Advancing quantum process tomography through quantum compilation

TL;DR

This work tackles the scalability bottleneck of quantum process tomography (QPT) by introducing compilation-based QPT (CQPT), which expresses unknown quantum processes via trainable Kraus operators or Choi matrices and optimizes them using Riemannian gradient descent. The method leverages quantum compilation concepts to reduce measurement and computational overhead, notably employing single-shot measurements and enforcing CPTP structure through Kraus or Choi representations. Numerical results demonstrate robust reconstruction for Haar-random unitary gates and common noise channels (dephasing, depolarizing, amplitude damping) across varying system sizes, with favorable efficiency scaling compared to standard QPT approaches. While CQPT significantly improves practicality for larger systems and near-term devices, it faces limitations from strong noise and SPAM errors, pointing to future work in error mitigation and circuit-level implementations.

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.

Figures (13)

• Figure 1: Graphical presentation. (a) Quantum channel representation with Kraus operators. (b) Visualization of Theorem \ref{['theo:1']}. (c) Quantum channel representation using the Choi matrix. (d) Visualization of Theorem \ref{['theo:2']}.
• Figure 2: Benchmarking Haar random unitary gates. (a) Convergence of the cost function $C(\Bbbk)$ over iterations. (b) Average infidelity as a function of the qubit numbers $N$.
• Figure 3: Benchmarking Haar random unitary gates. (a) Comparison of the initial and final states, $\rho_{\rm in}$ and $\rho_{\rm f}$, for $N = 2$, where $\rho_{\rm in}$ is selected from the testing set. Here, Re and Im denote the real and imaginary parts, respectively. Green indicates positive values, while red represents negative values. (b) Comparison of intermediate quantum states $\rho_\mathcal{E}$ and $\rho_\Bbbk$ to evaluate the transformation accuracy.
• Figure 4: CQPT for dephasing noise process. (a) Average infidelity $I_F(\rho_{\rm in}, \rho_{\rm f})$ versus $\gamma$. (b) Average infidelity $I_F(\rho_\mathcal{E}, \rho_{\mathbf{J}})$ versus $\gamma$, showing the effect of noise on the optimization performance.
• Figure 5: CQPT for dephasing noise process. (a) Comparison of quantum states $\rho_\mathcal{E}$ and $\rho_{\mathbf{J}}$ at $\gamma = 0.01$, demonstrating a close match. (b) Comparison at $\gamma = 0.95$, highlighting the growing deviation between the quantum states at higher noise.

Theorems & Definitions (8)

• Theorem 1
• proof
• Remark 1
• Remark 2
• Theorem 2
• proof
• Remark 3
• proof