# On quantum backpropagation, information reuse, and cheating measurement collapse

arXiv: https://arxiv.org/abs/2305.13362 · HTML: https://mlsanity.com/paper/2305.13362/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 17 of 17)

- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Wider or Deeper: Revisiting the ResNet Model for Visual Recognition](https://mlsanity.com/paper/1611.10080/) (2016)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Exponential separations between learning with and without quantum memory](https://mlsanity.com/paper/2111.05881/) (2021)
- [Online Learning of Quantum States](https://mlsanity.com/paper/1802.09025/) (2018)
- [Deep Generative Stochastic Networks Trainable by Backprop](https://mlsanity.com/paper/1306.1091/) (2013)
- [Quantum SDP-Solvers: Better upper and lower bounds](https://mlsanity.com/paper/1705.01843/) (2017)
- [Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits](https://mlsanity.com/paper/2001.00550/) (2020)

## Built on by (most cited first, 30 of 32)

- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Training-efficient density quantum machine learning](https://mlsanity.com/paper/2405.20237/) (2024)
- [Generative quantum advantage for classical and quantum problems](https://mlsanity.com/paper/2509.09033/) (2025)
- [Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data](https://mlsanity.com/paper/2306.07331/) (2023)
- [Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks](https://mlsanity.com/paper/2406.18316/) (2024)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [Opportunities and limitations of explaining quantum machine learning](https://mlsanity.com/paper/2412.14753/) (2024)
- [Quantum Doubly Stochastic Transformers](https://mlsanity.com/paper/2504.16275/) (2025)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Coreset selection can accelerate quantum machine learning models with provable generalization](https://mlsanity.com/paper/2309.10441/) (2023)
- [Exponential Quantum Communication Advantage in Distributed Inference and Learning](https://mlsanity.com/paper/2310.07136/) (2023)
- [Quantum Supervised Learning](https://mlsanity.com/paper/2407.17161/) (2024)
- [Enhancing variational quantum algorithms by balancing training on classical and quantum hardware](https://mlsanity.com/paper/2503.16361/) (2025)
- [Iterative Quantum Feature Maps](https://mlsanity.com/paper/2506.19461/) (2025)
- [Efficient Gradient Estimation for Parameterized Quantum Systems with Lie Algebraic Symmetries](https://mlsanity.com/paper/2404.05108/) (2024)
- [PALQO: Physics-informed Model for Accelerating Large-scale Quantum Optimization](https://mlsanity.com/paper/2509.20733/) (2025)
- [Accelerating Inference for Multilayer Neural Networks with Quantum Computers](https://mlsanity.com/paper/2510.07195/) (2025)
- [Hybrid Quantum-Classical Recurrent Neural Networks](https://mlsanity.com/paper/2510.25557/) (2025)
- [Scaling Quantum Machine Learning without Tricks: Full-Resolution and Diverse Image Generation](https://mlsanity.com/paper/2603.00233/) (2026)
- [Position: Zeroth-Order Optimization in Deep Learning Is Underexplored, Not Underpowered](https://mlsanity.com/paper/2605.15622/) (2026)
- [Scalable On-Hardware Training of Quantum Neural Networks and Application to Clinical Data Imputation](https://mlsanity.com/paper/2606.03517/) (2026)
- [Computing the gradients with respect to all parameters of a quantum neural network using a single circuit](https://mlsanity.com/paper/2307.08167/) (2023)
- [Randomized Benchmarking of Local Zeroth-Order Optimizers for Variational Quantum Systems](https://mlsanity.com/paper/2310.09468/) (2023)
- [Efficient Quantum Gradient and Higher-order Derivative Estimation via Generalized Hadamard Test](https://mlsanity.com/paper/2408.05406/) (2024)
- [Differential equation quantum solvers: engineering measurements to reduce cost](https://mlsanity.com/paper/2503.22656/) (2025)
- [Provably Robust Training of Quantum Circuit Classifiers Against Parameter Noise](https://mlsanity.com/paper/2505.18478/) (2025)
- [Sample-optimal learning of quantum states using gentle measurements](https://mlsanity.com/paper/2505.24587/) (2025)

## Abstract (arXiv)

The success of modern deep learning hinges on the ability to train neural networks at scale. Through clever reuse of intermediate information, backpropagation facilitates training through gradient computation at a total cost roughly proportional to running the function, rather than incurring an additional factor proportional to the number of parameters - which can now be in the trillions. Naively, one expects that quantum measurement collapse entirely rules out the reuse of quantum information as in backpropagation. But recent developments in shadow tomography, which assumes access to multiple copies of a quantum state, have challenged that notion. Here, we investigate whether parameterized quantum models can train as efficiently as classical neural networks. We show that achieving backpropagation scaling is impossible without access to multiple copies of a state. With this added ability, we introduce an algorithm with foundations in shadow tomography that matches backpropagation scaling in quantum resources while reducing classical auxiliary computational costs to open problems in shadow tomography. These results highlight the nuance of reusing quantum information for practical purposes and clarify the unique difficulties in training large quantum models, which could alter the course of quantum machine learning.