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arXiv:2606.25974

Tensor network characterization and mitigation of readout errors

Yuchen Guo, Shuo Yang

quant-phSubmitted Jun 24, 2026• Announced Jun 25, 2026• 0 citations• Revised Jul 23, 2026 (v2)
v1 · Jun 24, 2026v2 · Jul 23, 2026
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Abstract

Readout errors are a major bottleneck to extracting reliable information from near-term quantum processors, especially when spatial correlations are non-negligible. We present a unified tensor-network framework that models the readout process as a matrix product operator (MPO), enabling efficient characterization and mitigation beyond uncorrelated approximations. The MPO model is trained via likelihood optimization on calibration data and applies to multiple tasks, including nonlocal observable estimation, random circuit sampling, and random-measurement protocols, such as classical shadows and learning-based tomography. Experiments on a superconducting processor and numerical simulations up to 20 qubits show that the MPO model captures correlated readout errors that uncorrelated models miss, with a sample cost that grows only near-linearly with system size. When extended to two-dimensional systems, the framework can also be integrated with tensor-network quantum error-correction decoders by performing joint inference over data and readout errors. These results establish tensor-network readout error mitigation as a scalable and versatile approach for noise-aware quantum data processing.

Comments
21 pages, 13 figures

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Readout errors are a major bottleneck to extracting reliable information from near-term quantum processors, especially when spatial correlations are non-negligible. We present a unified tensor-network framework that models the readout process as a matrix product operator (MPO), enabling efficient characterization and mitigation beyond uncorrelated approximations. The MPO model is trained via likelihood optimization on calibration data and applies to multiple tasks, including nonlocal observable estimation, random circuit sampling, and random-measurement protocols, such as classical shadows and learning-based tomography. Experiments on a superconducting processor and numerical simulations up to 20 qubits show that the MPO model captures correlated readout errors that uncorrelated models miss, with a sample cost that grows only near-linearly with system size. When extended to two-dimensional systems, the framework can also be integrated with tensor-network quantum error-correction decoders by performing joint inference over data and readout errors. These results establish tensor-network readout error mitigation as a scalable and versatile approach for noise-aware quantum data processing.
Quantum simulation, the study of strongly correlated quantum matter using synthetic quantum systems, has been the most successful application of quantum computers to date. It often requires determining observables with high precision, for example when studying critical phenomena near quantum phase transitions. Thus, readout errors must be carefully characterized and mitigated in data postprocessing, using scalable and noise-model agnostic protocols. We present a readout error-mitigation protocol that uses only single-qubit Pauli measurements and avoids experimentally challenging randomized measurements. The proposed approach captures a very broad class of correlated noise models and is scalable to large qubit systems. It is based on a complete and efficient characterization of few-qubit correlated positive operator-valued measures, using overlapping detector tomography. To assess the effectiveness of the protocol, observables are extracted from simulations involving up to 100 qubits employing readout errors obtained from experiments with superconducting qubits.
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Abstract Quantum technologies rely heavily on accurate control and reliable readout of quantum systems. Current experiments are limited by numerous sources of noise that can only be partially captured by simple analytical models and additional characterization of the noise sources is required. We test the ability of readout error mitigation to correct noise found in systems composed of quantum two-level objects (qubits). To probe the limit of such methods, we designed a beyond-classical readout error mitigation protocol based on quantum state tomography (QST), which estimates the density matrix of a quantum system, and quantum detector tomography (QDT), which characterizes the measurement procedure. By treating readout error mitigation in the context of state tomography the method becomes largely readout mode-, architecture-, noise source-, and quantum state-independent. We implement this method on a superconducting qubit and evaluate the increase in reconstruction fidelity for QST. We characterize the performance of the method by varying important noise sources, such as suboptimal readout signal amplification, insufficient resonator photon population, off-resonant qubit drive, and effectively shortened T1 and T2 coherence. As a result, we identified noise sources for which readout error mitigation worked well, and observed decreases in readout infidelity by a factor of up to 30.
We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as input classical shadows corresponding to local randomized measurements, and outputs the tensors of an MPO maximizing a suitably defined fidelity with the experimental state. The tensor optimization is carried out sequentially, similarly to the well-known density matrix renormalization group algorithm. Our approach is provably efficient under certain technical conditions expected to be met in short-range correlated states and in typical noisy experimental settings. Under the same conditions, we also provide an efficient scheme to estimate fidelities between the learned and the experimental states. We experimentally demonstrate our protocol by learning entangled quantum states of up to N=96 qubits in a superconducting quantum processor. Our method upgrades classical shadows to large-scale quantum computation and simulation experiments.