COMPARTMENTAL MODELING AND SECOND-MOMENT ANALYSIS OF STATE SPACE SYSTEMS

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57799/1/CompartmentalSIMAX1993.pd

The Power of Quantum Fourier Sampling

A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer, unless the PH collapses. Aaronson and Arkhipov take this further by considering a distribution that can be sampled efficiently by linear optical quantum computation, that under two feasible conjectures, cannot even be approximately sampled classically within bounded total variation distance, unless the PH collapses. In this work we use Quantum Fourier Sampling to construct a class of distributions that can be sampled by a quantum computer. We then argue that these distributions cannot be approximately sampled classically, unless the PH collapses, under variants of the Aaronson and Arkhipov conjectures. In particular, we show a general class of quantumly sampleable distributions each of which is based on an "Efficiently Specifiable" polynomial, for which a classical approximate sampler implies an average-case approximation. This class of polynomials contains the Permanent but also includes, for example, the Hamiltonian Cycle polynomial, and many other familiar #P-hard polynomials. Although our construction, unlike that proposed by Aaronson and Arkhipov, likely requires a universal quantum computer, we are able to use this additional power to weaken the conjectures needed to prove approximate sampling hardness results

Optimal Output Feedback for Nonzero Set Point Regulation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57836/1/NonzeroSetpointTAC1987.pd

Some open problems in matrix theory arising in linear systems and control

Control theory has long provided a rich source of motivation for developments in matrix theory. Accordingly, we discuss some open problems in matrix theory arising from theoretical and practical issues in linear systems theory and feedback control. The problems discussed include robust stability, matrix exponentials, induced norms, stabilizability and pole assignability, and nonstandard matrix equations. A substantial number of references are included to acquaint matrix theorists with problems and trends in this application area.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30236/1/0000630.pd