SciPost Phys. Lect. Notes 4 (2018) ·
published 27 September 2018
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Free fermion systems enjoy a privileged place in physics. With their simple
structure they can explain a variety of effects, ranging from insulating and
metallic behaviours to superconductivity and the integer quantum Hall effect.
Interactions, e.g. in the form of Coulomb repulsion, can dramatically alter
this picture by giving rise to emerging physics that may not resemble free
fermions. Examples of such phenomena include high-temperature
superconductivity, fractional quantum Hall effect, Kondo effect and quantum
spin liquids. The non-perturbative behaviour of such systems remains a major
obstacle to their theoretical understanding that could unlock further
technological applications. Here, we present a pedagogical review of
"interaction distance" [Nat. Commun. 8, 14926 (2017)] -- a systematic method
that quantifies the effect interactions can have on the energy spectrum and on
the quantum correlations of generic many-body systems. In particular, the
interaction distance is a diagnostic tool that identifies the emergent physics
of interacting systems. We illustrate this method on the simple example of a
one-dimensional Fermi-Hubbard dimer.
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.
