1.0 Release Page.
Access to QSEPACK 1.0's software is immediate:
QSEPACK 1.0's main theory documentation (as distinct from the code documentation) is the manuscript Five promises from geometric quantum mechanics for efficient quantum simulation.
For a more extensive review of quantum simulation formalisms from a geometric point of view, see our QSE Group's arxiv preprint Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems.
If all you need is an overview of the main theoretical ideas behind QSEPACK, then simply read further on this page.
And finally, if you are in Seattle, you are welcome to visit us at our UW QSE Laboratory. Our QSE Group meetings (schedule here) are open to the public, and students especially are welcome.
QSEPACK 1.0 (including the beta-release version described here) is released under GPL 3.0.
QSEPACK 1.0 builds upon the geometric approach to quantum simulation that is described our QSE Group's recent Practical recipes for quantum simulation.
Specifically, QSEPACK builds upon three principles that blend quantum information science, the classical theory of model order reduction, and algebraic geometry:
Quantum information science: Quantum information science teaches the deep and useful mathematical principle that noise processes can always be simulated as equivalent quantum measurement processes. Physically speaking, noise processes in a quantum system can be conceived as originating in other observers who are covertly measuring the system.
In consequence: It is always logically permissible, and very often it is computationally efficient, to simulate nonlinear quantum phenomena (such as quantum jumps and uncertainty principles) as originating in competing measurement processes.
Model order reduction: Quantum measurement processes generically act to dynamically compress quantum trajectories onto lower-dimension state-spaces. This compression occurs via a dynamical mechanism that is both physically reasonable and computationally efficient: measurement processes are described by stochastic potentials whose gradient induces a "downhill" drift toward quantum states that are low-variance in the measured operator.
In consequence: High-noise quantum systems (including the important special case of quantum systems in thermal contact with zero-temperature reservoirs) exhibit a natural dynamical mechanism for model order reduction that makes them generically easier to simulate than zero-noise quantum systems (or error-corrected quantum systems). This same compression mechanism constitutes a powerful quantum informatic tool for deriving new quantum representations, for example the positive P-representation of the thermal density matrix that is derived in the Practical Recipes (see Section 3.2.2).
Algebraic geometry: The Kählerian geometry of the reduced-order quantum state-spaces (that are most popular with physicists) is algebraically ruled, with the rule tangent vectors constituting an over-complete local basis. Building upon the classical results of Goldberg and Kobayashi relating to holomorphic bisectional curvature, it is readily proved that these state-spaces exhibit negative sectional curvature on all sections that contain a rule tangent vector, and thus the Ricci and Riemann curvature of these manifolds is nonpositive. We note, however, that sections not containing a rule tangent can be found whose sectional curvature is positive, and in consequence the sectional curvature of these quantum state-spaces is perhaps best conceived as being "nearly negative" in a well-posed sense.
In consequence: Kählerian algebraic state-spaces have a natural hyperbolic embedding in the larger Hilbert state-space that is well-suited to the algorithmically compressed representation and high-efficiency computation of quantum trajectories (as discussed further in the Practical Recipes). Physically speaking, the "shape" of Kählerian algebraic state-spaces can be conceived as foliate (leaf-like), as depicted by the Hilbert curve that appears on the cover of the QSEPACK 1.0 documentation. The algebraic rule structure and Riemannian curvature of this foliate geometry is discussed at greater length in the Practical Recipes.
QSEPACK 1.0 builds upon these ideas to provide efficient algorithms for computing certain matrix-vector products that typically are rate-limiting in quantum trajectory simulations.
The following descriptions of QSEPACK 1.0's capabilities are fully equivalent and equally valid:
Abstract description: The key capability provided by QSEPACK 1.0 is an efficient algorithm for computing local musical isomorphisms along integrated quantum trajectories of n-spin systems, on large-dimension quantum state-spaces, using only O(n) time and space resources instead of the O(n2) resources that naively are required.
Covariant description: In quantum trajectory simulations, the upper indices of trajectory tangent vector components (sometimes called the "sharped" or "♯" indices) are covariantly coupled, via an index-lowering linear map, to the lower indices of quantum potential one-form components (sometimes called the "flatted" or "♭" indices). QSEPACK 1.0 exploits the intrinsic ruled structure of the algebraic geometry of widely used Kählerian state-spaces to efficiently compute the index-lowering linear map.
Prosaic description: QSEPACK 1.0 provides fast algorithms for the generic calculation of lowered indices. On state-spaces having dimension n, index-lowering is naively accomplished by storing the O(n2) components of the Hermitian metric tensor and calculating a matrix-vector product in O(n2) multiplications. But in large-n quantum trajectory simulations, naive O(n2) storage and index-lowering methods create unacceptable computational bottlenecks. QSEPACK 1.0 relieves these bottlenecks by storing the Kählerian metric tensor in an O(n) compressed algebraic representation and by providing an O(n) algorithm for the index-lowering linear map.
Computational description: QSEPACK 1.0 provides a new class of methods for fast matrix-vector multiplication of structured matrices that specifically are compatible with the algebraically structured Kählerian metric matrices that appear in large-scale quantum trajectory simulations. In recent years, similar fast-product methods have transformationally augmented the scientific and engineering capabilities of classical large-scale simulations. Now quantum simulation capability is undergoing a similar aacceleration, to which QSEPACK 1.0's tools contribute.
Concrete description: The practical benefit of QSEPACK 1.0's O(n) acceleration and compression is that large-scale quantum dynamical spin simulations—simulations so large that ordinarily they would require cluster-scale computing resources—can feasibly be computed on desktop-scale machines.
The capabilities of QSEPACK 1.0 point to fundamental mathematical questions that also have immediate practical implications.
Given that QSEPACK's index-lowering algorithm is O(n), how hard is index-raising? Using standard iterative templates, is index-raising O(n3), O(n2), or even O(n)? In practice, what preconditioning methods work best for iterative index-raising algorithms?
More fundamentally, what is the existence of these algorithms telling us about the quantum informatic content of the musical isomorphism on Kählerian state-spaces, relative to the algebraic geometry of these state-spaces?
Still more fundamentally, how can quantum information theory be integrated most naturally into Kählerian algebraic geometry? It is already clear that the study of Markovian drift-and-diffusion processes on Kählerian algebraic manifolds provides a natural starting point for these investigations.
From a teaching point of view, it would be particularly helpful to have a short, insightful answer to the question: "What is special about the Kählerian algebraic state-spaces of quantum simulation that makes index-lowering (and perhaps index-raising) easier than on generic state-spaces?" At present no insightful answer is known.
These fundamental mathematical questions are presently of great practical interest to the UW QSE Laboratory. We are actively seeking collaborators, and we are especially eager to collaborate with colleagues who have an interest in near-term applications of QSEPACK 1.0 in large-scale spin simulations.
