loom.eka.utilities.logical_operator_finding
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- loom.eka.utilities.logical_operator_finding.find_logical_operator_set(stabarr)[source]
Given a stabilizer array of a code, find a set of X and Z logical operators. The Z logical operators shall contain only Z operators while the X logical operators may contain both X and Z operators. They may not be in their simplified form.
This algorithm follows the notation and algorithm described in: Nielsen, M. A., & Chuang, I. L. (2011). (p.470-471) Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press,
How it works (ignoring signs):
1. The stabilizer array is first put into standard form. The standard form is of the form:
(I, A1, A2 | B, 0, C) (0, 0, 0 | D, I, E)
Note that the stabilizer array has to be reindexed to the standard form.
The Z logical operators are then given by:
(0, 0, 0 | A2^T, 0, I)
and the X logical operators are given by:
(0, E^T, I | C^T , 0, 0)
Reindex the logical operators to the original qubit order.