trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Counting even labels in a CNOT sequence

Visiting every nonzero even Boolean label between odd initial and final wire labels requires exponentially many updates and a linear return cost.

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DIRECT CONSEQUENCES1
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THEOREM

Visiting all even vectors forces a return cost

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Counting even labels in a CNOT sequenceCounting even labels in a CNOTsequenceThe worst-case CNOT lower bound for reflection symmetryThe worst-case CNOT lower boundfor reflection symmetry
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Magic/ReflectionDiagonalParityCounting
Repository path
D5/S3/Quantum/Magic/ReflectionDiagonalParityCounting.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.