# Learning Temporal Quantum Tomography

arXiv: https://arxiv.org/abs/2103.13973 · HTML: https://mlsanity.com/paper/2103.13973/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 97 references that are in the map.
- First posted on arXiv 25 Mar 2021.

## Builds on (most cited first, 8 of 8)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [Temporal Information Processing on Noisy Quantum Computers](https://mlsanity.com/paper/2001.09498/) (2020)
- [A Unifying Framework for Information Processing in Stochastically Driven Dynamical Systems](https://mlsanity.com/paper/1906.04608/) (2019)
- [Adaptive Quantum State Tomography with Neural Networks](https://mlsanity.com/paper/1812.06693/) (2018)
- [Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems](https://mlsanity.com/paper/1901.01653/) (2019)
- [Higher-Order Quantum Reservoir Computing](https://mlsanity.com/paper/2006.08999/) (2020)
- [Optimal short-term memory before the edge of chaos in driven random recurrent networks](https://mlsanity.com/paper/1912.11213/) (2019)

## Built on by (most cited first, 9 of 9)

- [Adaptive Online Learning of Quantum States](https://mlsanity.com/paper/2206.00220/) (2022)
- [Infinite-dimensional reservoir computing](https://mlsanity.com/paper/2304.00490/) (2023)
- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (2023)
- [Feedback-driven recurrent quantum neural network universality](https://mlsanity.com/paper/2506.16332/) (2025)
- [Iterative Quantum Feature Maps](https://mlsanity.com/paper/2506.19461/) (2025)
- [Quantum Noise-Induced Reservoir Computing](https://mlsanity.com/paper/2207.07924/) (2022)
- [Quantum-Classical Hybrid Information Processing via a Single Quantum System](https://mlsanity.com/paper/2209.00497/) (2022)
- [Multifunctional physical reservoir computing in soft tensegrity robots](https://mlsanity.com/paper/2507.21496/) (2025)
- [Quantum reservoir computing in Jaynes-Cummings models: Nonlinear memory and time-series prediction](https://mlsanity.com/paper/2510.00171/) (2025)

## Abstract (arXiv)

Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. The quantum state is characterized from experimental measurements, using a procedure known as tomography, which requires a vast number of resources. Furthermore, the tomography for a quantum device with temporal processing, which is fundamentally different from the standard tomography, has not been formulated. We develop a practical and approximate tomography method using a recurrent machine learning framework for this intriguing situation. The method is based on repeated quantum interactions between a system called quantum reservoir with a stream of quantum states. Measurement data from the reservoir are connected to a linear readout to train a recurrent relation between quantum channels applied to the input stream. We demonstrate our algorithms for quantum learning tasks followed by the proposal of a quantum short-term memory capacity to evaluate the temporal processing ability of near-term quantum devices.