Optimizing the information extracted by a single qubit measurement

Physical Review A, vol. 108

Abstract

We consider a quantum computation that only extracts one bit of information per $N$-qubit quantum state preparation. This is relevant for error mitigation schemes where the remainder of the system is measured to detect errors. We optimize the estimation of the expectation value of an operator by its linear decomposition into bitwise-measurable terms. We prove that optimal decompositions must be in terms of reflections with eigenvalues $\ifmmode\pm\else\textpm\fi{}1$. We find the optimal reflection decomposition of a fast-forwardable operator, and show a numerical improvement over a simple Pauli decomposition by a factor ${N}^{0.7}$.

Authors 3

1. Stefano Polla Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Google Quantum AI, 80636 München, Germany

   Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands

2. Gian-Luca Anselmetti

   Covestro (Germany)

   Affiliation as printed

   Covestro Deutschland AG, Leverkusen 51373, Germany

3. Thomas E. O’Brien Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Google Quantum AI, 80636 München, Germany

   Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands