Supported by extensive experimental efforts for realization of quantum computing devices, quantum computers of a hundred qubits are now within reach in the near future. This level of a quantum computer is not enough for fully fledged fault-tolerant quantum computing, but is still expected to have computational advantage against classical computers.
Such a noisy intermediate scale quantum computing (NISQ) device is thought to be a testbed for proof-of-principle experiments of quantum algorithms and verification of quantum physics in the limit of extremely high complexity.
In this talk, I will provide a general introduction to quantum computing starting from how and for what quantum computers work. Then I will provide an overview of the current status and prospects of the field of quantum computing. As the final part, I will also talk about our own activities on quantum-classical hybrid algorithm, which is a kind of quantum algorithms specifically designed for the NISQ devices.

Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half.

Although the term "gauge theory" is usually used in physical contexts, in the early 1980's, mathematicians found that gauge theory has many striking applications to purely mathematical problems. Most of typical applications are related to topology of 4-dimensional spaces. As a recent development in this direction, I used gauge theory to study "the shape of the space of all symmetris of a 4-dimensional space".

In the first one hour, I will explain a notion of mathematical spaces, called manifolds, and try to describe the idea: how mathematicians make use of gauge theory to study the topology of a 4-dimensional manifold.

In the second one hour, I will explain what the space of symmetries of a manifold means, and which type of theorems about the space of symmetries can be obtained using gauge theory.

Needless to say, conformal field theory is elemental in the study of string theory, statistical quantum systems, and various quantum field theories.
Two-dimensional conformal field theory is usually quantized by the so-called radial quantization. However, this is not the only way. As a matter of fact, there are two other distinctive choices for the time foliation, or equivalently, the Hamiltonian. One of these choices yields the continuous Virasoro algebra, while the other choice leads to the Virasoro algebra on a torus. The former case corresponds to the recently found (and perhaps less known) phenomenon, sine-square deformation. The latter yields the well-known entanglement entropy. I will present a comprehensive treatment of these three quantizations and discuss its physical implications.

GRIPS (Graduate-level Research in Industrial Projects for Students)-Sendai program was held last summer (June 18 - Aug. 10, 2018) with the support of iTHEMS as well as other institutions and companies. Two industrial projects were launched under the suggestion of TOYOTA and NEC, and two teams composed of US and Japanese students have worked intensively to find solutions of these problems. See for the details of the GRIPS program and the summary of activities at GRIPS-Sendai 2018.

This year, GRIPS-Sendai program will be held from June 17 through Aug. 9, 2019 with a larger scale under the support of iTHEMS. Stay tuned for further information.