elsd
Variational quantum chemistry pipelines report seed-ensemble spread as a property of a molecule's electronic landscape, but nothing in the standard toolchain checks whether the number is physics or arithmetic — or whether the ansatz that produced it was capable of correlation at all.
ELSD (Electronic Landscape Stability Diagnostic) pairs a GPU state-vector VQE with verifiers that share no code with it: a sparse in-sector Lanczos solver for an exact reference eigenvalue, and pure-numpy statevector audits of ⟨N⟩ and ⟨Sz⟩. Turned on my own published registry, they found the ansatz's double-excitation block had never fired in any archived run — 0.1% of correlation energy recovered, against 52.4% from the same engine, Hamiltonian and seed once fixed — and that the reported σ moved from 9.2× to 3.5× depending on an undocumented column choice, sitting within 2–22 float32 units of least precision at every system's energy magnitude. Rewriting the measurement path from dense contraction to Pauli bit-flip algebra cut peak autograd memory on a 20-qubit, 3100-term Hamiltonian from ~600 GB to under 2 GB, moving the workload from a 48 GB datacentre card to a 32 GB consumer GPU. Every finding reproduces from the deposited files with numpy alone.
The problem
ELSD (Electronic Landscape Stability Diagnostic) started from a simple question: variational quantum chemistry pipelines report seed-ensemble spread as a property of a molecule’s electronic landscape, but nothing in the standard toolchain checks whether the number is physics or arithmetic — or whether the ansatz that produced it was capable of correlation at all.
Approach
ELSD (Electronic Landscape Stability Diagnostic) is a GPU-accelerated variational quantum eigensolver built to be audited rather than trusted. A PySCF front end produces molecular integrals and an active-space Hamiltonian, which a Jordan-Wigner transform maps to a Pauli operator set; particle-number and spin penalties are appended as explicit operators so the optimizer is constrained to a chosen electronic sector rather than merely expected to stay there. The state vector is simulated densely in PyTorch on CUDA — 20 qubits, roughly a million complex amplitudes — with the ansatz differentiated end-to-end through autograd under gradient checkpointing, so the whole variational loop is a single differentiable graph on the GPU. The measurement path was rewritten to exploit the structure of Pauli operators directly: rather than contracting dense single-qubit matrices, each Pauli string is applied as a bit-flip permutation and a sign vector, with terms sharing a flip pattern folded into one gather. That reduced peak autograd memory on a 20-qubit, 3100-term Hamiltonian from roughly 600 GB to under 2 GB, putting workloads that previously required a 48 GB datacentre card onto a 32 GB consumer GPU at about four minutes a run. What distinguishes ELSD from a VQE implementation is the verification layer around it: a sparse in-sector Lanczos solver provides an exact reference eigenvalue independent of the variational path, post-hoc statevector audits measure ⟨N⟩ and ⟨Sz⟩ residuals against explicit thresholds, natural-orbital occupations flag multi-reference character before optimization begins, and a decision-grade gate refuses to certify any result whose truncation residual, resource envelope, or distance from the exact reference falls outside stated bounds. Current scope is small active spaces — up to 20 qubits, ~3000 Pauli terms — and the engine is explicit about what it cannot yet certify.
The verification layer is the point, and it generalizes beyond chemistry: independent checkers, falsification-first, and a decision gate that refuses to certify what it cannot verify — the same instinct behind the trustworthy-AI work elsewhere on this site.
Results
The audit program so far is two independent audits of my own published ELSD results, each using verifiers that share no code with the original pipeline.
Metalloenzyme registry (13 deposited-statevector systems): recomputation found the reported σ read from two different energy columns across systems; computed consistently, the headline apo/bound ratio moves from 9.2× to about 3.5×, and the σ values sit between 2 and 22 float32 ULPs at each system’s energy magnitude — at the resolution floor, not above it. One system, Cu_SOD_minimal_CuI, had all five seeds converge outside its intended sector (⟨N⟩ ≈ 11.00 against a target of 10, under 0.03% of amplitude in the intended block); the mechanistic claim built on it is withdrawn in the published correction.
Propulsion lane (methane–nickel, 15 runs): 15 of 15 statevectors sector-clean under independent verification. A matched control isolated the cause behind the σ discrepancies: the ansatz’s double-excitation block never fired in any archived run — 0.1% of correlation energy recovered, against 52.4% from the same engine, Hamiltonian, and seed once corrected. The “UCCSD depth 6” run labels are corrected to what the circuits actually executed, and the broad application-domain framing is explicitly not endorsed by the audit.
Exact reference: a sparse in-sector Lanczos solver, sharing no code with the variational path, supplies an exact reference eigenvalue each run is measured against — the check the original pipeline never had.
Limitations / scope
Current scope is small active spaces: up to 20 qubits, roughly 3000 Pauli terms. No system has yet passed all four decision-grade gates. The 5 Ha offset on Cu_SOD is unexplained. Truncation residuals on some systems exceed the decision-grade limit by three orders of magnitude. No accuracy or σ figures beyond those stated here are currently claimed as defensible. This is a living record: the findings above reflect the September 2026 analysis, the Zenodo versions are being updated as the audit program continues, and the engine is explicit about what it cannot yet certify.
Published corrections: 10.5281/zenodo.20318424 (metalloenzyme registry audit) and 10.5281/zenodo.20348697 (propulsion lane re-audit).