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).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).

Scientific ReportsAug 6, 20241 citation

Quantum process tomography: high fidelity methods

Станчо Станчев, Stancho G. Stanchev

The dissertation "Quantum Process Tomography: High Fidelity Methods" focuses on quantum tomographic methods using repeated (multi-pass) applications of quantum processes, which allows for the amplification of very small errors to measurable levels. The thesis is based on three studies that illustrate this approach. The first study introduces the Multi-pass Quantum Process Tomography (MQPT) method, which mitigates the measurement errors caused by state preparation and measurement (SPAM), readout errors, and statistical (shot noise) errors. The method employs some standard tomographic techniques applied to a multi-pass quantum gate or process, after which the single process is determined with significantly higher accuracy and precision through post-processing. The effectiveness of MQPT has been demonstrated through simulations and experiments on IBM Quantum processors, achieving substantial enhancement on accuracy and precision. The second study investigates the dynamics of quantum multi-level systems interacting with pulse sequences that exhibit Wigner-Majorana and Morris-Shore symmetries. Exact analytical formulas have been derived to describe these processes, revealing important characteristics of these interactions. The third study focuses on precision methods for characterization of high fidelity Raman qubit gates with Morris-Shore dynamic symmetry. By repeatedly applying the same gate, coherent errors are amplified to measurable levels, enabling more precise...The dissertation "Quantum Process Tomography: High Fidelity Methods" focuses on quantum tomographic methods using repeated (multi-pass) applications of quantum processes, which allows for the amplification of very small errors to measurable levels. The thesis is based on three studies that illustrate this approach. The first study introduces the Multi-pass Quantum Process Tomography (MQPT) method, which mitigates the measurement errors caused by state preparation and measurement (SPAM), readout errors, and statistical (shot noise) errors. The method employs some standard tomographic techniques applied to a multi-pass quantum gate or process, after which the single process is determined with significantly higher accuracy and precision through post-processing. The effectiveness of MQPT has been demonstrated through simulations and experiments on IBM Quantum processors, achieving substantial enhancement on accuracy and precision. The second study investigates the dynamics of quantum multi-level systems interacting with pulse sequences that exhibit Wigner-Majorana and Morris-Shore symmetries. Exact analytical formulas have been derived to describe these processes, revealing important characteristics of these interactions. The third study focuses on precision methods for characterization of high fidelity Raman qubit gates with Morris-Shore dynamic symmetry. By repeatedly applying the same gate, coherent errors are amplified to measurable levels, enabling more precise...

Sep 17, 20240 citations

Quantum Process Tomography with Digital Twins of Error Matrices

Tangyou Huang, Akshay Gaikwad, Ilya N. Moskalenko +19 more

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.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.

arXiv:2505.07725Physical Review LettersNov 13, 20251 citation

Parametrized process characterization with reduced resource requirements

Vicente Leyton‐Ortega, Tyler Kharazi, Raphael C. Pooser

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 $X$ and $Y$ 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.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 $X$ and $Y$ 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.

arXiv:2109.10873Physical Review AMay 5, 20220 citations

PCA-based post-processing in quantum process tomography: An experimental study

Md. Zubair, Md. Sazid-Al-Emon, Mohammad Obaidur Rahman +1 more

Quantum Process Tomography (QPT) is a fundamental technique to characterize quantum operations. However, its precision gets hampered while running in real quantum hardware due to inherent noise. In our study, we propose a post-processing method using principal component analysis (PCA) to improve the fidelity of noisy gates. We first implemented the standard QPT on various gates ranging from single-qubit to three-qubit in simulation under depolarizing error scenarios and on Fake IBM_Brisbane and ran single and two-qubit gates (H, CX, and SQSCZ) on real quantum hardware (IBM_Brisbane); the three-qubit CCX is evaluated in simulation only. After that, the reconstructed Choi matrix is decomposed into real and imaginary components. Then, by applying a PCA-based approach, we show steady improvements in a variety of quantitative performance indicators in addition to process fidelity while also maintaining the physical constraints of the Choi matrix. Additionally, PCA performed better or similarly when compared to CVX-based maximum-likelihood reconstruction and linear inversion. Although PCA improves QPT reconstructions, it is unable to address the fundamental scalability issue of QPT since it cannot overcome the exponential scaling with qubit number.Quantum Process Tomography (QPT) is a fundamental technique to characterize quantum operations. However, its precision gets hampered while running in real quantum hardware due to inherent noise. In our study, we propose a post-processing method using principal component analysis (PCA) to improve the fidelity of noisy gates. We first implemented the standard QPT on various gates ranging from single-qubit to three-qubit in simulation under depolarizing error scenarios and on Fake IBM_Brisbane and ran single and two-qubit gates (H, CX, and SQSCZ) on real quantum hardware (IBM_Brisbane); the three-qubit CCX is evaluated in simulation only. After that, the reconstructed Choi matrix is decomposed into real and imaginary components. Then, by applying a PCA-based approach, we show steady improvements in a variety of quantitative performance indicators in addition to process fidelity while also maintaining the physical constraints of the Choi matrix. Additionally, PCA performed better or similarly when compared to CVX-based maximum-likelihood reconstruction and linear inversion. Although PCA improves QPT reconstructions, it is unable to address the fundamental scalability issue of QPT since it cannot overcome the exponential scaling with qubit number.

AVS Quantum ScienceFeb 23, 20260 citations

Error-mitigated entanglement-assisted quantum process tomography

Zhihao Wu, Lingling Lao, Chengqi Zhuke +6 more

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.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.

arXiv:2502.10715Feb 15, 20250 citations

X

and

Y

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.

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0.03% for a CNOT gate and 88.1%

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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.