Enhanced Estimation of Quantum Properties with Common Randomized Measurements

We thank Daniel K. Mark and Steve Flammia for helpful discussions and Richard Kueng and Hsin-Yuan (Robert) Huang for their valuable comments on the manuscript. Work in Grenoble is funded by the French National Research Agency via the JCJC project QRand (Grant No. ANR-20-CE47-0005) and via the research programs EPIQ (Gran No. ANR-22-PETQ-0007, Plan France 2030), and QUBITAF (Grant No. ANR-22-PETQ-0004, Plan France 2030). B.V. acknowledges funding from the Austrian Science Fund (Grant No. P 32597 N). A.R. acknowledges support from the Laboratoire d’excellence LANEF in Grenoble (Grant No. ANR-10-LABX-51-01) and from the Grenoble Nanoscience Foundation. B.S. is supported by the Caltech Summer Undergraduate Research Fellowship. J.P. acknowledges funding from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research (Grants No. DE-NA0003525 and No DE-SC0020290), the U.S. Department of Energy Quantum Systems Accelerator, and the National Science Foundation (Grant No. PHY-1733907). The Institute for Quantum Information and Matter is a National Science Foundation Physics Frontiers Center. A.E. acknowledges funding by the German National Academy of Sciences Leopoldina under Grant No. LPDS 2021-02 and by the Walter Burke Institute for Theoretical Physics at Caltech. Our julia code uses ITensor [68] and PastaQ [57], and is available from Ref. [69].