Fitting quantum noise models to tomography data

Emilio Onorati1,2, Tamara Kohler1,3, and Toby S. Cubitt1

1University College London, Department of Computer Science, UK
2Technische Universität München, Fakultät für Mathematik, DE
3Instituto de Ciencias Matemáticas, Madrid, ES

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The presence of noise is currently one of the main obstacles to achieving large-scale quantum computation. Strategies to characterise and understand noise processes in quantum hardware are a critical part of mitigating it, especially as the overhead of full error correction and fault-tolerance is beyond the reach of current hardware. Non-Markovian effects are a particularly unfavourable type of noise, being both harder to analyse using standard techniques and more difficult to control using error correction. In this work we develop a set of efficient algorithms, based on the rigorous mathematical theory of Markovian master equations, to analyse and evaluate unknown noise processes. In the case of dynamics consistent with Markovian evolution, our algorithm outputs the best-fit Lindbladian, i.e., the generator of a memoryless quantum channel which best approximates the tomographic data to within the given precision. In the case of non-Markovian dynamics, our algorithm returns a quantitative and operationally meaningful measure of non-Markovianity in terms of isotropic noise addition. We provide a Python implementation of all our algorithms, and benchmark these on a range of 1- and 2-qubit examples of synthesised noisy tomography data, generated using the Cirq platform. The numerical results show that our algorithms succeed both in extracting a full description of the best-fit Lindbladian to the measured dynamics, and in computing accurate values of non-Markovianity that match analytical calculations.

Quantum computers offer the possibility of carrying out certain tasks far faster than their classical counterparts – such as simulating materials, optimisation problems, and fundamental physics. However quantum computers are very susceptible to errors – if no steps are taken to deal with noise in quantum computing devices then errors will quickly swamp the computation being carried out. Methods to characterise and understand noise processes in quantum devices are therefore crucial. In this paper we develop efficient algorithms to characterise noise processes in quantum computing devices, based on standard experimental techniques. These algorithms take the output of these experiments, and provide a description of the underlying physical process which best fits the experimental data. Knowledge of these physical processes can help engineers understand the behaviour of their device, and aid people using the devices in designing quantum algorithms which are resistant to the types of noise most prevalent in the device.

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[9] Markus Hasenöhrl and Matthias C. Caro, "Quantum and classical dynamical semigroups of superchannels and semicausal channels", Journal of Mathematical Physics 63 7, 072204 (2022).

[10] Emilio Onorati, Tamara Kohler, and Toby S. Cubitt, "Fitting time-dependent Markovian dynamics to noisy quantum channels", arXiv:2303.08936, (2023).

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