# Data is often loadable in short depth: Quantum circuits from tensor networks for finance, images, fluids, and proteins

arXiv: https://arxiv.org/abs/2309.13108 · HTML: https://mlsanity.com/paper/2309.13108/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 63 references that are in the map.
- First posted on arXiv 22 Sep 2023.

## Builds on (most cited first, 9 of 9)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions](https://mlsanity.com/paper/1811.00414/) (2018)
- [A divide-and-conquer algorithm for quantum state preparation](https://mlsanity.com/paper/2008.01511/) (2020)
- [Fast Black-Box Quantum State Preparation](https://mlsanity.com/paper/2009.10709/) (2020)
- [QFold: Quantum Walks and Deep Learning to Solve Protein Folding](https://mlsanity.com/paper/2101.10279/) (2021)
- [Quantum pixel representations and compression for N-dimensional images](https://mlsanity.com/paper/2110.04405/) (2021)
- [Spacetime-Efficient Low-Depth Quantum State Preparation with Applications](https://mlsanity.com/paper/2303.02131/) (2023)

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

- [Radio Signal Classification by Adversarially Robust Quantum Machine Learning](https://mlsanity.com/paper/2312.07821/) (2023)
- [Training quantum machine learning models on cloud without uploading the data](https://mlsanity.com/paper/2409.04602/) (2024)

## Abstract (arXiv)

Though there has been substantial progress in developing quantum algorithms to study classical datasets, the cost of simply textitloading classical data is an obstacle to quantum advantage. When the amplitude encoding is used, loading an arbitrary classical vector requires up to exponential circuit depths with respect to the number of qubits. Here, we address this ``input problem'' with two contributions. First, we introduce a circuit compilation method based on tensor network (TN) theory. Our method -- AMLET (Automatic Multi-layer Loader Exploiting TNs) -- proceeds via careful construction of a specific TN topology and can be tailored to arbitrary circuit depths. Second, we perform numerical experiments on real-world classical data from four distinct areas: finance, images, fluid mechanics, and proteins. To the best of our knowledge, this is the broadest numerical analysis to date of loading classical data into a quantum computer. The required circuit depths are often several orders of magnitude lower than the exponentially-scaling general loading algorithm would require. Besides introducing a more efficient loading algorithm, this work demonstrates that many classical datasets are loadable in depths that are much shorter than previously expected, which has positive implications for speeding up classical workloads on quantum computers.