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The seminars are on Wednesday, 11:30am-12:20pm, in the Harvey R. Bright building, room 302.

If you have questions, please contact Andreas Klappenecker.

Guy Battle Wednesday, November 17, 11:30am-12:20pm, HRBB 302

Quantum Computing Seminar Novel Approach to Sub-Wavelength Lithography M. Suhail Zubairy Institute of Quantum Studies and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242 Wednesday, November 10, 11:30am-12:20pm, HRBB 302 It is well known that the classical schemes for microscopy and lithography are restricted by the diffraction limit. The precision with which a pattern could be etched in interference lithography is limited by the wavelength of the light. In recent years, a number of schemes have been proposed via quantum interferometry to improve the resolution. Some of these schemes are based on quantum entanglement and multiphoton processes. In this talk I shall discuss a novel scheme for ’quantum’ lithography using classical light.

There is no seminar on Nov 3

Quantum Computing Seminar Progress toward NV diamond quantum repeaters Philip Hemmer, Department of Electrical and Computer Engineering, Texas A&M University Wednesday, October 27, 11:30am-12:20pm, HRBB 302 NV diamond has attracted much interest as a potential room temperature quantum computer. However the first application of quantum computing will likely be to quantum repeaters for long range secure teleportation. At cryogenic temperatures the NV can be used to make a quantum repeater. The status of experiments along these lines will be reviewed.

Quantum Computing Seminar Localizing Topological Quantum Computers Eric Rowell, Department of Mathematics, TAMU Wendesday, Oct 20, 11:30am-12:20pm, HRBB 302 In this talk I will start by describing the way in which the quantum circuit model and the topological model are equivalent. While both models have advantages over the other one might hope for a model that has all of the advantages of both: locality, universality and fault-tolerance. I will discuss recent work with Zhenghan Wang investigating this possibility.

Quantum Computing Seminar Topological Quantum Computations Eric Rowell, Department of Mathematics, Texas A&M University Wednesday, Oct 13, 2010, 11:30am-12:20pm, HRBB 302 I will survey the Freedman-Kitaev model for quantum computation based on (theoretical) exotic states of matter. I will emphasize the algebraic perspective, focusing on the role of the braid group in universality questions. This will set up a subsequent talk on joint work with Zhenghan Wang (Microsoft Research).

Quantum Computing Seminar Thermal noise engines (I) Laszlo Kish, ECE Department, Texas A&M University Wednesday, Oct 6, 11:30am-12:20pm, HRBB 302 Electrical heat engines driven by the Johnson-Nyquist noise of resistors are introduced. They utilize Coulomb's law and the fluctuation-dissipation theorem of statistical physics that is the reverse phenomenon of heat dissipation in a resistor. No steams, gases, liquids, photons, fuel, combustion, phase transition, or exhaust/pollution are present here. In these engines, instead of heat reservoirs, cylinders, pistons and valves, resistors, capacitors and switches are the building elements. For the best performance, a large number of parallel engines must be integrated and the characteristic size of the elementary engine must be at the 10 nanometers scale. At room temperature, in the most idealistic case, a two-dimensional ensemble of engines of 25 nanometers characteristic size integrated on a 2.5x2.5 cm silicon wafer with 12 Celsius temperature difference between the warm-source and the cold-sink would produce a specific power of about 0.8 Watt. Regular and coherent (correlated-cylinder states) versions are shown and both of them can work in either four-stroke or two-stroke modes. The coherent engines have properties that correspond to coherent quantum heat engines without the presence of quantum coherence. In the idealistic case, all these engines have Carnot efficiency, which is the highest possible efficiency of any heat engine, without violating the second law of thermodynamics.