A large class of fundamental questions in quantum simulation science has to do with the well-known ambiguity of the operator-sum representation of strictly positive maps (see Sec. 8.2 of Nielsen and Chuang's Quantum Computation and Quantum Information for an introduction, then see the Practical Recipes for some practical implications).
The quantum operation ambiguity is usually presented as a global algebraic invariance, but in the context of quantum trajectory simulation it can be understood more broadly as a "gauge-like" local geometric invariance. The necessary mathematical ideas and tools are reviewed in Terence Tao's wonderfully lucid weblog essay What is a gauge?, which directly stimulated the following discussion.
At each step of a noisy quantum trajectory simulation, we can ask the fundamental question "What quantum operation gauge for the noise should I choose, on the next time-step, to most effectively compress this particular wave function onto a lower-dimension state-space?" Because we are allowed to examine the wave function before making our choice of operation, this question acquires a local gauge-like character.
It is natural to ask—without necessarily having a clear idea of what the answer might be—whether this freedom to choose a local quantum operation gauge allows us to guide the flow of probability associated with Fokker-Planck equations (which are also known as Kolmogorov equations). We have the intuition that the (exponentially many) degrees of freedom in the choice of operation gauge allows us to tune (with exponentially many degrees of freedom) the Fokker-Planck probability current.
A somewhat similar situation arises in the theory of integrable dynamical systems, and it is well-known that the classification of dynamical solutions (often of soliton type) is greatly simplified by the dynamical invariances of the solutions.
One immediate benefit of this operation-gauge point of view is that we gain an appreciation that noisy quantum systems are generically rich in mathematical invariances (exponentially rich, in fact) relative to noise-free (or error-corrected) quantum systems. Roughly speaking, each spin-1/2 particle we add to a noisy system doubles the dimensionality of the state-space, thus making simulation harder, but also doubles the number of invariances available for tuning the Kolmogorov dynamics of the system, thus making simulation easier.
In comparison, noise-free quantum systems exhibit dimension-doubling, but no compensating invariance-doubling. The absence of invariance-doubling is a keystone of Feynman's famous argument that efficient computational simulation of low-noise quantum systems is infeasible, which in Feynman's lecture formally rests upon the large-dimension scaling of Kolmogorov-type equations (these equations).
A key innovation of modern simulation science is to exploit the gauge invariance of quantum operations to structure the matrix-vector products that appear in these Kolmogorov-type equations such that the products can be evaluated by (computationally efficient) implicit/iterative techniques as contrasted with (computationally infeasible) explicit/direct techniques. The algorithms and documentation of QSEPACK 1.0 are explicitly based upon this idea, and it is fair to say too that many software packages for ab initio quantum chemistry implicitly embody the same gauge-theoretic principle.
We thus appreciate that the gauge invariance of quantum operation representations allows simulations of noisy quantum systems to evade Feynman's infeasibility arguments, not only in an abstract sense, but in a practical sense. The mathematics of gauge theory provides us with a vocabulary and a conceptual toolset that helps us recognize the ubiquity of gauge-type invariances in quantum simulation science, which in turn suggests reasonably definite research paths for further development of these ideas.
As one concrete example (out of many that might be suggested) we can ask whether Adler's analysis of Itô representations of Lindblad generators (which is briefly reviewed and applied in the Five Promises QSEPACK documentation) might be gauge-generalized to globally characterize the class of Fokker-Planck representations of the thermal density matrix whose canonical exemplar is the positive P-representation derived in the Practical Recipes (see Sec. 3.2.2)?
In other words, in what mathematical sense (if any) is the class of gauge-equivalent representations of the thermal density matrix so large that it necessarily contains (informatically compact) P-representations?
Such an analysis might improve our understanding of fundamental questions that are asked (but not answered) in the Practical Recipes, namely, why do positive P-representations exist, and why do they have a simple analytic form? In the context of quantum simulation science, these questions have both fundamental and practical importance.
In our present state of knowledge it is not yet clear what a global description of noisy-system quantum simulations might look like. From a practical engineering point of view, it would be immensely valuable if mathematical reasoning along these gauge-theoretic lines helped us to a broader and more rigorous understanding of the (commonplace) empirical observation that noisy quantum systems are generically easy to simulate.
The insight that noisy quantum systems are generically easy to simulate—if it could be given rigorous gauge-theoretic and quantum informatic foundations—would nicely complement the fundamental principle of quantum computing, that low-noise (and/or error-corrected) quantum systems are generically hard to simulate.
At a fundamental level, we don't really understand how the informatic, algebraic, differential, and geometric elements of quantum simulation fit together.
An important symptom of our present relative ignorance is that large-scale quantum simulations not infrequently—and very surprisingly—work enormously better that our present mathematical and physical understanding suggests that they should.
Quantum simulation research provides a natural venue for unifying our mathematical understanding. The section Looking ahead to QSEPACK 2.0 offers (preliminary) suggestions for unifying research directions.
QSEPACK 1.0 is implemented as a template library that is compatible with the LAPACK-based library Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods.
The QSEPACK 1.0 templates themselves are written in MATLAB (or OCTAVE), with innermost loops optimized as calls to the BLAS.
Documention is provided via a Knuth-style literate programming environment that is implemented in a (customized) version of nuweb.
The QSEPACK 1.0 documentation begins with a series of seven epigraphs (immediately below), which are provided both as a guide to the evolution and philosophy of QSEPACK and as an appreciation of authors whose works provided the foundations for QSEPACK.
The epigraphs range from abstract (at top) to concrete (at bottom). However, we are going to discuss them in the opposite order, from concrete-to-abstract (bottom-to-top), because this order more nearly reflects QSEPACK's actual development. To borrow a passage from Terence Tao, the field of quantum trajectory simulation "has proven to be the type of mathematics where progress generally starts in the concrete and then flows to the abstract, rather than vice versa."
We begin with Donald Knuth's ideal of literate programming, which is "explaining to human beings what we want a computer to do." Because large-scale simulations (both classical and quantum) have become central to large-scale enterprises, the role of simulation software now includes explaining what goals we are working toward and why we should be confident that these goals are achievable.
Our second epigraph is from Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, which belongs to the LAPACK family of codes. The LAPACK family of codes is among the seminal achievements of the twentieth century, not only as a computational toolset, but also as a major educational resource. QSEPACK hopes to contribute to LAPACK's continued growth and value as an open resource.
Our third epigraph is from Anne Greenbaum's Iterative Methods for Solving Linear Systems. Prof. Greenbaum's book is valuable for its outstandingly lucid exposition of the mathematical ideas underlying the Templates book. The QSE community looks forward to seeing these ideas extended from large-scale systems of linear equations (as in classical simulation) to large-scale systems of Kählerian algebraic equations (as in quantum simulation).
