Fig. 4: Comparing optimal measurement circuits on different quantum processors.

a,b, The mean m.s.e. and minimum m.s.e. across all qubits with different quantum processors for the single- (a) and two-copy (b) measurements, respectively. No error mitigation is used in these figures. Each m.s.e. is averaged over 600 experimental runs, corresponding to five different angles, each using 512 shots. c,d, The m.s.e. with and without error mitigation (EM) for the single- and two-copy measurements, respectively. In all but four cases error mitigation is beneficial. The data in c and d correspond to the average of 400 individual experimental runs, each using 512 shots. For all figures, error bars correspond to one standard deviation obtained by bootstrapping. The different IBM Q processors tested are Belem (Bl), Bogota (Bg), Casablanca (Cs), Guadalupe (Gu), Jakarta (Ja), Lima (Li), Manhattan (Ma), Quito (Qu), Santiago (Sa), Toronto (To), Yorktown (Yo) and the F-IBM QS1 device (QS1). Also shown is the Rigetti Aspen-9 superconducting device (RA9), JenQuant (JQ) and the AQTION trapped-ion device (UIBK). For the Rigetti Aspen-9 device, only one qubit or pair of qubits was tested, hence the mean m.s.e. and minimum m.s.e. are equal. For the AQTION device, the mean m.s.e. and minimum m.s.e. are equal as only one ion or pair of ions was loaded into the trap. Empty spaces correspond to processors where a particular experiment could not be carried out.