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arXiv:2505.07725 · Physical Review Letters

Quantum Process Tomography with Digital Twins of Error Matrices

Tangyou Huang, Akshay Gaikwad, Ilya N. Moskalenko, Anuj Aggarwal, Tahereh Abad, Marko Kuzmanović, Yu‐Han Chang, Ognjen Stanisavljević, Emil Hogedal, Christopher Warren, Irshad Ahmad, Janka Biznárová, Amr Osman, Mamta Dahiya, Marcus Rommel, Anita Fadavi Roudsari, Andreas Nylander, Liangyu Chen, Jonas Bylander, Gheorghe Sorin Paraoanu, Anton Frisk Kockum, Giovanna Tancredi

Published Nov 13, 2025• 1 citation
arXivHTMLPDF

Abstract

Accurate and robust quantum process tomography (QPT) is crucial for verifying quantum gates and diagnosing implementation faults in experiments aimed at building universal quantum computers. However, the reliability of QPT protocols is often compromised by faulty probes, particularly state preparation and measurement (SPAM) errors, which introduce fundamental inconsistencies in traditional QPT algorithms. We propose and investigate enhanced QPT for multiqubit systems by integrating the error matrix in a digital twin of the identity process matrix, enabling statistical refinement of SPAM error learning and improving QPT precision. Through numerical simulations, we demonstrate that our approach enables highly accurate and faithful process characterization. We further validate our method experimentally in superconducting quantum processors, achieving at least an order-of-magnitude fidelity improvement over standard QPT. Our results provide a practical and precise method for assessing quantum gate fidelity and enhancing QPT on a given hardware.

