On heavy-hex hardware, routing imbalance in symmetric quantum circuits is an assignment choice whenever the patch shape permits, and for four-part rings a simple closed-form assignment achieves zero spread.
Theoretical guarantees for permutation- equivariant quantum neural networks,
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Balanced Routing for Symmetric Quantum Circuits
On heavy-hex hardware, routing imbalance in symmetric quantum circuits is an assignment choice whenever the patch shape permits, and for four-part rings a simple closed-form assignment achieves zero spread.