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arXiv · 2410.03961

Algorithm to Verify Local Equivalence of Stabilizer States

Adam Burchardt·Jarn de Jong·Lina Vandré
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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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Adam Burchardt, Jarn de Jong, Lina Vandré. 2024-10-04. Algorithm to Verify Local Equivalence of Stabilizer States. https://arxiv.org/abs/2410.03961

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