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Advanced Quantum Technologies

Advancing Quantum Process Tomography Through Quantum Compilation

Huynh Le Dan Linh, Vu Tuan Hai, Le Bin Ho

Published Feb 1, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.1002/qute.202500494

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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.
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.
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.
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.
We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems by learning a process representation using Kraus operators. The Kraus form ensures that the reconstructed process is completely positive. To make the process trace preserving, we use a constrained gradient-descent (GD) approach on the so-called Stiefel manifold during optimization to obtain the Kraus operators. Our ansatz uses a few Kraus operators to avoid direct estimation of large process matrices, e.g., the Choi matrix, for low-rank quantum processes. The GD-QPT matches the performance of both compressed-sensing (CS) and projected least-squares (PLS) QPT in benchmarks with two-qubit random processes, but shines by combining the best features of these two methods. Similar to CS (but unlike PLS), GD-QPT can reconstruct a process from just a small number of random measurements, and similar to PLS (but unlike CS) it also works for larger system sizes, up to at least five qubits. We envisage that the data-driven approach of GD-QPT can become a practical tool that greatly reduces the cost and computational effort for QPT in intermediate-scale quantum systems.
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).
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of quantum gates, that may be used as the building blocks of quantum computers. We here consider unitary (possibly dense, i.e. without sparsity constraints) processes, which corresponds to isolated systems. Moreover, we develop a QPT method applicable to a significant number of qubits and hence to a high state space dimension, which allows one to tackle more complex problems. Using the unitarity of the process allows us to propose a method that first achieves part of QPT by performing an eigenanalysis of the estimated density matrix of a process output. We then complete the QPT by using another state differently. The relevance of our method is validated by means of simulations.