Our fourth epigraph is from Donald Knuth's forward to the (wonderful) book A=B by Marko Petkovsek, Herbert Wilf, and Doron Zeilberger. Professor Knuth provocatively distinguishes "science" from "art" and reminds us progress occurs (ideally) on both sides of this boundary. In Knuthian terms, the goal of QSEPACK is to help advance both the science and the art of quantum system engineering.
The fifth, sixth, and seventh epigraphs respectively come from the disciplines of model order reduction, quantum information science, and algebraic geometry. The quantum system engineering (QSE) community regards these disciplines as being Knuthian artistic aspects of an overarching discipline that someday might be called "mathematical foundations of QSE."
In the fifth epigraph, Michaɫ Rewieński and Jacob White remind us of the urgent need for better methods for simulating large-scale nonlinear systems. A key lesson from QSEPACK theory is that quantum simulation has great advantages over classical simulation: dynamical universality, noise-measurement equivalence, and a reduced-order Kählerian algebraic state-space whose computational properties are comparably favorable to linear state-spaces.
The sixth epigraph quotes from Michael Nielsen's and Isaac Chuang's seminal textbook Quantum Computation and Quantum Information. QSEPACK approaches quantum simulation via the same postulates as Nielsen's and Chuang's textbook, but with the contrasting objective of simulating noisy (or low-temperature) large-scale quantum systems rather than computing with low-noise (or error-corrected) large-scale quantum computing devices. Nielsen's and Chuang's textbook is essential reading for all quantum system engineers.
The seventh and final epigraph is from Shing-Tung Yau's review (and tribute to Shiing-Shen Chern) titled Perspectives on geometric analysis. A passage about negative Kählerian curvature was selected because, for reasons that at present are not understood, the confluence of quantum information theory with the requirement of efficient model order reduction seems to lead inexorably to algebraic Kählerian state-spaces that have negative intrinsic curvature (details here). The strength and depth of the geometric and algebraic foundations that are surveyed in Prof. Yau's article provide us with confidence that the developing art and science of quantum system engineering will find abundant mathematical opportunities for discovery and innovation.
The central challenge of quantum system engineering is to synthesize the ideas of these great works into the tools of a new engineering discipline, and then to apply these tools in service of urgent needs and global-scale enterprises.
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The following are further screen-shots from the QSEPACK documentation. If you are interested to learn more, please consider becoming a QSEPACK beta-tester and/or manuscript reviewer, and please consider also joining us in QSEPACK's further development.
There is plenty of work that needs doing, plenty of fundamental challenges to be investigated, and plenty of colleagues who possess valuable knowledge that can fruitfully be brought to bear.
That is why quantum system engineering is fun.
We are especially keen to collaborate with colleagues who potentially have an interest in near-term applications of QSEPACK 1.0 along the lines described on the following preface page to the QSEPACK 1.0 documentation:
We foresee that QSEPACK 2.0 will develop along the lines described in the prologue to the QSEPACK 1.0 documentation.
Your email suggestions are very welcome.
The on-line guidances are:
The on-line talks (latest versions) are:
The documents are guidances to a GEN-4 Engineering Research Center (ERC) that is now being organized.
Gen-4 science and engineering initiatives are now in the early planning stages. These initiatives will be the successors to the NSF's highly successful Gen-3 initiatives.
We foresee that quantum system engineering (QSE) will play a key role in many Gen-4 initiatives.
Building on the computational toolset of our ARO-MURI Group's Practical recipes for quantum simulation, the UW QSE Group has contributed the following Gen-4-enabling objective to the Computing Community Consortium's public initiative Visions for Theoretical Computer Science:
Computing in Large-Dimension State-SpacesMore and more modern computational tasks have the property that the size of the state space is a matter of discretion and design. For example, in simulating quantum systems researchers can choose to work in the native Hilbert state-space (thus preserving invariances), or alternatively in reduced-order spaces (thus bringing geometry to bear), or alternatively in the larger-than-Hilbert dictionary spaces of compressive sensing and sampling theory (thus bringing information theory to bear).
These new design choices are ubiquitous in both classical and quantum state-spaces. Increasingly, they are relevant to large-scale calculations in every branch of science and engineering.
A program that specifically focusses on the question "What general computational principles and techniques are broadly applicable to systems having large-dimension state-spaces?", as defined in a series of conferences, white papers, test-beds, and rapid-prototyping software, will cross-fertilize and invigorate many disciplines.
Industrial Participation Will Be Encouraged
Science and engineering work best---generate the most new ideas, new enterprises, jobs, and prosperity---when there is a vigorous two-way flow of ideas, from the abstract to the concrete and from the concrete to the abstract. Large-scale state-spaces are an emerging arena within which this two-way flow of ideas is outstandingly vigorous.
The United States' science and technology community is uniquely well-positioned to take advantage of these new opportunities, by virtue of its culture of enterprise and innovation. Mathematics and computation are the two keys that open this new door.
Building on our ARO-MURI Group's Practical recipes, and focussing upon specific applications, our presentation The Mission, Status, and Outlook of the Institute for Soldier Healing (ISH) is now on-line.
The ISH is the third element of our QSE Group's fundamental R&D triad:
This triad will be the focus of a planned GEN-4 Engineering Research Center (ERC) that is now being organized.
The arXiv server now has our ARO-MURI Group's Practical Recipes online as 0805.1844.
A discussion of the Practical Recipes material on compressive sampling (CS) has been added to our on-line talk How does the Stern-Gerlach Effect really work?
The added material reflects our emerging appreciation that compressive sampling (CS) and quantum model order reduction (QMOR) are concerned with the same fundamental mathematical topic: compressible objects.
In the slide above, Goldilocks and the Three Bears provides an allegorical context for three state-spaces that are useful in quantum simulation: the "baby" state-space of Kählerian algebraic varieties, the "mama" Hilbert space of linear quantum mechanics, and the "papa" state-space that is defined by associating a Hamming metric to the sampling dictionaries of compressive sampling (CS) theory.
More formally, the mutual embrace of compressive sampling (CS) theory and quantum model order reduction (QMOR) theory provides new insights to both disciplines. One example: coding theory proves to be helpful in constructing RIP matrices that are useful for applying convex optimization algorithms to practical problems in large-scale quantum simulation.
The practical consequence of the above QSE-CS convergence is that the scale and scope of next-generation technology development are being expanded, and the pace of that development is being accelerated.
It is an exciting time to be a quantum system engineer.
Our UW QSE Group's Practical Recipes compendium now has a new nine-page final section: Section 4.6: Quantum state reconstruction from sparse random projections. The material in this section establishes a number of nontrivial connections between quantum simulation and the emerging discipline of compressive sensing.
In particular, topics like the following are extended to quantum state-spaces:
These connections are so natural—and so useful—that we have (provisionally) retitled the manuscript Practical recipes for the model order reduction, dynamical simulation, and optimization by Dantzig selection of large-scale open quantum systems.
It remains only to draft a new Conclusions section … which requires that we consider in some detail what these connections mean. This is no easy task, and feedback from colleagues is especially welcome.
