Quantum / CONCEPT
Song and Lin's parity conjecture for zero transfer is false
On the connected oriented circulant graph G(Z_30, {5, 6, 9, 20}) the continuous-time quantum walk never moves amplitude between the vertex 0 and the even vertex 2, so the parity restriction conjectured for orders n = 2 (mod 4) fails at n = 30.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH4
DOCUMENT LINKS1
The counterexample n = 30, C = {5, 6, 9, 20}, v = 2
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- A 23-edge coupling realizes the ten-mode Fourier transformstructural-affinity · Closed
- A property-T circulant with universal perfect state transferstructural-affinity · Closed
- Analytic Flow Generationstructural-affinity · Closed
- Conservation And Autonomy Are Distinctstructural-affinity · Closed
- CZX parent Lindbladian steady statestructural-affinity · Closed
- Hamiltonian Effect Completion Generatorstructural-affinity · Closed
- Infinitesimal Reducing Criterionstructural-affinity · Closed
- No perfect state transfer at time pi on rational paths with 2^k + 1 verticesstructural-affinity · Closed
- Projection Probability Flowstructural-affinity · Closed
- The twin end vertex of P'_9 is not sharply 1/9-sedentarystructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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