All elements of a qubit k-RDM can be measured with O(3^k log^{k-1} N) circuits, and all elements of a fermionic 2-RDM with O(N^2) circuits, matching a new Ω(N^2) lower bound for Clifford measurements.
Scal- able quantum simulation of molecular energies,
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Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States
All elements of a qubit k-RDM can be measured with O(3^k log^{k-1} N) circuits, and all elements of a fermionic 2-RDM with O(N^2) circuits, matching a new Ω(N^2) lower bound for Clifford measurements.