The QSE Roadmap and Journal is undergoing a major upgrade this week (Dec. 18-25) to a new graphical interface. Some of the Roadmap entries may be temporarily truncated: they will return after they have been converted. Happy Holidays to all!

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To 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).

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Entry #5: Wednesday, November 29, 2006

Welcome to the UW QSE Group's Roadmap and Journal. Each entry first comments upon our (working) QSE Roadmap, and then describes our recent activities.

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QSE Roadmap Comments

Linus Pauling's 1946 Roadmap for Biomedical Research

The slide below includes the introductory page of Linus Pauling's federative 1946 proposal The Possibilities for Progress in the Fields of Biology and Biological Chemistry (the complete text of Pauling's proposal was made available to us by MIT historian Lily Kay; download here).

High-resolution PDF versions: (top level), (lower level), (entire roadmap)

Although Pauling's proposal is little-known to practicing biologists, it was the first system biology roadmap; it is remains a valid roadmap today; and it is reasonable to regard it as one of the seminal documents of federative science. For further details, consult our QSE Group's web page Atomic-Resolution Microscopy: Roadmaps from the 1940s and 1950's.

The influence of Linus Pauling's 1946 Roadmap on the QSE Roadmap

Much of Pauling's roadmap for system biology remains directly applicable to our QSE Roadmap. In particular, Pauling conceived system biology as a federative effort, involving scientists and engineers of many disciplines, conducted in large measure as a survey discipline, and driven in large measure by advances in instrument capabilities.

These federative ideas and principles directly inspired the overall strategy of the QSE Roadmap (and for similar reasons the figures in the QSE Journal's banner, including Pauling, were selected for their federative achievements in science and technology, broadly conceived).

The federative challenge of modern science and technology

The most challenging part of a science and technology development effort is achieving federation. The technology subsystems must work together, the people developing these subsystems must work together, and not least, the agencies—both public and private—that sponsor the development effort must work together.

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Journal entry for Wednesday, November 29, 2006

Spin-Dust Models for QMOR Testing and Validation

Traditional methods for quantum simulation rely upon physical assumptions to restrict the quantum trajectories; these assumptions typically include low temperature, rotational symmetry, or a regular lattice of interactions.

Unfortunately, none of these usual assumptions apply in quantum spin microscopy, because the spin temperature is typically high, and generic biological molecules have no rotationally symmetry or lattice-like regularities.

We therefore validate our quantum model order reduction (QMOR) algorithms in spin-dust models. Given a completely unordered set of n spins, a spin-dust model is created by linking each spin to four randomly chosen neighbors, using a dipole interaction model with a separation vector that is chosen randomly and independently for each pairwise dipole interaction.

Each spin is also coupled to an external magnetic field whose direction is similarly chosen randomly and independently for each spin. The coupling strengths are adjusted such that the mean square energy per spin is unity.

By design, the resulting spin-dust system has no physical symmetries whatsoever (similar to biological spin systems).

The next two steps are key to the feasibility of large-scale QMOR emulations:

1. Markovian magnetic noise is introduced, acting independently on each spin, such that the spin decorrelation time is T1=10 (with the per spin energy being unity).
2. We then convert this noise to an equivalent covert measurement process that takes a time ~T1=10 to acquire information about each spin's local direction.

As is well known, measurement processes destroy high-order quantum correlations, and in the context of QMOR, it is this suppression of these correlations that ensures the accuracy of the above QMOR representaton of ψ(t).

Evidence for "one-spin, one processor" algorithmic complexity

The figure below compares the exact wave-function trajectory ψ(t) (x-axis) to the QMOR representation of that trajectory (y-axis). Several standard measures of quantum fidelity are plotted, and good agreement between ψ(t) and its QMOR representation is indicated by straight-line scatter plots.

This figure answers the question, how many c-number parameters are needed for reasonably accurate QMOR representation? Broadly speaking, the answer is "At least five QMOR parameters per spin are needed, twenty parameters are better, and fifty values suffice for high-accuracy QMOR representation."

We hypothesisize that this result—fifty parameters per spin yielding good QMOR fidelity—will scale to much larger simulation. Much of our work for the coming year will we devoted to testing this hypothesis, both in spin-dust models, but even more important, in real-world spin models that are directly relevant to practical quantum spin microscopy.

QMOR's present limitations

It should be clearly understood that our present QMOR algorithms have two major limitations:

1. The quenching of high-order quantum correlations by noise makes QMOR unsuited to the simulation of quantum computers.
2. QMOR is numerically feasible if and only if compact matrix representations of the dynamical Hamiltonian can be found.

These two limitations do not substantially impact the ability of our QMOR algorithms to emulate the quantum spin microscopy of biological molecules, in which noise is naturally present due to distant spins, and in which dipole spin interactions have a natural compact representation.

QMOR's emerging capabilities

QMOR's emerging capacity to support the emulation of large, mildly noisy quantum systems makes it applicable not only to quantum spin microscopy by MRFM (the present main focus of our UW QSE Group's efforts), but also to other important new technologies, like spintronic solid-state devices and high-power interferometric gravity-wave observatories.

QMOR's future challenges

The main present limitation of QMOR is that it can be quite challenging to construct sparse Hamiltonian representations for the general case of strongly correlated quantum systems (e.g., superconductors, hadronic physics, lattice gauge theory, and ab initio quantum chemistry).

QMOR's federative opportunities

We anticipate that in coming years, our QSE Group's algebraic/geometric QMOR methods—which we regard as fundamentally grounded in the quantum theory of noise and information—will increasingly merge with related methods that are being applied in condensed matter physics. These methods include most notably the matrix product state (MPS) representations that are finding increasingly wide application in quantum chemistry and in dynamic density matrix renormalization group (DDMRG) calculations.

There is an enormous amount of work to be done in this area—both fundamental and applied—and the longest single part of our QSE Roadmap is devoted to these topics (see journal entries 17–31).

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