A qubit readout has assignment errors and

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Physical realizations and quantum technologies · Physical realizations and quantum technologies

Quantum Information and Technology, Ch What a qubit must do: requirements, tomography and benchmarking

Problem

A qubit readout has assignment errors M10=P(read 1∣true 0)=0.03M_{10} = P(\text{read }1\mid\text{true }0) = 0.03 and M01=P(read 0∣true 1)=0.05M_{01} = P(\text{read }0\mid\text{true }1) = 0.05. An unknown state is measured many times and the fraction of shots reading 11 is 0.420.42. ((a)) Write P(read 1)P(\text{read }1) in terms of the true probability pp of the state being ∣1⟩|1\rangle and the two assignment errors. ((b)) Solve for the readout-corrected estimate of pp.

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