Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography

Filip B. Maciejewski1,2,3, Zoltán Zimborás4,5,6, and Michał Oszmaniec2,3

1University of Warsaw, Faculty of Physics, Ludwika Pasteura 5, 02-093 Warszawa, Poland
2International Centre for Theory of Quantum Technologies, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland
3Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
4Wigner Research Centre for Physics of the Hungarian Academy of Sciences, H-1525 Budapest, P.O.Box 49, Hungary
5BME-MTA Lendület Quantum Information Theory Research Group, Budapest, Hungary
6Mathematical Institute, Budapest University of Technology and Economics, P.O.Box 91, H-1111, Budapest, Hungary

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We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.

Most researchers believe that quantum computing, if ever actually developed, could offer major advances in numerous areas of scientific research. Yet, this technology is currently in its infancy, and the state of the art devices suffer from various problems. One of the most serious obstacles we need to overcome is the noise affecting the qubits. In this context, an important task arises of developing methods to reduce the errors.

In this work, we focus on the noise affecting quantum measurements. We propose a simple procedure to mitigate measurement errors via classical post-processing of the experimental outcome statistics. The procedure works perfectly provided measurement noise is classical and one operates in the infinite-statistics regime. Naturally, neither of those two assumptions is fulfilled exactly in practice, therefore we study the performance of our mitigation scheme in the presence of their violations. Importantly, we show how to validate the model of noise via the procedure known as Quantum Detector Tomography, which allows one to obtain the classical description of the quantum detector.

Our aim is to present a paper exploring the whole procedure of readout error mitigation: from the detailed description of necessary assumptions, through validation of those, finishing at the implementation of presented ideas on the actual quantum hardware from IBM and Rigetti. We believe that such an approach makes the work accessible to readers not necessarily familiar with the formalism of quantum measurements.

To encourage the practical realization of our findings, we developed an open-source GitHub repository implementing the ideas from the paper

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[1] E. O. Kiktenko, A. O. Malyshev, A. S. Mastiukova, V. I. Man'ko, A. K. Fedorov, and D. Chruściński, "Probability representation of quantum dynamics using pseudostochastic maps", arXiv:1908.03404, Physical Review A 101 5, 052320 (2020).

[2] Benjamin Nachman, Miroslav Urbanek, Wibe A. de Jong, and Christian W. Bauer, "Unfolding Quantum Computer Readout Noise", arXiv:1910.01969.

[3] Hyeokjea Kwon and Joonwoo Bae, "A hybrid quantum-classical approach to mitigating measurement errors", arXiv:2003.12314.

[4] Pranav Gokhale, Ali Javadi-Abhari, Nathan Earnest, Yunong Shi, and Frederic T. Chong, "Optimized Quantum Compilation for Near-Term Algorithms with OpenPulse", arXiv:2004.11205.

[5] Megan N. Lilly and Travis S. Humble, "Modeling Noisy Quantum Circuits Using Experimental Characterization", arXiv:2001.08653.

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