Computer Algebra in Quantum Information and Computation

Yasuhito Kawano
NTT Communication Science Laboratories, NTT Corporation


Kiyoshi Shirayanagi
NTT Communication Science Laboratories, NTT Corporation

Aim and Scope
Quantum information and quantum computation come under the spotlight recently. They have been studied for a long time, and developed explosively in this decade. This is because many technological applications, which were predicted theoretically based on quantum mechanics, can be realized by recent developments of techniques of physical experiments. Theory of quantum information and computation relates to wide areas, such as physics, chemistry, information science, and mathematics. Researchers from various major fields are participating in researching the field of quantum information and computation.

Algebraic theory has also a deep relation to quantum information and computation. For example, quantum error-correcting codes are studied algebraically. This session aims at the exchange of recent research about algebraic aspects of quantum information and quantum computation. In particular, the following fields are considered:
  • Algebraic analysis of quantum algorithms
  • Quantum algorithms for algebraic problems
  • Algebraic treatments for quantum error-correcting codes
  • Algebraic approach to decomposing unitary matrices
  • Quantum simulation
  • Quantum approach to making existing algebraic algorithms efficient

List of talks
  1. An algorithm for decomposing unitary matrices using Cartan decomposition
    by Yumi Nakajima, Yasuhito Kawano, and Hiroshi Sekigawa
    (NTT Communication Science Laboratories, JAPAN)

  2. Computer Algebra-Aided Tool for Simulation of Quantum Circuits
    by Vladimir P.Gerdt and Vasily Severyanov
    (Laboratory of Information Technologies Joint Institute for Nuclear Research, Russia)

  3. On generalized quantum turing machine and its application
    by Satoshi Iriyama and Masanori Ohya (Tokyo University of Science, Japan)

  4. Semidefinite Programming for the Equivalence of Finite Automata and Quantum Circuits
    by David Avis(McGill Univ., Canada), Takeshi Koshiba(Saitama Univ., Japan),
    Kazuo Iwama and Rudy Raymond(Kyoto Univ./ERATO Quantum Computation and
    Information Project, Japan)

  5. Comparison between quantum Turing machines with advice and circuits
    by Harumichi Nishimura
    (ERATO Quantum Computation and Information Project, Japan)