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Tensor-network representation and compute feasibility audit
Initial decision: Conditional evidence workflow. First dossier, 9 October 2026 Australia/Brisbane. No buyer validation or profitability evidence has been established.
Research finding
Family 265 claims an entropy area law from a full-system spectral gap for unique ground states on finite induced square lattices. A companion states existence of polynomial-bond PEPS approximations to uniformly gapped nearest-neighbor square-grid ground states with global vector error at most L^-1. The PEPS abstract explicitly calls this an existence theorem.
Problem and buyer
A quantum simulation team needs to decide whether a theoretically compact representation will reduce its actual ground-state computation budget. Storage, state construction, contraction, convergence and observable accuracy can dominate in different regimes.
What the finding could enable
An engineering workbench can report representation size separately from preparation and contraction cost, and attach the new area-law assumptions to a run. Custom tensor-network planners can use the claimed existence result as a research target while benchmarking an existing executable method. This does not turn existence into a new efficient simulator.
Technical and commercial limits
A uniform gap and ground-state uniqueness may themselves be difficult to establish. Unknown polynomial exponents or constants make asymptotic storage bounds poor budget estimates. Global vector error is not automatically the same as a requested energy-density error or a local truncation tolerance. No efficient PEPS construction or contraction procedure is asserted by the inspected abstracts.
Minimal architecture
Hamiltonian/local-dimension manifest -> gap evidence -> PEPS representation ledger -> actual construction and contraction profiler -> exact small-model comparison -> cost/accuracy report. Store tensor ranks, numeric precision, truncation history, measured observables and hardware. Reuse the algorithm feasibility workbench rather than creating another proof store.
Existing alternatives and differentiation
Quimb already exposes PEPS/simple-update simulation with bond truncation and approximate local expectations. The proposed contribution is a source-aware storage-versus-compute audit across existing backends. Quimb PEPS documentation.
Monetization hypothesis
Hypothesis: AUD 8,000–20,000 for a scoped simulation budget review, with recurring integration only after saved compute or researcher time is measured. At a hypothetical AUD 12,000 project price and 45 expert hours costed at AUD 180/hour, AUD 3,900 remains before compute, support, sales and overhead. This is an illustrative contribution calculation, not a margin forecast.
Validation experiment
Compare exact small-square diagonalization with an existing tensor method over several bond dimensions. Measure construction time, contraction time, peak memory and global overlap where feasible. Check whether the report prevents a representation-only cost claim and changes a resource decision.
Conditions to reject or defer
Reject a standalone planner if a backend profiler already supplies the useful output or if gap evidence is unavailable for the target models. Defer a faster simulator claim until an executable algorithm and end-to-end crossover are established.
Next concrete action
Extract the theorem’s dependence on local dimension, interaction strength and gap, then scope one public finite-square benchmark.