Algorithm to Verify Local Equivalence of Stabilizer States

• URL: http://arxiv.org/abs/2410.03961v1
• Date: Fri, 4 Oct 2024 22:51:11 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 equivalence between two graph states takes a specific form, naturally generalizing the class of local Clifford (LC) equivalences. 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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