Quantum Computing Seminar Nearring Perfection Andreas Klappenecker Wednesday, September 22, 11:30am-12:20pm, HRBB 302 We investigate a generalization of the Pauli matrices that consist of shift operators and phase operators which form a basis of the vector space of complex n x n matrices. The operators are parameterized by a nearring, an algebraic structure that has an addition and multiplication operation, is a group with respect to addition, a semigroup with respect to multiplication, and has the left distributive law (but not necessarily the right distributive law). We will call a nearring nice if it supports the construction of a basis of the complex n x n matrices consisting of shift and phase operators. We classify all distributively generated nice nearrings. Furthermore, we show that all nearfields are nice. Nice nearrings and their associated bases are a new class of fundamental primitives that find applications in quantum algorithms and quantum error-correcting codes.

On a Generalization of Clifford Codes Andreas Klappenecker Tuesday, Apr 13, 2:20-3:20pm, HRBB 302 In 2005, Ed Loeb suggested to generalize the concept of Clifford codes and asked my opinion about it. He suggested to use *arbitrary* subgroups of the abstract error group for the code construction instead of *normal* subgroups. Although this generalization appears to be very natural, it is technically very difficult. Isaacs writes in his famous book on character theory of finite groups that “very little can be said about the restriction [of an irreducible character to a subgroup H]. The situations is quite different if H is normal.” For this reason, I suggested to Ed Loeb that he might direct his attention to more tractable problems such as the construction of Clifford codes. Even now I am unaware of any progress in the representation theory of finite groups that would allow one to understand the restriction of irreducible representations of abstract error groups to arbitrary subgroups. In this talk, I will show that Loeb’s suggested generalization does not lead to any new quantum codes if the abstract error group has an abelian index group.

Quantum-Type Reversible Circuits and Algorithms Walter C. Daugherity, Department of CSE, Texas A&M University Tuesday, April 6, 2:20-3:20pm, HRBB 302 Quantum circuits (and their corresponding algorithms) are intrinsically reversible, since the quantum gates from which they are composed (except for measurement operations) are reversible. This makes it straightforward to construct the inverse of a quantum circuit from the inverses of the original quantum gates. In contrast, classical combinational Boolean logic circuits (composed of AND gates, OR gates, etc.) are not in general reversible. Consequently, designing the inverse of a non-trivial circuit is essentially a new problem requiring significant time and effort. There are important practical problems where the inverse circuit is harder to design than the original; for example, multiplication versus factorization, or modular exponentiation versus discrete logarithms. The fact that factorization and discrete logarithms are harder than multiplication and modular exponentiation forms the basis for the security of the RSA and Diffie-Hellman cryptosystems, respectively. Thus an efficient technique for obtaining the inverse of a circuit is useful. We first discuss the requirements for invertibility of a function, and how these requirements can be met; next we discuss how invertible Boolean logic gates can be implemented with the Boolean logic implementation of a generalized Toffoli gate. As an example, we apply this process to construct a Boolean logic circuit for the difficult problem of factorization and demonstrate that the circuit performs as intended, using a graphical quantum circuit editor implemented by my student Steven Sensarn. We have thus provided a practical solution to two problems: (1) the problem of designing and constructing logic circuits for two functions, both an invertible function and its inverse, with only the amount of effort required to design and construct a logic circuit for one of the two, and (2) the problem of more efficiently designing and constructing a logic circuit for a function which is harder to design and construct than its inverse.

Fault-Tolerant Quantum Computing Andreas Klappenecker Tuesday, Mar 30, 2:20-3:20pm, HRBB 302 A quantum computer is susceptible to noise. This talk gives a short introduction to the key ideas of fault-tolerant quantum computing, where all computations are performed on quantum bits that are protected by quantum error-correcting codes.

Quantum Computing Seminar Second Generation Clifford Subsystem Codes Andreas Klappenecker Tuesday, March 23, 2010, 2:20-3:20pm, HRBB 302 Subsystem codes were recently introduced to allow the protect quantum information by both active (but potentially error-prone) and passive (error-free) mechanisms. So far, the construction of such codes was limited to prime power dimensions. Furthermore, one was not able to mix e.g. spin-1/2 and spin-1 systems. The second generation Clifford subsystem codes overcomes these limitations. We will discuss how representation theory of finite groups can be used to construct such codes. The key ingredient for our new construction is a geometric approach to nilpotent groups of class 2.

