# Learning Quantum Processes with Quantum Statistical Queries

arXiv: https://arxiv.org/abs/2310.02075 · HTML: https://mlsanity.com/paper/2310.02075/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 111 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 30 of 31)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Efficient quantum tomography II](https://mlsanity.com/paper/1612.00034/) (2016)
- [Exponential separations between learning with and without quantum memory](https://mlsanity.com/paper/2111.05881/) (2021)
- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [Optimal Quantum Sample Complexity of Learning Algorithms](https://mlsanity.com/paper/1607.00932/) (2016)
- [A General Characterization of the Statistical Query Complexity](https://mlsanity.com/paper/1608.02198/) (2016)
- [Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix](https://mlsanity.com/paper/2212.04471/) (2022)
- [Quantum statistical query learning](https://mlsanity.com/paper/2002.08240/) (2020)
- [Efficient estimation of Pauli observables by derandomization](https://mlsanity.com/paper/2103.07510/) (2021)
- [Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problem](https://mlsanity.com/paper/1810.10938/) (2018)
- [Quantum Local Differential Privacy and Quantum Statistical Query Model](https://mlsanity.com/paper/2203.03591/) (2022)
- [Foundations for learning from noisy quantum experiments](https://mlsanity.com/paper/2204.13691/) (2022)
- [Neural network state estimation for full quantum state tomography](https://mlsanity.com/paper/1811.06654/) (2018)
- [Quantum Learning Boolean Linear Functions w.r.t. Product Distributions](https://mlsanity.com/paper/1902.08753/) (2019)
- [On the average-case complexity of learning output distributions of quantum circuits](https://mlsanity.com/paper/2305.05765/) (2023)
- [On the Hardness of PAC-learning Stabilizer States with Noise](https://mlsanity.com/paper/2102.05174/) (2021)
- [Quantum Algorithms for Sampling Log-Concave Distributions and Estimating Normalizing Constants](https://mlsanity.com/paper/2210.06539/) (2022)
- [Query-optimal estimation of unitary channels in diamond distance](https://mlsanity.com/paper/2302.14066/) (2023)
- [Classical Verification of Quantum Learning](https://mlsanity.com/paper/2306.04843/) (2023)
- [On the Role of Entanglement and Statistics in Learning](https://mlsanity.com/paper/2306.03161/) (2023)
- [Quantum Physical Unclonable Functions: Possibilities and Impossibilities](https://mlsanity.com/paper/1910.02126/) (2019)
- [Breaking Symmetric Cryptosystems using Quantum Period Finding](https://mlsanity.com/paper/1602.05973/) (2016)
- [Quantum non-malleability and authentication](https://mlsanity.com/paper/1610.04214/) (2016)
- [A Unified Framework For Quantum Unforgeability](https://mlsanity.com/paper/2103.13994/) (2021)
- [Learning Classical Readout Quantum PUFs based on single-qubit gates](https://mlsanity.com/paper/2112.06661/) (2021)
- [Unforgeable Quantum Encryption](https://mlsanity.com/paper/1709.06539/) (2017)

## Built on by (most cited first, 4 of 4)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Agentic Publication Protocol: An Attempt to Modernize Scientific Publication](https://mlsanity.com/paper/2606.27386/) (2026)
- [Noise-tolerant learnability of shallow quantum circuits from statistics and the cost of quantum pseudorandomness](https://mlsanity.com/paper/2405.12085/) (2024)

## Abstract (arXiv)

In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with respect to diamond distance. For the former, we present an efficient average-case algorithm along with a nearly matching lower bound with respect to the number of observables to be predicted. For the latter, we present average-case query complexity lower bounds for learning classes of unitaries. We obtain an exponential lower bound for learning unitary 2-designs and a doubly exponential lower bound for Haar-random unitaries. Finally, we demonstrate the practical relevance of our access model by applying our learning algorithm to attack an authentication protocol using Classical-Readout Quantum Physically Unclonable Functions, partially addressing an important open question in quantum hardware security.