Universal framework for simultaneous tomography of quantum states and SPAM noise

Abhijith Jayakumar; Stefano Chessa; Carleton Coffrin; Andrey Y. Lokhov; Marc Vuffray; Sidhant Misra

doi:10.22331/q-2024-07-30-1426

Universal framework for simultaneous tomography of quantum states and SPAM noise

Abhijith Jayakumar¹, Stefano Chessa^1,2,3, Carleton Coffrin⁴, Andrey Y. Lokhov¹, Marc Vuffray¹, and Sidhant Misra¹

¹Theoretical Division, Los Alamos National Laboratory, 87545, NM, USA
²NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126, Pisa, Italy
³Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, 61801, IL, USA
⁴Los Alamos National Laboratory, Los Alamos, 87545, NM, USA

Published:	2024-07-30, volume 8, page 1426
Eprint:	arXiv:2308.15648v6
Doi:	https://doi.org/10.22331/q-2024-07-30-1426
Citation:	Quantum 8, 1426 (2024).

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Abstract

We present a general denoising algorithm for performing $\textit{simultaneous tomography}$ of quantum states and measurement noise. This algorithm allows us to fully characterize state preparation and measurement (SPAM) errors present in any quantum system. Our method is based on the analysis of the properties of the linear operator space induced by unitary operations. Given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge freedom is unavoidable in the general case, but this degeneracy can be generally broken using prior knowledge on the state or noise properties, thus fixing the gauge for several types of state-noise combinations with no assumptions about noise strength. Such combinations include pure quantum states with arbitrarily correlated errors, and arbitrary states with block independent errors. This framework can further use available prior information about the setting to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes existing approaches to the problem, and includes as special cases common settings considered in the literature requiring an uncorrelated or invertible noise matrix, or specific probe states.

Popular summary

The state of a quantum computer cannot be directly observed; instead, it needs to be reconstructed from outcomes of carefully chosen measurements made repeatedly on the computer. This reconstruction task is called quantum tomography.

Quantum computers are affected by many sources of noise. Even a perfect quantum computer with no noise will produce random outputs due to the inherently stochastic nature of quantum measurements, as demonstrated by Schrödinger's cat. In our work, we present a very general tomographic algorithm that allows users to reconstruct the quantum state and the state preparation and measurement (SPAM) noise matrix simultaneously by post-processing the outputs of quantum measurements.

This is a challenging problem because it is often not possible to uniquely reconstruct the state in the presence of this type of noise. The observed randomness can be due to either the quantum nature of measurement or the noise in the system, and it can be shown that these two sources cannot be unambiguously discriminated solely from the measurements. However, we demonstrate several cases in which this ambiguity can be resolved by using additional information about the system.

Our tomography algorithm can be implemented on a qubit-based quantum computer by making randomized measurements on the system. Our theoretical analysis of this algorithm explicitly shows that the problem becomes progressively harder as the computer becomes noisier.

► BibTeX data

@article{Jayakumar2024universalframework,
  doi = {10.22331/q-2024-07-30-1426},
  url = {https://doi.org/10.22331/q-2024-07-30-1426},
  title = {Universal framework for simultaneous tomography of quantum states and {SPAM} noise},
  author = {Jayakumar, Abhijith and Chessa, Stefano and Coffrin, Carleton and Lokhov, Andrey Y. and Vuffray, Marc and Misra, Sidhant},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1426},
  month = jul,
  year = {2024}
}

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Cited by

[1] Sangwoo Park and Osvaldo Simeone, "Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning", arXiv:2304.03398, (2023).

[2] Mengru Ma and Jiangwei Shang, "Corrupted sensing quantum state tomography", arXiv:2405.14396, (2024).

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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.