Meanwhile, here are some quantum states that have been reconstructed from sparse random projections (Fig. 13 of the manuscript). Yes, compressive sampling theory really works in the quantum domain!
The 2008 Gordon Conference Mechanical Systems in the Quantum Regime has concluded ... it was a great conference!
Our ARO/MURI Team's talk How does the Stern-Gerlach Effect really work? is now on-line:
Comments are welcome.
The 2007 Spinometer Seminar is RunningThe 2007 Spinometer Seminar is up-and-running, and we have upgraded it from a seminar to a noncredit course on model reduction (MOR) methods in quantum system engineering (QSE). The curriculum and recommended reading for this course are here.
Lectures are given on the first and third Wednesday of each month, at 3:00 pm, in room 119 of the Mechanical Engineering Building. All are welcome.
A New Year's 2007 Essay: What is Quantum System
Engineering?Our QSE Group's short essay entitled What is Quantum System Engineering? is on-line here.
The essay has now been updated to version 1.0, and we sincerely thank all our colleagues who reviewed earlier drafts.
This essay was written originally as the introduction to a review article on large-scale quantum simulation, and it equally serves to provide a paragraph-by-paragraph tribute and acknowledgment of the influence of Prof. Jonathan Israel's Enlightenment Contested on our engineering research (as discussed in an appendix to the essay).
Faculty Position in Quantum System
EngineeringTo apply for the UW ME Department's tenure-track faculty position(s) in quantum system engineering, please see this advertisement.
The ME Department encourages any and all qualified applicants, from both theoretical and experimental backgrounds, who seek to create and teach new technologies that push against the bounds that quantum mechanics imposes on the speed, accuracy, sensitivity, size, and power consumption of modern mechatronic devices.
This position provides a wonderful opportunity to participate in creating and teaching the new, exciting, strategically important, and rapidly growing engineering discipline of quantum system engineering (QSE).
Quantum
System Engineering (QSE)Following the KIAS-KAIST 2006 Workshop on Quantum Information Science (held August 28-30) we spoke at the JEOL Corporation in Japan (on August 31).
We thank both KIAS-KAIST and the JEOL Corporation for their kind hospitality!
The slides from the JEOL talk are available here:
These JEOL slides are a superset of the KIAS-KAIST talk given earlier in the week (links below); the JEOL talk has extra slides dealing with "quantum shinkansen". These extra slides grew out of many wonderful conversations in Korea. Here is the title slide from the JEOL talk, as influenced by the KIAS-KAIST Workshop:
KIAS-KAIST 2006 Workshop on Quantum Information ScienceOur UW QSE Group's presentation is on-line:
Note: a longer version of the KIAS-KAIST talk was given at JEOL (JEOL slides here);Here is the abstract to the KIAS-KAIST Workshop talk.
From Quantum Physics to Quantum System Engineering:
Simulating Single-Spin and Multiple-Spin Imaging
in Magnetic Resonance Force Microscopy
John A. Sidles, Ph.D.
Quantum System Engineering Group
University of Washington
Seattle, Washington, USA
URL: http://www.mrfm.orgThis talk will describe a new technique for model order reduction in large-scale quantum spin simulations. The technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an informatically equivalent continuous measurement process, and finally, the projection of the resulting quantum trajectory onto state-space manifolds of low dimensionality, specifically, finite-rank product-sum manifolds of Beylkin-Mohlenkamp type. These manifolds are shown to have a Kahler-type complex geometry.
The practical application of this technique is illustrated by numerical simulations of single-spin detection by magnetic resonance force microscopy (MRFM): excellent agreement with experimental results is obtained. In the Markovian noise limit, the statistics of single-spin detection are predicted to all orders, and are found to be those of a random telegraph signal with added white noise.
These methods are then applied to larger-scale quantum simulations, in the context of a deliberately challenging spin-dust model that has no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low-dimensionality Kahler state-space manifolds is demonstrated. The informatic invariance associated with Choi's Theorem, and the scalar Ricci curvature and Ricci flow of the Kahler manifold state-space, are both shown to play important roles in achieving high-fidelity projection. It is concluded that model order reduction by projection onto a Kahler manifold state-space allows a large class of quantum systems to be simulated with polynomial space and time resources.
The talk will conclude by discussing the implications of these new techniques for product development, and more broadly, for the emerging profession of quantum system engineering.
EMSL Worshop at Richland, WAOur UW QSE Group's presentation is on-line: (schedule here)
Our UW QSE Group's presentations are on-line:
The QSE Daily Journal is now on-line.
The web page UW Quantum System Engineering Seminar Write-up summarizes the findings of a two-year UW Quantum System Engineering (QSE) Seminar, informally known as the Spinometers Seminar.
Until recently the Spinometers Seminar site was password-protected, and was open only to participants in the seminar. As of May 1, 2006 we are opening access to the general public.
The educational component of our VINCI/Vanguard Program has now been defined in a three-page white paper that we are circulating for public comment (click here for PDF).
Note: this white paper was initially written for UW local review, as the first draft of a pre-proposal to the W. M. Keck Foundation's Science and Engineering Program. Because this document is an initial draft, it is intended solely for local review, public comments, and teambuilding.
The FREE Program's Roadmap The UW FREE Program—Federative Resources for Engineering Enterprises—is our UW QSE Group's working roadmap for helping to strengthen engineering and science education at the UW. As the white paper states:
We envision that the UW FREE Program will help pioneer a new frontier for American engineering: a frontier that is energized by immersive teaching, vitalized by new technological resources, and funded by strategic service.
The FREE Program's Objectives The objective of the FREE Program will be to teach engineering and science skills by immersive apprenticeship in hardware development and advanced theoretical research, in an environment that embraces teaching, research, and service as a single federative enterprise.
The FREE Program's Projects The FREE Program will tackle grand challenges in engineering and science. Its initial focus will be quantum microscopy: a technology for directly observing the entire biomolecular universe with atomic-scale resolution.
The FREE Program's Federative Focus In engineering, the word federation generally refers to a combination of knowledge and techniques from multiple disciplines. In modeling and simulation, federation has acquired a more specific meaning: an assembly of dissimilar components whose interactions are considered in a systematic, explicitly quantitative way. By focussing on federative skills and technology, the FREE Program will prepare its students for leadership roles in 21st Century engineering and science.
VINCI/Vanguard 2006 LinksOverview of VINCI/Vanguard 2006 VINCI is our QSE Group's open-source, federated quantum system engineering environment, and Vanguard 2006 is this year's primary VINCI objective: end-to-end quantum modeling of the anti-HIV drug nevirapine.
VINCI/Vanguard 2006 federates three key advances: GNU Radio, P-time quantum simulation algorithms, and downselection of nevirapine as an imaging target (see below).
