Alexei Ashikhmin, Bell Labs

Abstract

In recent years quantum computers moved much closer to reality.  There are a number of companies that are making rapid progress toward building a large-scale quantum computer. In particular,  IBM T. J. Watson Research Center in Yorktown, NY, made quantum computing available via the cloud to anyone interested in access to an IBM 20-qubit quantum processor. Thus, anyone can run quantum algorithms and experiments that involve up to 20 physically instantiated qubits. The quantum technology used is scalable and, therefore, it is expected that a larger quantum computer will be built within several years. It is important to remember that a quantum computer of only 50 logical qubits would be able to solve certain tasks that are not feasible for any of today’s supercomputers.

One of the main difficulties in building a real-life quantum computer is that any real physical system cannot be completely isolated from its environment. This causes unavoidable environmental and control error in quantum circuits and quantum memory. An efficient way of fighting this problem is using methods of Quantum Information Theory for quantum error correction and quantum storage.  Quantum Information Theory is significantly more diverse and complex than its classical counterpart. It is enough to say that the capacities of some basic quantum channels, like the quantum counterpart of the classical binary symmetric channel, are still not known. Even less is known about the performance of finite length quantum codes.

In this talk I will present my recent results on the converse and achievability bounds for finite length codes in the quantum erasure channel. The obtained bounds significantly improve on the previously known bounds, and in some scenarios  are very tight. I will also share some  counter intuitive and surprising effects of quantum mechanics, for example, Elitzur–Vaidman quantum bomb tester and information transmission with data rates exceeding the classical channel capacity.

Special Note: The Theory of Computing Seminar is being held online. Contact the organizers for the link to the seminar. 

See: https://theory.cs.rutgers.edu/theory_seminar