SciPost Phys. Core 4, 014 (2021) ·
published 28 May 2021
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We construct local generalizations of 3-state Potts models with exotic
critical points. We analytically show that these are described by non-diagonal
modular invariant partition functions of products of $Z_3$ parafermion or
$u(1)_6$ conformal field theories (CFTs). These correspond either to
non-trivial permutation invariants or block diagonal invariants, that one can
understand in terms of anyon condensation. In terms of lattice parafermion
operators, the constructed models correspond to parafermion chains with
many-body terms. Our construction is based on how the partition function of a
CFT depends on symmetry sectors and boundary conditions. This enables to write
the partition function corresponding to one modular invariant as a linear
combination of another over different sectors and boundary conditions, which
translates to a general recipe how to write down a microscopic model, tuned to
criticality. We show that the scheme can also be extended to construct critical
generalizations of $k$-state clock type models.
SciPost Phys. 3, 021 (2017) ·
published 9 September 2017
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This review presents an entry-level introduction to topological quantum
computation -- quantum computing with anyons. We introduce anyons at the
system-independent level of anyon models and discuss the key concepts of
protected fusion spaces and statistical quantum evolutions for encoding and
processing quantum information. Both the encoding and the processing are
inherently resilient against errors due to their topological nature, thus
promising to overcome one of the main obstacles for the realisation of quantum
computers. We outline the general steps of topological quantum computation, as
well as discuss various challenges faced it. We also review the literature on
condensed matter systems where anyons can emerge. Finally, the appearance of
anyons and employing them for quantum computation is demonstrated in the
context of a simple microscopic model -- the topological superconducting
nanowire -- that describes the low-energy physics of several experimentally
relevant settings. This model supports localised Majorana zero modes that are
the simplest and the experimentally most tractable types of anyons that are
needed to perform topological quantum computation.
Dr Lahtinen: "Thank you very much again to c..."
in Submissions | report on A Short Introduction to Topological Quantum Computation