VINCI/Vanguard will be the Year 2006 focus of our ARO/MURI Program for Achieving Single Nuclear Spin Detection. Our full ARO/MURI research plan is here (in PDF).
GNU Radio On-Line Our QSE
Group's lead software engineer Jon Jacky now has his GNU Radio installation instructions on-line. This is a
major step forward in our VINCI Program for open-engineering
hardware-in-the-loop (HWIL) quantum system development.
As background, GNU Radio is an NSF- and DoD-sponsored open-source hardware and software environment, originally designed for radio-frequency signal processing, that our QSE Group has extended to encompass quantum system modeling, simulation, and control.
Nevirapine Case Study
On-Line Our QSE Group's premed student Chris Kikuchi
now has a preprint online Assessing the Capabilities of Quantum Microscopy for Drug
Development: Nevirapine as a Case Study and Design
Target.
The nevirapine case study will play a central design role when we unite it with our GNU Radio hardware-in-the-loop capability and our new P-time quantum simulation algorithms. More precisely, in the modern terminology of modeling and simulation, we will "federate" these technologies.
Quantum Microscopy's "Sputnik Moment" To describe our quantum microscopy project in terms of its parallels with the Space Program, the quantum microscopy community has already achieved the equivalent of Sputnik: this was the IBM MRFM Group's historic single-spin MRFM experiment, led by Dan Rugar.
Preparing for an "Apollo Moment" Quantum microscopy's next major engineering milestone is to calculate the equivalent of an Apollo lunar mission trajectory, that is, to calculate realistic end-to-end simulations of quantum imaging missions that are medically, strategically, scientifically, and commercially important.
The Central Role of Trajectory Calculations For engineering purposes, it is essential that reliable trajectory calculations be performed as early as possible in a project. For example, early lunar trajectory calculations largely determined the design of the Saturn V rocket and all its payloads. For identical engineering reasons, the calculation of end-to-end quantum imaging trajectories is driving the design of our next-generation nanotechnology (i.e., the cantilevers, sensors, and magnetic tips).
IBM's Pivotal Role Apollo's lunar trajectories were calculated at NASA's famous IBM real-time computer complexes (RTCCs) as described in this IBM Journal of Research and Development article. In NASA's own history we read:
The story of computers in manned mission control is largely the story of a close and mutually beneficial partnership between NASA and IBM. [...] When Project Vanguard, and later NASA, approached IBM with the requirements for computers to do telemetry monitoring, trajectory calculations, and commanding, IBM found a market for its largest computers and a vehicle for developing ways of creating software to control multiple programs executing at once, capable of accepting and handling asynchronous data, and of running reliably in real time. These things the company was able to do quite successfully, and the groups it assigned to the job impressed their NASA counterparts. When asked about IBM's performance in this field, one NASA manager said without hesitation: "IBM is the best".
The early Vanguard orbital calculations were done on an IBM 709. The IBM 709 seems primitive today (it used vacuum tubes!) but it provided the starting point for IBM's subsequent, enormously successful, product line of commercial computers. Even more famously, these IBM computers and their calculations provided the foundations for President Kennedy's famous "We will go to the moon" speech (text and audio here).
Vanguard 2006 Our program's next quantum imaging target will be the anti-HIV drug nevirapine, as described in the above Kikuchi preprint; we will integrate the dynamical equations supplied by our new P-time quantum simulation algorithms; and these equations will be embodied in Dr. Jacky's hardware-in-the-loop (HWIL) simulation environment. The resulting quantum system engineering environment will allow our QSE Group to proceed with rapid, concurrent development of multiple quantum microscopy subsystems.
We call this year-long project "Vanguard 2006", since it plays a similar role in our overall quantum microscopy program to Vanguard's role in the Apollo Program
The VINCI Toolset We call our federated quantum system engineering environment "VINCI". VINCI was originally an acronym for "Virtual Instrument Control Interface", but nowadays we use it to refer to our entire integrated toolset.
VINCI's new P-time quantum trajectory algorithms are essential to the design of the nanotechnological elements of quantum microscopy (i.e., the cantilevers, sensors, and magnetic tips), and to "flight control" of the ensuing quantum imaging missions. As with the IBM/NASA RTCCs, VINCI's mission is to ensure that "What we build works".
VINCI Flight Control The similarity between flying a satellite and running a quantum microscopy experiment is so strong that our QSE Group designates a "flight controller" for each experiment.
Our present flight controller is Joe Malcomb (at left). As with Gene Kranz and other NASA flight controllers, for whom, famously, "failure was not an option", quantum microscopy flight control is a job for young people who have an outstanding aptitude for real-time problem-solving and system analysis.
No human lives are immediately at risk when Joe guides our micron-scale quantum spacecraft a few nanometers above a cryogenic specimen, under real-time control, watching dozens of channels information simultaneously. In fact, these experiments are a lot of fun for the whole group!
But simultaneously, we are aware that quantum microscopy was envisioned in 1992 as a tool for creating better treatments for HIV/AIDS, and we also realize that today, fourteen years later, the HIV/AIDS pandemic still rages around the world, with no vaccine and no cure (yet).
So in a larger sense—like all engineers and scientists—we too are conscious that "failure is not an option," if our diligence can prevent that failure.
For this reason—and many others—our QSE Group takes each mission seriously: we try not to disappoint our flight director, who tries not to disappoint us, and we all appreciate that each mission brings our team—and all humanity—closer to transformational new scientific and medical capabilities, and also, fulfillment of a long-held dream of Richard Feynman, John von Neumann, and Linus Pauling.
VINCI's Challenges VINCI's quantum trajectories are considerably harder to calculate than the classical spacecraft trajectories that guided the Apollo Program. For this reason, the new and highly efficient algorithms that our VINCI initiative has developed for calculating quantum imaging trajectories are likely to find spin-off applications in many other areas of quantum science and engineering.
Even with these new algorithms, the quantum computational challenges of VINCI are sufficiently great that they can only be met by state-of-the-art computer hardware and software. In the 20th Century the required technologies were not available, thus VINCI is a 21st Century toolset.
VINCI's Scope Like IBM/NASA's real-time computer complexes, VINCI encompasses the federated missions of design, modeling, simulation, control, diagnostics, and data analysis.
A major strategic consideration is that the new frontier that VINCI is exploring—quantum biospace—is as large and rich as outer space, and yet the individual vehicles for exploring this frontier—quantum microscopes—will be far smaller and more affordable than Saturn V boosters: they will be tabletop-scale, in fact.
Given the inherent small scale of quantum microscope technology, we foresee an era in which many tens of thousands of quantum microscopes are in simultaneous operation, each transmitting a continuous stream of structural observations from the nearly infinite informatic richness of biospace. Also, there will be numerous applications of quantum microscopy in materials science and microelectronics.
Our UW QSE Group therefore anticipates that VINCI's federated tools for quantum system engineering will be widely disseminated, and VINCI has embraced an open-source development model for this reason.
