Algorithm to Verify Local Equivalence of Stabilizer States

• URL: http://arxiv.org/abs/2410.03961v2
• Date: Wed, 12 Feb 2025 20:08:10 GMT
• Title: Algorithm to Verify Local Equivalence of Stabilizer States
• Authors: Adam Burchardt, Jarn de Jong, Lina Vandré,
• Abstract summary: We present an algorithm for verifying the local unitary equivalence of graph and stabilizer states. Our approach reduces the problem to solving a system of linear equations in modular arithmetic.
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• Abstract: We present an algorithm for verifying the local unitary (LU) equivalence of graph and stabilizer states. Our approach reduces the problem to solving a system of linear equations in modular arithmetic. Furthermore, we demonstrate that any LU transformation between two graph states takes a specific form, naturally generalizing the class of local Clifford (LC) transformations. Lastly, using existing libraries, we verify that for up to $n=11$, the number of LU and LC orbits of stabilizer states is identical.

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