Spring Break

Quantum Computing Seminar Brownian Circuits and Brownian Cellular Automata: Exploiting Noise in Computation Dr. Ferdinand Peper, University of Hyogo, Himeji, Japan and NICT Tuesday, March 9, 2:20-3:20pm, HRBB 302 Noise and fluctuations are usually considered obstacles in the operation of electronic and mechanical devices, and most strategies to deal with them revolve around suppression, but at higher integration densities this may no longer work due to the lower signal levels used. We will explore an alternative strategie in which fluctuations are used as a factor to drive computation. We discuss a token-based circuit that becomes universal only under the condition that the tokens can undergo fluctuations. We show simulations of a fluctuation-driven circuit implemented on a Cellular Automaton. Bio: Ferdinand Peper 1989: Ph.D. Delft University of Technology (The Netherlands), Computer Science 1990-1993: PostDoc at National Institute of Information and Communications Technology (NICT), and working at software company, Japan 1993-now: Senior Researcher at NICT, Japan 1997-1998: Visiting PostDoc at UCSF, Keck Center of Integrated Neuroscience 1999-now: Visiting Professor at the University of Hyogo in Himeji, Japan Currently at NICT: member of Nano ICT group

CSCE 681 Seminar Clifford Subsystem Codes Andreas Klappenecker 4:10 p.m., Wednesday, March 3, 2010 Room 124, Bright Building Quantum computing is one of the most exciting developments in computer science. It is conjectured that quantum computers will be able to solve certain problems faster than any classical computer. It is quite encouraging that some small scale quantum computers exist, but further progress is needed to enable fully-scalable fault-tolerant quantum computing. In fault-tolerant quantum computing, the quantum information is encoded with the help of a quantum error-correcting code. All operations are performed on the encoded quantum bits. Even though the error-correction itself is faulty, one can achieve reliable computation with a modest overhead as long as the error rate of the quantum operations is below a threshold. The speaker has developed with others the theory of subsystem codes. They have the advantage that they underlie fewer constraints than other codes that have been used so far in fault-tolerant quantum computation. Subsystem codes can offer encoding algorithms that allow for noisy auxiliary quantum bits, can offer better decoding algorithms and sometimes allow one to realize fault-tolerant operations more efficiently than with other methods. The talk will outline the evolution of Clifford subsystem codes, from inception and arrested development to the most versatile class of quantum codes in existence today. The talk will outline how quantum systems of mixed dimensions can be protected by Clifford subsystem codes.

Quantum Computing Seminar Searching on a Quantum Computer Andreas Klappenecker Tuesday, Feb 23, 2:20pm-3:20pm, HRBB 302. I give an exposition of Grover's search algorithm and its application to speed-up certain NP-hard problems.

Quantum Computing Seminar Noise-based Logic: Introduction and Applications Tuesday, Feb 16, 2:20p-3:20pm, HRBB 302 Speakers: Laszlo Kish and Sunil Khatri In the second seminar (February 16), it will be shown how the noise based hyperspace can be used to represent entangled? vectors similar to quantum information. A string search engine, which is faster than Grover's quantum search algorithm, will be shown with the same hardware complexity as the quantum algorithm. Finally, we will show the generalization of noise-based logic and its hyperspace for spike noise to provide a model for brain logic. There are striking similarities with quantum informatics however the noise-based brain scheme is more efficient because of its deterministic logic nature.

