# Variational Quantum Circuits for Quantum State Tomography

arXiv: https://arxiv.org/abs/1912.07286 · HTML: https://mlsanity.com/paper/1912.07286/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2019.

## Built on by (most cited first, 8 of 8)

- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Quantum State Tomography using Quantum Machine Learning](https://mlsanity.com/paper/2308.10327/) (2023)
- [Energy-dependent barren plateau in bosonic variational quantum circuits](https://mlsanity.com/paper/2305.01799/) (2023)
- [Reinforcement learning to learn quantum states for Heisenberg scaling accuracy](https://mlsanity.com/paper/2412.02334/) (2024)
- [Guess, SWAP, Repeat : Capturing Quantum Snapshots in Classical Memory](https://mlsanity.com/paper/2504.14459/) (2025)
- [Knowledge Distillation for Variational Quantum Convolutional Neural Networks on Heterogeneous Data](https://mlsanity.com/paper/2509.16699/) (2025)
- [Terminal-Register Certification for Finite-Measurement Learning of Multiscale Quantum States](https://mlsanity.com/paper/2609.33567/) (2026)
- [Simulation-Based Quantum System Inference with Neural Posterior Estimation](https://mlsanity.com/paper/2609.34995/) (2026)

## Abstract (arXiv)

Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth, so that only polynomial measurements are required, even for highly-entangled states. After that, a subsequent classical circuit simulator is used to transform the information of the target quantum state from the variational quantum circuit into a familiar format. We demonstrate our method by performing numerical simulations for the tomography of the ground state of a one-dimensional quantum spin chain, using a variational quantum circuit simulator. Our method is suitable for near-term quantum computing platforms, and could be used for relatively large-scale quantum state tomography for experimentally relevant quantum states.