Robustness and measurement-induced percolation of the surface code
- URL: http://arxiv.org/abs/2311.14338v1
- Date: Fri, 24 Nov 2023 08:27:36 GMT
- Title: Robustness and measurement-induced percolation of the surface code
- Authors: Thomas Botzung, Michael Buchhold, Sebastian Diehl and Markus M\"uller
- Abstract summary: We examine the robustness of a logical qubit in the planar surface code subject to'measurement-errors', i.e., to local Pauli measurements at known positions.
This yields a measurement-only dynamics, which is driven by the competition between local Pauli measurements and stabilizer measurements.
We argue that the loss of the logical qubit in this setting can still be understood by percolation theory and underpin our arguments with numerical simulations.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We examine the robustness of a logical qubit in the planar surface code
subject to 'measurement-errors', i.e., to local Pauli measurements at known
positions. This yields a measurement-only dynamics, which is driven by the
competition between local Pauli measurements and stabilizer measurements. The
setup differs from the conventional surface code for which errors are caused by
decoherence and their positions are unknown. Yet, our setting allows us to
examine the dynamics of the encoded logical qubit by using a combination of
analytical arguments based on percolation theory and numerical simulations.
Firstly, we show that for a single round of Pauli measurements only, the
threshold corresponding to the irreversible loss of the logical qubit depends
only on the rate of $ \hat X$- and $\hat Z$-measurements, and that this loss of
logical quantum information is equivalent to the bond percolation transition in
a 2D square lattice. Local $\hat Y$-measurements, which affect both $X$ and $Z$
stabilizers, erase the logical qubit only if all physical qubits along one of
the diagonals are measured, and are thus negligible at large code distance.
Secondly, we examine the dynamics in the code by considering the interplay
between rounds of Pauli measurements and rounds of stabilizer measurements.
Focusing on the lifetime of the logical qubit, we obtain a rich phase diagram
featuring different dynamical regimes. We argue that the loss of the logical
qubit in this setting can still be understood by percolation theory and
underpin our arguments with numerical simulations.
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