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

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

doi:10.1109/QCE57702.2023.00021

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

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

VTT Technical Research Centre of Finland

Aalto University

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

2 Citations (Scopus)

Abstract

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 language	English
Title of host publication	2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023
Subtitle of host publication	Proceedings
Editors	Hausi Muller, Yuri Alexev, Andrea Delgado, Greg Byrd
Publisher	IEEE Institute of Electrical and Electronic Engineers
Pages	111-119
Number of pages	9
ISBN (Electronic)	9798350343236
DOIs	https://doi.org/10.1109/QCE57702.2023.00021
Publication status	Published - 2023
MoE publication type	A4 Article in a conference publication
Event	4th IEEE International Conference on Quantum Computing and Engineering, QCE 2023 - Bellevue, United States Duration: 17 Sept 2023 → 22 Sept 2023

Conference

Conference	4th IEEE International Conference on Quantum Computing and Engineering, QCE 2023
Country/Territory	United States
City	Bellevue
Period	17/09/23 → 22/09/23

Keywords

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

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10.1109/QCE57702.2023.00021Licence: CC BY

Cite this

Galvis-Florez, C. A., Reitzner, D., & Särkkä, S. (2023). Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs. In H. Muller, Y. Alexev, A. Delgado, & G. Byrd (Eds.), 2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023: Proceedings (pp. 111-119). IEEE Institute of Electrical and Electronic Engineers. https://doi.org/10.1109/QCE57702.2023.00021

Galvis-Florez, Cristian A. ; Reitzner, Daniel ; Särkkä, Simo. / Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs. 2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023: Proceedings. editor / Hausi Muller ; Yuri Alexev ; Andrea Delgado ; Greg Byrd. IEEE Institute of Electrical and Electronic Engineers, 2023. pp. 111-119

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title = "Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs",

abstract = "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.",

keywords = "quantum computing, quantum state estimation, quantum tomographic transfer function, quantum tomography, symmetric informationally complete positive operator-valued measurements",

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editor = "Hausi Muller and Yuri Alexev and Andrea Delgado and Greg Byrd",

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Galvis-Florez, CA, Reitzner, D & Särkkä, S 2023, Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs. in H Muller, Y Alexev, A Delgado & G Byrd (eds), 2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023: Proceedings. IEEE Institute of Electrical and Electronic Engineers, pp. 111-119, 4th IEEE International Conference on Quantum Computing and Engineering, QCE 2023, Bellevue, United States, 17/09/23. https://doi.org/10.1109/QCE57702.2023.00021

Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs. / Galvis-Florez, Cristian A.; Reitzner, Daniel; Särkkä, Simo.
2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023: Proceedings. ed. / Hausi Muller; Yuri Alexev; Andrea Delgado; Greg Byrd. IEEE Institute of Electrical and Electronic Engineers, 2023. p. 111-119.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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AU - Reitzner, Daniel

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PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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ER -

Galvis-Florez CA, Reitzner D, Särkkä S. Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs. In Muller H, Alexev Y, Delgado A, Byrd G, editors, 2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023: Proceedings. IEEE Institute of Electrical and Electronic Engineers. 2023. p. 111-119 doi: 10.1109/QCE57702.2023.00021

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

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