# Single-preparation unsupervised quantum machine learning: concepts and applications

arXiv: https://arxiv.org/abs/2101.01442 · HTML: https://mlsanity.com/paper/2101.01442/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 124 references that are in the map.
- First posted on arXiv 5 Jan 2021.

## Builds on (most cited first, 5 of 5)

- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Learning Independent Features with Adversarial Nets for Non-linear ICA](https://mlsanity.com/paper/1710.05050/) (2017)
- [Classification and reconstruction of optical quantum states with deep neural networks](https://mlsanity.com/paper/2012.02185/) (2020)
- [Quantum Hamiltonian Identification with Classical Colored Measurement Noise](https://mlsanity.com/paper/1905.01625/) (2019)
- [Quantum process tomography with unknown single-preparation input states](https://mlsanity.com/paper/1909.08401/) (2019)

## Built on by (most cited first, 2 of 2)

- [Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning](https://mlsanity.com/paper/2304.03398/) (2023)
- [Beyond the density operator and Tr(ρ A): Exploiting the higher-order statistics of random-coefficient pure states for quantum information processing](https://mlsanity.com/paper/2204.10031/) (2022)

## Abstract (arXiv)

The term "machine learning" especially refers to algorithms that derive mappings, i.e. intput/output transforms, by using numerical data that provide information about considered transforms. These transforms appear in many problems, related to classification/clustering, regression, system identification, system inversion and input signal restoration/separation. We here first analyze the connections between all these problems, in the classical and quantum frameworks. We then focus on their most challenging versions, involving quantum data and/or quantum processing means, and unsupervised, i.e. blind, learning. Moreover, we propose the quite general concept of SIngle-Preparation Quantum Information Processing (SIPQIP). The resulting methods only require a single instance of each state, whereas usual methods have to very accurately create many copies of each fixed state. We apply our SIPQIP concept to various tasks, related to system identification (blind quantum process tomography or BQPT, blind Hamiltonian parameter estimation or BHPE, blind quantum channel identification/estimation, blind phase estimation), system inversion and state estimation (blind quantum source separation or BQSS, blind quantum entangled state restoration or BQSR, blind quantum channel equalization) and classification. Numerical tests show that our framework moreover yields much more accurate estimation than the standard multiple-preparation approach. Our methods are especially useful in a quantum computer, that we propose to more briefly call a "quamputer": BQPT and BHPE simplify the characterization of the gates of quamputers; BQSS and BQSR allow one to design quantum gates that may be used to compensate for the non-idealities that alter states stored in quantum registers, and they open the way to the much more general concept of self-adaptive quantum gates (see longer version of abstract in paper).