# Classical Simulation of Variational Quantum Classifiers using Tensor Rings

arXiv: https://arxiv.org/abs/2201.08878 · HTML: https://mlsanity.com/paper/2201.08878/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 21 Jan 2022.

## Builds on (most cited first, 8 of 8)

- [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)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Wide Compression: Tensor Ring Nets](https://mlsanity.com/paper/1802.09052/) (2018)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Supervised Learning with Projected Entangled Pair States](https://mlsanity.com/paper/2009.09932/) (2020)
- [TensorNetwork for Machine Learning](https://mlsanity.com/paper/1906.06329/) (2019)

## Built on by (most cited first, 3 of 3)

- [Multi-task Hierarchical Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/2305.12633/) (2023)
- [Tensor Ring Optimized Quantum-Enhanced Tensor Neural Networks](https://mlsanity.com/paper/2310.01515/) (2023)
- [Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimization](https://mlsanity.com/paper/2307.03884/) (2023)

## Abstract (arXiv)

In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the boundaries of the classical simulation of VQCs to effectively benchmark the algorithms. Classically simulating VQCs can also provide the quantum algorithms with a better initialization reducing the amount of quantum resources needed to train the algorithm. This manuscript proposes an algorithm that compresses the quantum state within a circuit using a tensor ring representation which allows for the implementation of VQC based algorithms on a classical simulator at a fraction of the usual storage and computational complexity. Using the tensor ring approximation of the input quantum state, we propose a method that applies the parametrized unitary operations while retaining the low-rank structure of the tensor ring corresponding to the transformed quantum state, providing an exponential improvement of storage and computational time in the number of qubits and layers. This approximation is used to implement the tensor ring VQC for the task of supervised learning on Iris and MNIST datasets to demonstrate the comparable performance as that of the implementations from classical simulator using Matrix Product States.