VINCI's Future To meet the challenges of space flight, the IBM/NASA RTCCs developed and grew through successive Vanguard, Mercury, Gemini, and Apollo programs. Our VINCI development effort is presently focussing on its "Vanguard 2006" objective of nevirapine simulation, but it is already clear that VINCI-type tools will continue to develop and grow, in order that we may achieve one of the 21st Century's most exciting and strategically vital Grand Challenges: the exploration of quantum biospace.
Achieving Quantum Molecular Microscopy in Five
YearsDuring December 19-21, we were pleased to preview for the Army/ARL, NSF, NIH, and the Albert Einstein School of Medicine, what will be our UW QSE Group's main focus for 2006: Achieving Quantum Molecular Microscopy in Five Years: Following in the Footsteps of Apollo.
The presentation can be downloaded from this directory in both PowerPoint and PDF versions. An animation file for the end-to-end quantum simulation of the IBM single-spin experiment is included. These files are large; the PDF file is sixty slides totalling 70 MBytes.
During the coming weeks we will be dividing this presentation into single-slide HTML pages, with commentary for each slide. Here is the presentation's concluding slide:
Our QSE Group's talk Emerging Techniques for Solving NP-Complete Problems in Mathematics, Biology, Engineering, and Physics is now available from the Institute for Mathematics and Its Applications as a streaming video (click here).
Note: on OS X, the video seems to work best when opened with the RealOne Player. Note also that the first thirty seconds of the talk were not captured (so the initial gap is not a bug in the player). Fortunately, the meaning of the first slide becomes clear from context. The PDF and PowerPoint slides for the talk are available here.
Here is the abstract of the talk:
Emerging Techniques for Solving NP-Complete Problems
in Mathematics, Biology, Engineering ... and Physics
John A. Sidles, Ph.D.
Professor, UW School of Medicine
Adjunct Professor, Mechanical Engineering
Adjunct Professor, Bioengineering
Complex systems are ubiquitous in mathematics, biology, engineering, and
physics, and the past ten years have witnessed an exponential increase in
the literature associated such systems. A shared conceptual framework is
becoming apparent among challenges as seemingly different as the following:
the search by mathematicians for exact high-order trigonometric identities,
the search by engineers for stable control systems, the search by
biologists for stable protein structures, and the search by condensed
matter physicists for ground states.
Recent work has shown that separated product-sum representations provide a
powerful and broadly applicable tool for analyzing complex systems. Beylkin
and Mohlenkamp provide a good introduction to these representations in their
recent preprint "Algorithms for Numerical Analysis in High Dimensions" (*).
This talk will review some of the basic ideas of separated product-sum
representations, and discuss how our UW Quantum System Engineering (QSE)
Group is applying these ideas in polynomial-time simulations of large-scale
quantum spin systems.
Our QSE Group has found that Beylkin and Mohlenkamp's methods can be
readily extended to dynamical systems by a two-fold trick: (1) introduce
noise, and (2) convert the noise to an equivalent measurement processes.
The second step exploits the same unitary invariance of operator-sum
representations that plays a central role in quantum computing theory. The
resulting quantum trajectories are readily projected onto low-dimensional
manifolds of Beylkin-Mohlenkamp type, where they can be integrated using
polynomial-time numerical algorithms.
The practical consequence is that a broad class of problems in quantum
physics and engineering that were previously thought to be in the
(intractable) complexity class EXP can now be solved by algorithms that are
in the (much simpler) complexity class NP. The lecture will close with an
informal survey of physics problems that might be addressed by these methods.
(*) http://amath.colorado.edu/activities/preprints/archive/519.pdf
Professor Joe Garbini named to Morrison Endowed Chair of
Mechanical Engineering
On October 21,
UW Mechanical Engineering Professor Joe Garbini, who is lead engineer of our Quantum System
Engineering Group, was named to the newly-endowed Morrison Chair in Mechanical Engineering.
This chair is the generous gift of Henry Schatz, who is CEO of General Plastics Manufacturing Company. Mr. Schatz was a student of Mechanical Engineering Professor Jim Morrison, for whom the chair is named.
Joe was awarded the Morrison Chair on the strength of his outstanding record of teaching, service, and research, and also for his equally outstanding personal traits of kindness, humanity, and creativity, which are greatly cherished by us, Joe's colleagues and students. He is everything an engineer should be. Our heartiest and most sincere congratulations go to Joe!
Quantum Microscopy under ARO/MURI: Making "Radar for
Molecules" HappenThis past November 13 saw the kickoff meeting in Seattle of our new ARO/MURI Program for Achieving Single Nuclear Spin Detection.
Informally, we call our ARO/MURI program "Radar for Molecules", because as scientists and engineers, we have reasonable technical grounds to foresee that quantum microscope technology (FAQ here) will exert a global strategic and economic impact similar to radar during 1930–1960, and to semiconductor technology during 1950–2000.
Our ARO/MURI white paper outlines what "radar for molecules" would mean strategically (p. 22):Our NIH white paper outlines what "radar for molecules" would mean for science and medicine (p. 4):Just as radar was envisioned as an urgently-needed means for military and civil defense against aircraft threats, quantum microscopy can be envisioned as an urgently-needed means for military and civil defense against chemical and biological terrorist threats. Also like radar—but to an even greater extent—quantum microscope technology promises to provide new foundations for the national and global economic prosperity upon which modern military strategy relies.
Our expectation is that the next generation of molecular biologists will routinely, quickly, and easily obtain images showing the full three-dimensional structure of the molecules they are studying, in situ, with all their ligands, cross-links, and glycosylation in place. Our hope is that this will substantially accelerate the development of effective treatments for presently intractable disorders.
Thanks largely to experimental breakthroughs at IBM in 2004, and also to the advent in 2005 of new, highly-efficient design tools for quantum system engineering, we have become reasonably confident that our ARO/MURI "Radar for Molecules" program can go all the way to deployment in the next five years.
The rest of this web page describes what is needed to make that happen, emphasizing particularly recent developments that are not covered in the above white papers.
Acknowledgments
We thank Freeman Dyson for crucial encouragement (click here) in the early days of quantum microscopy.
We thank historians Alan Beyerchen, Williamson Murray, and Allan Millet, whose writings (click here) taught our QSE Group the vital role of simple, open explanations.
We thank MIT historian Lily Kay (recently deceased) for the material she provided (click here) relating to work in the 1940s and 1950s of Linus Pauling, John von Neumann, and Richard Feynman in atomic-resolution microscopy.
We thank physicists Michael Neilsen, Isaac Chuang, and Carlton Caves, and also mathematicians Gregory Beylkin and Martin Mohlenkamp, for providing our QSE Group—at precisely the right time—with the new physical ideas (click here) and new mathematical tools (click here) we needed to design quantum devices that work.
