From optimization to construction: Expanding quantum measurement designs

arXiv:2611.14986v1 Announce Type: new Abstract: Estimating molecular energies on quantum computers requires repeated measurements of many Pauli terms, making sampling a major resource cost. Measurement design chooses which compatible terms are measured together and allocates a finite shot budget among bases to minimize the variance of an energy estimator. We introduce variance-guided measurement group construction (VGMC), which reduces variance beyond optimization on existing measurement bases by changing which Hamiltonian terms share measurement shots. After including every Hamiltonian term measurable in each existing basis, we jointly optimize estimator coefficients and shot allocations to separate inefficient use of these measurements from limitations of their measurement combinations.