# Input Redundancy for Parameterized Quantum Circuits

arXiv: https://arxiv.org/abs/1901.11434 · HTML: https://mlsanity.com/paper/1901.11434/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2019.

## Built on by (most cited first, 30 of 33)

- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
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- [Quantum Recurrent Neural Networks for Sequential Learning](https://mlsanity.com/paper/2302.03244/) (2023)
- [Quantum Deep Hedging](https://mlsanity.com/paper/2303.16585/) (2023)
- [Let Quantum Neural Networks Choose Their Own Frequencies](https://mlsanity.com/paper/2309.03279/) (2023)
- [Potential and limitations of random Fourier features for dequantizing quantum machine learning](https://mlsanity.com/paper/2309.11647/) (2023)
- [Training robust and generalizable quantum models](https://mlsanity.com/paper/2311.11871/) (2023)
- [High Dimensional Quantum Machine Learning With Small Quantum Computers](https://mlsanity.com/paper/2203.13739/) (2022)
- [Reduction of finite sampling noise in quantum neural networks](https://mlsanity.com/paper/2306.01639/) (2023)
- [A Comparative Analysis of Adversarial Robustness for Quantum and Classical Machine Learning Models](https://mlsanity.com/paper/2404.16154/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuits](https://mlsanity.com/paper/2310.07528/) (2023)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Overfitting in quantum machine learning and entangling dropout](https://mlsanity.com/paper/2205.11446/) (2022)
- [A Leap among Quantum Computing and Quantum Neural Networks: A Survey](https://mlsanity.com/paper/2107.03313/) (2021)
- [Quantum neural network autoencoder and classifier applied to an industrial case study](https://mlsanity.com/paper/2205.04127/) (2022)
- [Expressive variational quantum circuits provide inherent privacy in federated learning](https://mlsanity.com/paper/2309.13002/) (2023)
- [Symmetry-invariant quantum machine learning force fields](https://mlsanity.com/paper/2311.11362/) (2023)
- [Generative quantum combinatorial optimization by means of a novel conditional generative quantum eigensolver](https://mlsanity.com/paper/2501.16986/) (2025)
- [Layerwise Federated Learning for Heterogeneous Quantum Clients using Quorus](https://mlsanity.com/paper/2510.06228/) (2025)
- [Quantum neural networks force fields generation](https://mlsanity.com/paper/2203.04666/) (2022)
- [BCQQ: Batch-Constraint Quantum Q-Learning with Cyclic Data Re-uploading](https://mlsanity.com/paper/2305.00905/) (2023)
- [Post-variational quantum neural networks](https://mlsanity.com/paper/2307.10560/) (2023)
- [Spectral invariance and maximality properties of the frequency spectrum of quantum neural networks](https://mlsanity.com/paper/2402.14515/) (2024)
- [Concept learning of parameterized quantum models from limited measurements](https://mlsanity.com/paper/2408.05116/) (2024)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [Expressibility-Enhancing Strategies for Quantum Neural Networks](https://mlsanity.com/paper/2211.12670/) (2022)
- [Fourier series weight in quantum machine learning](https://mlsanity.com/paper/2302.00105/) (2023)

## Abstract (arXiv)

The topic area of this paper parameterized quantum circuits (quantum neural networks) which are trained to estimate a given function, specifically the type of circuits proposed by Mitarai et al. (Phys. Rev. A, 2018). The input is encoded into amplitudes of states of qubits. The no-cloning principle of quantum mechanics suggests that there is an advantage in redundantly encoding the input value several times. We follow this suggestion and prove lower bounds on the number of redundant copies for two types of input encoding. We draw conclusions for the architecture design of QNNs.