Dispatch belief-propagation message updates on NormNetwork - #157
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Dispatches belief-propagation message updates on the factor-graph type so operator-valued messages are preserved end to end. Belief propagation on a `NormNetwork` (the doubled ⟨ψ|ψ⟩ network) produces bond operators pairing a ket leg with a bra leg. The previous `message_update!` recovered that structure by inspecting each message's type inline. Now the generic method contracts into a plain bond vector normalized by its entrywise sum, and a `NormNetwork` method re-wraps the contraction as an operator carrying the network's own ket/bra link names and normalizes by the trace, which is sign-correct on fermionic bonds where the entrywise sum can flip the odd-parity block's sign. `vertex_scalar` and `edge_scalar` unwrap operator messages before contracting, so `bethe_free_energy` works on them too. Adds a belief-propagation test on a norm network over U1 and fermion-parity sites, checking that the converged messages keep their operator structure and that belief propagation stays exact on a tree.
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## main #157 +/- ##
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+ Coverage 84.43% 84.79% +0.36%
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Files 15 15
Lines 681 684 +3
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+ Hits 575 580 +5
+ Misses 106 104 -2
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`edge_scalar` is a single binary contraction, so it uses `*` directly instead of `contract_network`. Binary `*` dispatches through the operator product, so operator-valued messages contract to a scalar without unwrapping, preserving operators. `vertex_scalar` is N-ary and still routes through `contract_network`, whose lazy path only accepts plain operands, so it keeps the `state` unwrap for now.
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Summary
Dispatches belief-propagation message updates on the factor-graph type so operator-valued messages are preserved end to end. Belief propagation on a
NormNetwork(the doubled ⟨ψ|ψ⟩ network) produces bond operators pairing a ket leg with a bra leg. The previousmessage_update!recovered that structure by inspecting each message's type inline. Now the generic method contracts into a plain bond vector normalized by its entrywise sum, and aNormNetworkmethod re-wraps the contraction as an operator carrying the network's own ket/bra link names and normalizes by the trace, which is sign-correct on fermionic bonds while the entrywise sum is basis dependent.vertex_scalarandedge_scalaralso handle operator-valued messages, sobethe_free_energyworks on them too.Adds a belief-propagation test on a norm network over U1 and fermion-parity sites, checking that the converged messages keep their operator structure and that belief propagation stays exact on a tree.