Adaptive constant-depth circuits for manipulating non-abelian anyons
- URL: http://arxiv.org/abs/2205.01933v2
- Date: Wed, 28 Sep 2022 12:11:14 GMT
- Title: Adaptive constant-depth circuits for manipulating non-abelian anyons
- Authors: Sergey Bravyi, Isaac Kim, Alexander Kliesch, Robert Koenig
- Abstract summary: Kitaev's quantum double model based on a finite group $G$.
We describe quantum circuits for (a) preparation of the ground state, (b) creation of anyon pairs separated by an arbitrary distance, and (c) non-destructive topological charge measurement.
- Score: 65.62256987706128
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We consider Kitaev's quantum double model based on a finite group $G$ and
describe quantum circuits for (a) preparation of the ground state, (b) creation
of anyon pairs separated by an arbitrary distance, and (c) non-destructive
topological charge measurement. We show that for any solvable group $G$ all
above tasks can be realized by constant-depth adaptive circuits with
geometrically local unitary gates and mid-circuit measurements. Each gate may
be chosen adaptively depending on previous measurement outcomes. Constant-depth
circuits are well suited for implementation on a noisy hardware since it may be
possible to execute the entire circuit within the qubit coherence time. Thus
our results could facilitate an experimental study of exotic phases of matter
with a non-abelian particle statistics. We also show that adaptiveness is
essential for our circuit construction. Namely, task (b) cannot be realized by
non-adaptive constant-depth local circuits for any non-abelian group $G$. This
is in a sharp contrast with abelian anyons which can be created and moved over
an arbitrary distance by a depth-$1$ circuit composed of generalized Pauli
gates.
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