Efficient Learning Algorithms for Noisy Quantum State and Process Tomography

TL;DR

This paper presents a scalable, efficient, and noise-robust quantum state and process tomography method that requires polynomial resources, enabling practical characterization of large quantum systems.

Contribution

The authors develop a provably efficient, structure-agnostic learning framework for noisy quantum states and channels, extending to both unital and non-unital processes with polynomial sample complexity.

Findings

Requires only polynomial samples and classical processing

Achieves high success probability over local random circuit ensembles

Demonstrates robustness and accuracy through numerical simulations

Abstract

Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system size. Here, we introduce a provably efficient and structure-agnostic learning framework for noisy $n$-qubit quantum circuits under generic noise with arbitrary noise strength. We first develop a sample-efficient learning algorithm for unital noisy quantum states. Building on this result, we extend the framework to quantum process tomography, obtaining a unified protocol applicable to both unital and non-unital channels. The resulting approach is input-agnostic and does not rely on assumptions about specific input distributions. Our theoretical analysis shows that both state and process learning require only polynomially many samples and polynomial classical post-processing in the number of qubits, while achieving near-unit success probability over ensembles generated by local random circuits. Numerical simulations of two-dimensional Hamiltonian dynamics further demonstrate the accuracy and robustness of the approach, including for structured circuits beyond the random-circuit setting assumed in the theoretical analysis. These results provide a scalable and practically relevant route toward characterizing large-scale noisy quantum devices, addressing a key bottleneck in the development of quantum technologies.