DA-CASE: reusable measurements for adaptive quantum subspaces

• URL: http://arxiv.org/abs/2608.08739v1
• Date: Sun, 09 Aug 2026 14:35:52 GMT
• Title: DA-CASE: reusable measurements for adaptive quantum subspaces
• Abstract summary: We present theDyadic Adaptive Clifford-Algebra Subspace Eigensolver (DA-CASE)<n>We make that trade explicit on a frozen eight-qubit H$_4$ Hamiltonian.<n>Independently, a dyadic commuting hierarchy reduces thedeterminant bank from 913 qubit-wise-commuting settings to 64 fully commutingsettings.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum subspace methods are often compared by basis dimension or energyerror, although their dominant experimental costs arise from different statepreparations, measurement settings, and shot allocations. We present theDyadic Adaptive Clifford-Algebra Subspace Eigensolver (DA-CASE), whose basisstates are virtual directions $A_i|ψ\rangle$ generated from one reference.Overlap, Hamiltonian, and observable matrices are reconstructed from onecached set of Pauli expectations on that reference. The method thereforetrades multiple prepared basis states for a potentially wide measurement bank.We make that trade explicit on a frozen eight-qubit H$_4$ Hamiltonian. Twogenerator resolutions reach the same nine-dimensional subspace and the sameenergy to machine precision, while the retained bank changes from 7371 to 2240Pauli words. A reference-conditioned symmetry test certifies the narrower spanwithout asserting that its individual Pauli words conserve the sector asabstract operators. Independently, a dyadic commuting hierarchy reduces thedeterminant bank from 913 qubit-wise-commuting settings to 64 fully commutingsettings, while exposing the added logical-CX cost. In a separate four-qubitfinite-shot diagnostic, covariance-aware allocation reduces theprojected-matrix variance target by 68.9%. Mode-wise overlap regularizationremoves the observed catastrophic energy estimates and lowers RMSE, butdoubles the median error relative to a fixed cutoff. These are small-instanceexact and Monte Carlo results, not a hardware demonstration, scaling result,or quantum advantage claim. The contribution is a single-referencemeasurement architecture and a resource ledger that keeps contexts, settings,shots, circuit depth, and post-selection retries in their proper units.

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