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Cross-backend benchmark and a which-backend-when decision table #4

Description

@Michele-Minervini

benchmarks/scaling.py still measures only the dense backend — it predates the tensor-network, circuit, Pauli-propagation and JAX engines. With six backends that have genuinely different sweet spots, the single most useful thing the docs could add is a measured comparison.

What to do

Extend the benchmark to sweep, per backend, over qubit count and Hamiltonian structure (chain vs all-to-all, commuting vs non-commuting, high vs low temperature), recording wall-clock, memory and accuracy against the dense reference where it exists.

Then turn the numbers into a decision table in the README: given n qubits, this connectivity, this temperature, and this quantity — use backend X.

Expected findings, to check rather than assume

  • tensor network wins on 1-D / low entanglement, loses on all-to-all
  • Pauli propagation is topology-agnostic and cheap at high temperature, dense at low
  • dense is unbeatable below ~12 qubits
  • circuit is for hardware fidelity, not speed

Acceptance

  • a reproducible script writing CSV + plots
  • the table in the README, with the measurement conditions stated

Activity

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