Quantum Computing Seminar Noise-based logic: applications for quantum-mimic and brain logic, Tuesday, Feb 09, 2:20-3:20pm, HRBB 302 Speakers: Laszlo Kish and Sunil Khatri When noise dominates an information system, like in nano-electronic systems of the foreseeable future, a natural question occurs: can we perhaps utilize the noise as an information carrier? Another question is: can a deterministic logic scheme be constructed that may explain how the brain can efficiently process information, with random neural spike trains of less than 100 Hz frequency, and with similar number of neurons than the number of transistors in a 16 GB Flash dive? The answers to these questions are yes. In the first seminar (February 9), continuum-noise based logic will be introduced. The aspects of speed and energy dissipation will be discussed. Universal gates will be shown. We also introduce the notion of a noise-based hyperspace and show a simple and efficient application for the combinational verification problem.

Quantum Computing Seminar Title: Implementing Digital Logic with Sinusoidal Supplies Speaker: Sunil P. Khatri Time: Tuesday, Feb 2, 2:20-3:20pm Venue: HRBB 302 A new type of combinational logic circuit realization is presented. Logic values are implemented as sinusoidal signals. Sinusoidal signals of the same frequency are phase shifted by 180 degrees to destructively interfere with each other, and represent the logic 0 and 1 values of Boolean Logic. We demonstrate the SPICE level realization of one and two input gates using this approach. Due to orthogonality of sinusoid signals with different frequencies, multiple sinusoids could be transmitted on a single wire. This provides a natural way of implementing multilevel logic. Signals traveling long distances could take advantage of this fact and can share interconnect lines. Another possible generalization of this work is to implement logic values using noise sources, which will be the topic of future seminars in this series. This is joint work with Kalyana Bollapalli and Laszlo Kish. Speakar: Sunil P Khatri is an Assistant Professor in the ECE Department of Texas AM University, with research interests in VLSI design and CAD.

Quantum Computing Seminar Title: Simple Quantum Circuits Speaker: Andreas Klappenecker Venue: HRBB 302 Time: Tuesday, Jan 26, 2:20-3:20pm The modest goal of this talk is to explain and illustrate some simple examples of the quantum circuit model. The talk is intended for those who wish to learn about quantum computing.

Quantum Computing Seminar Dr. Martin Roetteler NEC Laboratories America Princeton, NJ Thursday January 21, 2010, 2:20pm-3:20pm, HRBB 302 "Quantum algorithms for highly non-linear Boolean functions" We provide new examples for exponential separations between quantum and classical query complexity by considering hidden shift problems over families of highly non-linear Boolean functions. These so-called bent functions arise in cryptography, where their property of having perfectly flat Fourier spectra on the Boolean hypercube gives them resilience against certain types of attack. We present quantum algorithms that solve the hidden shift problems for several well-known classes of bent functions in polynomial time and with a polynomial number of queries, while the classical query complexity is shown to be exponential. Our approach uses a technique that exploits the duality between bent functions and their Fourier transforms. See also http://arxiv.org/abs/0811.3208 Martin Roetteler received the Ph.D. degree in computer science from the University of Karlsruhe, Germany, in 2001. Subsequently, he held a post-doc position at the Institute for Quantum Computing at the University of Waterloo. Currently, he is the leader of the Quantum IT group at NEC Laboratories America, located in Princeton, NJ. He has published more than 60 refereed journal and conference papers on quantum computing and is co-author of one book on quantum information. Martin Roetteler's research focuses on quantum algorithms and quantum error-correcting codes.

Quantum Computing Seminar Title: An Introduction to the Quantum Circuit Model Speaker: Andreas Klappenecker Venue: HRBB 516 Time: Dec 9, 10:30am-noon There exist some surprisingly good quantum algorithms that have a superpolynomial speed-up over their (known) classical counterparts. This includes for example number theoretic algorithms to factor integers, estimate Gaussian sums, find generators of the unit group of a number field, and more. The modest goal of this talk is to explain the basics of the quantum circuit model, suitable for those who wish to learn about this exciting new field of computer science.

- Previous Seminars (from 2001-now)

The Quantum Computing Seminar is supported by the National Science
Foundation.

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