We particularly thank IBM's MRFM Group, led by Dan Rugar, for their 2004 breakthrough (click here): the first single-spin detection by magnetic resonance force microscopy. Our QSE Group regards the IBM single-spin experiment as being as significant as Fermi's 1942 demonstration of a nuclear chain reaction.
Finally, we acknowledge IBM CEO Sam Palmisano for valuable insights (click here) on the globalization of science, engineering, and strategic technology development.This material is based on a presentation we gave at UW Condensed Matter Physics Seminar on October 11 (we extend our thanks to the seminar's organizer, David Cobden) and on November 8 at the Frontiers in Imaging Workshop, sponsored by the Institute for Mathematics and Its Applications (IMA). The full presentation (all slides) is available on-line (click here).
Contents and Commentary
We will updating these comments every day between now and November 13, 2005, which is the date of our ARO/MURI Program's kick-off meeting.
We greatly welcome your comments, and we will do our best to respond to them constructively.
The UW Quantum System Engineering (QSE) Group takes its responsibility to help win the Global War on Terrorism (GWOT) very seriously, and our group's specific role under ARO/MURI is described at length in our Army-sponsored MURI White Paper.
Our QSE Group's broader contributions to winning the GWOT—as we conceive this contributions—are described in these slides, and can be summarized as "opening new resource frontiers".
We are equally committed to our NIH-sponsored mission "to uncover new knowledge that will lead to better health for everyone" and our NSF-sponsored mission "to promote the progress of science; to advance the national health, prosperity, and welfare; and to secure the national defense."
Our QSE Group's role in these NIH and NSF missions is described in these slides and in our FAQ, and can be summarized as "creating a Corps of Discovery."
I(a). Why failure is not an option
As engineers, our QSE Group believes that in the next few decades either all three sponsor missions will be achieved swiftly and efficiently, or all three will falter. There's not much middle ground, because these missions are closely coupled.
We therefore regard each of our sponsor missions as being so crucial that in the words of Apollo flight director Gene Kranz, "failure is not an option." Meaning, not that failure is impossible, but rather that all possible measures must be undertaken to prevent it.
We, the scientists and engineers of the QSE Group and the ARO/MURI Program, are developing technologies that will provide some of the key strategic resources that are required for victory in the GWOT. Thus, the slide below is the talk's central focus: all the other slides either lead up to it, or draw conclusions from it.
Click here for further discussion, and to see the slide without the fly-in banner.
As background, our QSE Group's work for the last several years has focussed on quantum microscopy, namely, a new kind of microscope for observing individual atoms, in situ, in three dimensions, non-destructively, with Angstrom-scale resolution (see our FAQ for more details).
The slide below gives an overview of the "biospace" resource frontier that quantum microscopy will open: a frontier sufficiently vast as to exert a transforming effect on the economics and strategy of winning the GWOT, and also to help achieve urgent NIH and NSF missions far more swiftly and efficiently.
II(a). The scientific breakthroughs are in-hand
The scientific breakthroughs needed to achieve quantum microscopy are already in-hand, thanks in large measure to the remarkable single-spin experiments of Dan Rugar's IBM Group.
II(b). The role of quantum system engineering (QSE)
With the advent of the ARO/MURI Program, our QSE Group is now beginning to focus on the next development stage, which includes quantum system simulation/emulation/integration, information-based performance metrics, confidence-building in the broader scientific community, and teamwork among sponsor agencies.As quantum system engineers, our job is to develop and deploy enabling tools for exploring this new biospace frontier, and to create a uniting environment within which individual scientific, engineering, business, and strategic breakthroughs can happen easily.
We are firm believers in a saying of Paul Dirac, that a Golden Age occurs when "ordinary people can make extraordinary contributions." The main strategic role of quantum system engineering, in our view, is to provide radically new tools that will help create such a golden age in the 21st Century.
Click here to see the slide without the fly-in banner.
While waiting for seminar rooms to fill, we show this "preview" slide on the screen. Its main purpose was to give the mathematicians in the audience some abstract ideas to think about.
With a war to help win, and urgent engineering problems to solve, our QSE Group welcomes all the help we can get from pure mathematicians and fundamental physicists.
Even abstract questions—like the question on the slide—sometimes lead to answers that have profound engineering consequences, and therefore important strategic consequences too, and so we don't mind asking such questions.
III(a). Reading list
A basic reading list for this talk is chapters 2, 8, and 9 of Michael Neilsen and Isaac Chuang's excellent and comprehensive textbook Quantum Computation and Quantum Information (widely known to physics students as "Mike and Ike"), plus a preprint by Beylkin and Mohlenkamp (available here).
At a more advanced level, the on-line technical essays by Carlton Caves are well worth reading.
Further discussion
For further discussion (and to see the slide without the fly-in banner) click here.
The slide below pays tribute to Gregory Beylkin and Martin Mohlenkamp's pioneering work, which provides the main starting point for our QSE Group's new P-time algorithms for quantum system simulation.
In a nutshell, our QSE Group has found that Beylkin and Mohlenkamp's methods can be readily extended to dynamical systems by a two-fold trick: (1) introduce noise, and (2) convert the noise to an equivalent measurement processes. The second step exploits the same unitary invariance of operator-sum representations that plays a central role in quantum measurement and computing theory.
The noise-equivalent measurement process compresses quantum trajectories onto low-dimensional manifolds—which we call "gabions"—where the trajectories can be integrated using polynomial-time algorithms of Beylkin-Mohlenkamp type.
The illustration at lower left shows a gabion. The word "gabion" is an engineer-type joke, a gabion being a commonplace object that everyone has seen, but only engineers can name (here's a modern gabion and some older gabions). We will see that the name "gabion" is quite descriptive of the fuzzy definition and porous boundaries of the manifold of noise-compressed trajectories.
Analogous to the satellite, quantum computing technologies fly high above the gabion manifold; they require high-order quantum coherence, and therefore belong to simulation complexity class EXP. Analogous to the helicopter, quantum microscopes fly low over the gabion manifold; they require only low-order quantum coherence, and so belong to the simpler simulation complexity class of P-space and P-time.
IV(a). Formal definitions and conjectured nesting relations
Formally, it is natural to define a gabion as a set consisting of a pair of mathematical objects: an LBM manifold and a synoptic set. Based on strong numerical evidence, our QSE Group conjectures that these two objects can be nested, as described below.
LBM manifolds have an algebraic definition: "An LBM manifold is the set of Hilbert states that can be represented as a sum of product states of Beylkin-Mohlenkamp type, as further constrained by a link matrix". Link matrices are defined on this slide; they are additional linear constraints applied to Beylkin-Mohlenkamp separated representations.
Synoptic sets have an information-theoretic definition: "A synoptic set is the set of Hilbert states sampled by quantum simulation trajectories in the presence of a noise-equivalent measurement process." The word "synoptic" reminds us that noise has been replaced by an equivalent measurement process, such that a hidden observer is acquiring covert information.
