Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs

Cristian A. Galvis-Florez, Daniel Reitzner, Simo Särkkä

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Current quantum computers have the potential to overcome classical computational methods, however, the capability of the algorithms that can be executed on noisy intermediate-scale quantum devices is limited due to hardware imperfections. Estimating the state of a qubit is often needed in different quantum protocols, due to the lack of direct measurements. In this paper, we consider the problem of estimating the quantum state of a qubit in a quantum processing unit without conducting direct measurements of it. We consider a parameterized measurement model to estimate the quantum state, represented as a quantum circuit, which is optimized using the quantum tomographic transfer function. We implement and test the circuit using the quantum computer of the Technical Research Centre of Finland as well as an IBM quantum computer. We demonstrate that the set of positive operator-valued measurements used for the estimation is symmetric and informationally complete. Moreover, the resources needed for qubit estimation are reduced when direct measurements are allowed, keeping the symmetric property of the measurements.
Original languageEnglish
Title of host publicationProceedings - 2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023
EditorsHausi Muller, Yuri Alexev, Andrea Delgado, Greg Byrd
Number of pages9
ISBN (Electronic)979-8-3503-4323-6
ISBN (Print)979-8-3503-4324-3
Publication statusPublished - 30 Nov 2023
MoE publication typeA4 Conference publication
EventIEEE International Conference on Quantum Computing and Engineering - Bellevue, WA, USA, Bellevue, United States
Duration: 17 Sept 202322 Sept 2023


ConferenceIEEE International Conference on Quantum Computing and Engineering
Abbreviated titleQCE
Country/TerritoryUnited States


  • quantum state estimation
  • quantum tomography
  • symmetric informationally complete positive operator-valued measurements
  • quantum tomographic transfer function
  • quantum computing


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