# Energy-dependent barren plateau in bosonic variational quantum circuits

arXiv: https://arxiv.org/abs/2305.01799 · HTML: https://mlsanity.com/paper/2305.01799/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 96 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 15 of 15)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Universal discriminative quantum neural networks](https://mlsanity.com/paper/1805.08654/) (2018)
- [Adversarial quantum circuit learning for pure state approximation](https://mlsanity.com/paper/1806.00463/) (2018)
- [Learning quantum data with the quantum Earth Mover's distance](https://mlsanity.com/paper/2101.03037/) (2021)
- [Variational Quantum Circuits for Quantum State Tomography](https://mlsanity.com/paper/1912.07286/) (2019)
- [Mitigating barren plateaus of variational quantum eigensolvers](https://mlsanity.com/paper/2205.13539/) (2022)
- [Complex Networks from Classical to Quantum](https://mlsanity.com/paper/1702.08459/) (2017)
- [Towards Large-Scale Quantum Networks](https://mlsanity.com/paper/1909.08396/) (2019)
- [Entanglement formation in continuous-variable random quantum networks](https://mlsanity.com/paper/2005.12934/) (2020)

## Built on by (most cited first, 1 of 1)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)

## Abstract (arXiv)

Bosonic continuous-variable Variational quantum circuits (VQCs) are crucial for information processing in cavity quantum electrodynamics and optical systems, widely applicable in quantum communication, sensing and error correction. The trainability of such VQCs is less understood, hindered by the lack of theoretical tools such as t-design due to the infinite dimension of the physical systems involved. We overcome this difficulty to reveal an energy-dependent barren plateau in such VQCs. The variance of the gradient decays as 1/EMnu, exponential in the number of modes M but polynomial in the (per-mode) circuit energy E. The exponent nu=1 for shallow circuits and nu=2 for deep circuits. We prove these results for state preparation of general Gaussian states and number states. We also provide numerical evidence that the results extend to general state preparation tasks. As circuit energy is a controllable parameter, we provide a strategy to mitigate the barren plateau in continuous-variable VQCs.