Part II Literature Reviews 2019/20 |
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Abstract: A significant obstacle to the construction of a
quantum computer is
the need to avoid "decoherence" of the quantum degrees of freedom (the
"qubits") by random, unwanted, couplings to the environment. It has
been proposed that decoherence can be avoided by using special quantum
systems which have so-called "topological" degrees of freedom; these
are associated with global properties of the quantum system and are
expected to be immune to most random couplings to the environment.
The review will discuss the theoretical ideas behind topological
quantum computing, as well as the physical quantum systems which are
believed to have appropriate "topological" degrees of freedom.
Starting
points:
Reviews and papers by John Preskill.
Review
talk by Steven Simon.
Anyons and non-Abelions
Abstract: Theory permits the quantum mechanical exchange
statistics of identical
particles that are constrained to move only in 2 spatial dimensions to
differ from the usual cases of "Bose" and "Fermi" statistics. Instead
of behaving as simple bosons or fermions, particles in 2 dimensions
can behave as "anyons" or "non-abelions". The review will address the
physical situations that are believed to lead to
anyon and non-abelian
exchange statistics, and the prospects for their experimental
observation.
Starting
points:
The original paper on anyons:
J M
Leinaas and J Myrheim Nuovo Cimento B 37 1 (1977)
Quantum mechanics and
field theory with fractional spin and statistics, S. Forte, Rev Mod Phys,
64, 193 (1992).
Quantum Mechanics of Fractional-Spin Particles, F. Wilczek PRL 49, 957 (1982).
The
Quantum Hall Effect, Prange & Girvin (1987).
Review
talk by Steven Simon. (Non-abelions.)
Quantum Computers in the Solid State
Abstract: The construction of a "quantum computer" would require the ability to adjust the wavefunction of a large number of objects ("qubits") in a controlled fashion. There have been many proposals for how this might be achieved in practice. One limiting factor is the time that the wavefunction can survive before being affected by an uncontrolled interaction ("dephased"). The review will determine what are the measured (or expected) dephasing times in systems based on solid-state devices.
Starting
points:
Centre for Quantum Computation
Centre
for Quantum Computer Technology
Semiconductor devices (spin): Kane
quantum computer
Superconducting devices: Nature 421, 823 - 826 (2003)
Experimental evidence for Luttinger Liquids