DOI
10.1103/dpgy-rtxr

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Accurate and robust quantum process tomography (QPT) is crucial for verifying quantum gates and diagnosing implementation faults in experiments aimed at building universal quantum computers. However, the reliability of QPT protocols is often compromised by faulty probes, particularly state preparation and measurement (SPAM) errors, which introduce fundamental inconsistencies in traditional QPT algorithms. We propose and investigate enhanced QPT for multiqubit systems by integrating the error matrix in a digital twin of the identity process matrix, enabling statistical refinement of SPAM error learning and improving QPT precision. Through numerical simulations, we demonstrate that our approach enables highly accurate and faithful process characterization. We further validate our method experimentally in superconducting quantum processors, achieving at least an order-of-magnitude fidelity improvement over standard QPT. Our results provide a practical and precise method for assessing quantum gate fidelity and enhancing QPT on a given hardware.
We introduce a method to enhance the precision and accuracy of Quantum Process Tomography (QPT) by mitigating the errors caused by state preparation and measurement (SPAM), readout and shot noise. Instead of performing QPT solely on a single gate, we propose performing QPT on a sequence of multiple applications of the same gate. The method involves the measurement of the Pauli transfer matrix (PTM) by standard QPT of the multipass process, and then deduce the single-process PTM by two alternative approaches: an iterative approach which in theory delivers the exact result for small errors, and a linearized approach based on solving the Sylvester equation. We examine the efficiency of these two approaches through simulations on IBM Quantum using ibmq_qasm_simulator. Compared to the Randomized Benchmarking type of methods, the proposed method delivers the entire PTM rather than a single number (fidelity). Compared to standard QPT, our method delivers PTM with much higher accuracy and precision because it greatly reduces the SPAM, readout and shot noise errors. We use the proposed method to experimentally determine the PTM and the fidelity of the CNOT gate on the quantum processor ibmq_manila (Falcon r5.11L).
In the era of noisy intermediate-scale quantum computing, it is of crucial importance to verify quantum processes and extract information. Quantum process tomography is a typical approach, however, both resource-intensive and vulnerable to state preparation and measurement errors. Here, we propose an error-mitigated entanglement-assisted quantum process tomography (EM-EAPT) framework to address these limitations. By leveraging a maximally entangled state to reduce state preparation complexity and integrating error mitigation techniques, our method significantly enhances robustness against SPAM errors. Experimental validation on a superconducting processor demonstrates the efficacy of EM-EAPT for two-qubit and three-qubit quantum processes. Results show more accurate average gate fidelities close to the realistic estimation, achieving 98.1±\pm± 0.03% for a CNOT gate and 88.1%±\pm± 0.04% for a cascaded CNOT process after error mitigation, compared to non-mitigated implementations. This work advances practical quantum verification tools for NISQ devices, enabling higher-fidelity characterization of quantum processes under realistic noise conditions.
We introduce a method to enhance the precision and accuracy of Quantum Process Tomography (QPT) by mitigating the errors caused by state preparation and measurement (SPAM), readout and shot noise. Instead of performing QPT solely on a single gate, we propose performing QPT on a sequence of multiple applications of the same gate. The method involves the measurement of the Pauli transfer matrix (PTM) by standard QPT of the multipass process, and then deduce the single-process PTM by two alternative approaches: an iterative approach which in theory delivers the exact result for small errors, and a linearized approach based on solving the Sylvester equation. We examine the efficiency of these two approaches through simulations on IBM Quantum using IBMQ_QASM_SIMULATOR. Compared to the Randomized Benchmarking type of methods, the proposed method delivers the entire PTM rather than a single number (fidelity). Compared to standard QPT, our method delivers PTM with much higher accuracy and precision because it greatly reduces the SPAM, readout and shot noise errors. We use the proposed method to experimentally determine the PTM and the fidelity of the CNOT gate on the quantum processor IBMQ_MANILA (Falcon r5.11L).
In the current work we address the problem of quantum process tomography (QPT) in the case of imperfect preparation and measurement of the states which are used for QPT. The fuzzy measurements approach which helps us to efficiently take these imperfections into account is considered. However, to implement such a procedure one should have a detailed information about the errors. An approach for obtaining the partial information about them is proposed. It is based on the tomography of the ideal identity gate. This gate could be implemented by performing the measurement right after the initial state preparation. By using the result of the identity gate tomography we were able to significantly improve further QPT procedures. The proposed approach has been tested experimentally on the IBM superconducting quantum processor. As a result, we have obtained an increase in fidelity from 89% to 98% for Hadamard transformation and from 77% to 95% for CNOT gate.
Quantum process tomography (QPT) is a powerful tool to characterize quantum operations, but it requires considerable resources, making it impractical for more than two-qubit systems. This work proposes an alternative approach that requires significantly fewer resources for unitary process characterization with a built-in method for state preparation and measurement error mitigation. By measuring the quantum process as rotated through the XXX and YYY axes on the Bloch sphere, we can acquire enough information to reconstruct the quantum process matrix $\ensuremath{\chi}$ and measure its fidelity. We test the algorithm's performance against standard QPT using simulated and physical experiments on several IBM quantum processors and compare the resulting process matrices. We demonstrate with numerical experiments that the method can improve gate fidelity via a noise reduction in the imaginary part of the process matrix, along with a stark decrease in the number of experiments needed to perform the characterization.
ABSTRACT Quantum process tomography (QPT) plays a central role in characterizing quantum gates and circuits, diagnosing quantum devices, calibrating hardware, and supporting quantum error correction. However, conventional QPT methods face challenges related to scalability and sensitivity to noise. In this work, we propose a QPT framework based on quantum compilation, which represents quantum processes using optimized Kraus operators and Choi matrices. By formulating QPT as a compilation and optimization problem, our approach significantly reducing measurement and computational overhead while maintaining reconstruction accuracy. We benchmark the method using numerical simulations of Haar‐random unitary gates and demonstrate a reliable process reconstruction. We further apply the framework to dephasing channels with both time‐homogeneous and time‐inhomogeneous noise, as well as to depolarizing and amplitude‐damping channels, where stable performance is observed across different noise regimes. These results indicate that quantum compilation–based QPT can serve as a practical alternative to standard QPT methods for quantum process characterization and device validation.