Our
numerical work suggests that synoptic sets and LBM manifolds can be
nested, rather like the Russian matryoshka dolls at left. That
is, for a specified noise level in a quantum simulation, then for a
sufficiently large (but still polynomial) rank, an LBM manifold
exists that is large enough to hold (most of) the synoptic set. And
conversely, for a specified LBM manifold that is embedded in a
Hilbert space endowed with a specified (but arbitrary) dynamical
Hamiltonian, then for a sufficiently large noise-equivalent
measurement process, an arbitrarily large fraction of synoptic
trajectories will fit within that LBM manifold.
In practical terms, suppose we have a LBM manifold and a synoptic set, and we wish to nest them; this nested structure we will call a gabion. We can either (1) increase the noise level of the synoptic trajectories (or alternatively, adapt the noise-equivalent quantities being measured) until the synoptic set shrinks to fit within the LBM gabion, or (2) we can increase the rank (or alternatively, adjust the link matrix) of the LBM manifold until it grows large enough (and has the proper shape, as adjusted by the link matrix) to hold the synoptic set.
In either case, the practical engineering consequence is that we can then simulate the quantum system using only P-time and P-space resources (as described in a later slide).
Formal proofs of such "nesting relations" (as our QSE Group calls them) would be a welcome and very necessary addition to the literature on P-time and P-space quantum simulation. These proofs would strongly resemble well-known finite-element proofs, which show that by the use arbitrarily small finite elements, various continuum mechanical processes can be simulated within arbitrarily small error. The construction of such proofs is challenging, and there is a vast and still-growing literature on them, because possibilities like chaotic dynamical behavior must be taken into account.
IV(b). Compatibility with quantum error correction
As an aside, nesting relations do not obstruct progress in quantum computation, for the following reason: the ancilla bits used in quantum error correction represent (effectively) a continuous enlargement of the Hilbert space, such that the above nesting relations—which are conjectured for fixed-dimension Hilbert spaces—do not constrain the design of error-correcting quantum computers.
Click here to see the slide without the fly-in banner.
This slides shows that Beylkin and Mohlenkamp's work can be extended to yield robust dynamical simulation algorithms for "tough" quantum systems: no symmetry, no spatial ordering, high temperature, noisy environments.
Such non-ideal systems are ill-suited to the analysis techniques used by most quantum physicists. Yet they are ubiquitous in quantum system engineering, and so we require new analysis techniques that can handle them robustly and efficiently.
Click here to see the slide without the fly-in banner.
The presentation covered (in considerable detail) how to further extend these robust techniques to analyze systems of hundreds of spins, or even thousands, using only P-space and P-time resources.
Our engineering target is, of course, the intricate spin systems comprised by biological tissues, since the magnetic moments of these spins constitute the imaging signature of our "radar for molecules" technology.
The linked-representation quantum equations of motion are the key to our P-time simulation algorithms. These are the blue equations in the slide below (they are more easily seen with the banner removed).
Click here to see the slide without the fly-in banner.
Next, we reviewed the strategic roles of large-system engineering simulation. The literature on such simulations is growing exponentially, and has become predominantly Chinese. This raises numerous "hot button" issues, such as globalization, chronic trade imbalances, declining engineering enrollments in the western nations, the indeterminate loyalty of multinational corporations, and the shifting balance of strategic power.
A paradox of the large-system simulation literature is that it is remarkably open, and it yet has central strategic significance. So why aren't these capabilities kept secret, as was common practice in the 20th Century?
The force of this paradox is reduced if we recall that completely open strategies can be remarkably subtle: chess for example combines complete strategic openness with great subtlety.
In the globalized 21st Century marketplace, the advantages of open system engineering over closed system engineering are becoming increasingly dominant. Open system engineering projects find it easier to build technical confidence, attract investors, and (eventually) assert market dominance. Also, in market segments that are wide-open and fully competitive, the added costs and slower pace of closed system engineering projects can no longer be tolerated.
In addition, a widespread culture of open system engineering greatly benefits engineering education. For any expanding technical economy, preserving the vigor of engineering education is a strategic necessity.
The citations in the slide below were drawn from a BibTeX database containing 1,978 recent articles appearing in the Chinese Journal of System Simulation (CJSS). The open display of top-level engineering talent in journals like CJSS has been essential in transforming China into an irresistible high-technology business partner for such traditionally American companies as General Electric and IBM.
Bowing to market pressure, these companies recognize that they can no longer be "American"; their primary loyalty must now be to their multinational shareholders and customers. As IBM's CEO Sam Palmisano famously told The New York Times: "IBM wants to be part of China's strategy."
Hence, the new vitality, in the 21st Century, of a famous Chinese business strategy that is mentioned on the slide: "Deceive the sky to cross the ocean." In other words, if your plans will be fulfilled in any case, then you need make no secret of them. This is the strategy we call "Open Strategic Advantage" (OSA).
Click here to see the slide without the fly-in banner.
VIII. Creating an American Strategy for the 21st Century
VIII(a) The urgent need for an American Strategy
Some analysts assert that America has no viable strategic response to globalization. E.g., Clyde Prestowitz:
If you ask an American CEO if he or she wants to be part of America's strategy, none of them can answer the question. Because America doesn't have a strategy.
Other analysts assert that no strategy is necessary. E.g., the Economist for October 1, 2005:
For years to come, China will be more likely to assemble the best computers than to design them.
As engineers, we strongly disagree with the Economist's negative opinion of China's innovative capability. We have the highest respect for the talents of our Chinese engineering colleagues, and in our view, it is only a matter of time (a very short time) before even flagship American companies like Intel and Boeing face direct competition from China at the highest technological levels.
IBM CEO Sam Palmisano outlined what we consider to be a viable American technological strategy in a resent speech (summary here, complete text here) delivered at Rensselaer Polytechnic Institute:In the 21st century, innovation is not a nice-to-have. In an era when commoditization happens at unprecedented speed, innovation has become an economic and societal imperative. ...Our first task must be to embrace a new model of innovation—one that is open, collaborative, multidisciplinary and global.
Second: for collaborative innovation to flourish, we must rethink our ideas about intellectual property.
Finally: we must focus on developing the next generation of innovation leaders.
Our QSE Group broadly agrees with the strategy that Palmisano advocates.
In Palmisano's brief speech (only 4200 words), the words "innovation" and "innovative" appear more than sixty times, in strongly-worded passages like these:
Let's take a step back and consider the global transformation that is now underway, and the urgency this transformation brings to our national innovation agenda. ...Will America keep up with the pace of innovation being now set in places like Korea, Finland, India and China, or will we fall behind? Will we restore the innovation prowess that drove our success in the 20th century? Make no mistake: this isn't a space race. This is not about America against the world. But it is very much about America maintaining its strength and competitiveness in an increasingly integrated world economy. ...
Our future inn