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• I2Lab Seminars
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. Thu 02/21 (QIS Seminar)

Peter Hoyer (University of Calgary, Canada)

TBA

. Thu 11/29, 11:30 am in MAP 318 (Mathematics Colloquium Series)

David W. Kribs (University of Guelph, Canada)
Complementarity in Quantum Error Correction and Quantum Cryptography

Quantum channels are described mathematically by completely positive maps. Error-correcting codes for quantum channels are the key vehicles used to avoid noise such as decoherence induced by physical attempts to build quantum computers. On the other hand, Private codes fo quantum channels play a central role in the development of private quantum communication networks designed to prevent adversarial attacks by eavesdroppers. It turns out that a code is private for a channel precisely when it is correctable for a complementary channel, and there is a straightforward algebraic recipe that allows to move between the two perspectives. Moreover, an approximate version of the relationship can be quantified in terms of diamond (or completely bounded) norms for channels.

. Mon 11/26, 4:30 pm in MAP 318 (CMP seminar)

Lov Grover (Alcatel-Lucent/Bell labs)
Fixed Point Quantum Searching

Quantum Searching was invented in order to carry out database searching efficiently using the intrinsic parallelism of quantum mechanics. Here it gave a square-root advantage over the best classical algorithms. It has since been applied to a number of other problems in very different contexts. One of its recent applications has been in the area of error correction, which is the dominant problem in quantum computation.

. Tue 04/17, 11:00 am in Harris Center 125(QIS seminar)

Dominik Janzing (University of Central Florida)
Exploring the power of quantum computation by constructing new BQP-complete problems

The complexity class BQP is the class of problems that can be solved in polynomial time on a quantum computer. In order to understand the power of quantum computing it is therefore helpful to identify BQP-complete problems, i.e., the hardest problems in BQP. It is easy to formulate BQP-complete problems which are directly related to the simulation of the dynamics of complex quantum systems. However, in order to understand the power of quantum computing, one should try to find natural ``non-quantum problems''.

We have identified a simple BQP-complete problem in linear algebra related to the estimation of diagonal entries of powers of large sparse matrices. It follows that the quantum computer is better at linear algebra than the classical computer unless the class of efficiently solvable problems coincide for both types of computers (i.e. BQP=BPP).

Moreover, we have constructed a BQP-complete combinatorial problem concerning the number of walks on a sparse graph leading from one node to another. Our result shows that the quantum computer is also more powerful in analyzing classical random walks unless BQP=BPP.

These results suggest that a broad class of problems could be solved more efficiently on a quantum computer. Given the delicate nature of quantum states, a quantum computer.

. Mon 03/19, 3:30 pm in MAP 318 (QIS seminar)

Nick Bonesteel (Floridate State University)
Quantum Computing with Braids

Given the delicate nature of quantum states, a quantum computer will require some method to protect these states from the outside world while at the same time allowing for their coherent manipulation. A particularly elegant proposal for doing this is called "topological quantum computation" (TQC). In TQC quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum computation is carried out by dragging particle-like excitations quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding computation depends only on the topology of the braids formed by these world-lines. In this talk I will review the basic ideas behind TQC, and describe recent work showing how to find braids which can be used to perform arbitrary quantum computations using quasiparticles which are thought to exist in a recently observed fractional quantum Hall state.

. Mon 05/04 in I2 Lab(QIS seminar)

Lov K. Grover (Bell Lab)
Quantum Searching - Old & New

Computers as we know them, are classical. Recently it was realized that using computers based on quantum mechanics would allow unprecedented improvements in efficiency by allowing entirely new algorithms to be executed. The quantum search algorithm is just one of two such algorithms that has been discovered. In its simplest form it allows an unstructured database of size N to be searched in only square-root(N) steps (any classical algorithm would clearly need N steps). It has been applied to a number of problems ranging from cryptography to precision measurement. It continues to find application in new areas, the most recent of which is laser resonator design.

. Mon 11/21, 4pm in HC 365 (QIS seminar)

Dan Marinescu (University of Central Florida)
Quantum Error Correction of Time-Correlated Errors

We make a distinction between time-correlated quantum errors which re-occur with a certain probability and new errors, uncorrelated with past errors. The obvious choice to deal with time-correlated errors, is to design a quantum error correcting code capable to correct errors.