Permutation Invariant Encodings for Quantum Machine Learning with Point
Cloud Data
- URL: http://arxiv.org/abs/2304.03601v1
- Date: Fri, 7 Apr 2023 11:53:17 GMT
- Title: Permutation Invariant Encodings for Quantum Machine Learning with Point
Cloud Data
- Authors: Jamie Heredge, Charles Hill, Lloyd Hollenberg and Martin Sevior
- Abstract summary: We show a permutation invariant quantum encoding method, which exhibits superior generalisation performance.
We show that a permutation invariant encoding improves in accuracy as the number of points contained in the point cloud increases.
- Score: 0.27342795342528275
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum Computing offers a potentially powerful new method for performing
Machine Learning. However, several Quantum Machine Learning techniques have
been shown to exhibit poor generalisation as the number of qubits increases. We
address this issue by demonstrating a permutation invariant quantum encoding
method, which exhibits superior generalisation performance, and apply it to
point cloud data (three-dimensional images composed of points). Point clouds
naturally contain permutation symmetry with respect to the ordering of their
points, making them a natural candidate for this technique. Our method captures
this symmetry in a quantum encoding that contains an equal quantum
superposition of all permutations and is therefore invariant under point order
permutation. We test this encoding method in numerical simulations using a
Quantum Support Vector Machine to classify point clouds drawn from either
spherical or toroidal geometries. We show that a permutation invariant encoding
improves in accuracy as the number of points contained in the point cloud
increases, while non-invariant quantum encodings decrease in accuracy. This
demonstrates that by implementing permutation invariance into the encoding, the
model exhibits improved generalisation.
Related papers
- Supervised binary classification of small-scale digits images with a trapped-ion quantum processor [56.089799129458875]
We show that a quantum processor can correctly solve the basic classification task considered.
With the increase of the capabilities quantum processors, they can become a useful tool for machine learning.
arXiv Detail & Related papers (2024-06-17T18:20:51Z) - Non-Unitary Quantum Machine Learning [0.0]
We introduce several novel probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning.
Among our contributions are quantum native implementations of Residual Networks (ResNet); demonstrating a path to avoiding barren plateaus.
We also show how this framework can be used to parameterise and control the amount of symmetry in an encoding.
arXiv Detail & Related papers (2024-05-27T17:42:02Z) - Enforcing exact permutation and rotational symmetries in the application of quantum neural network on point cloud datasets [0.0]
Recent developments in the field of quantum machine learning have promoted the idea of incorporating physical symmetries in the structure of quantum circuits.
We provide a novel structure of QNN that is exactly invariant to both rotations and permutations.
arXiv Detail & Related papers (2024-05-18T02:40:30Z) - Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
Quantum computing sets the foundation for new ways of designing algorithms.
New challenges arise concerning which field quantum speedup can be achieved.
Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
arXiv Detail & Related papers (2024-02-26T09:32:07Z) - Variational Quantum and Quantum-Inspired Clustering [0.0]
We present a quantum algorithm for clustering data based on a variational quantum circuit.
The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum (NISQ) devices.
arXiv Detail & Related papers (2022-06-20T17:02:19Z) - Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard.
We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware.
The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
arXiv Detail & Related papers (2021-07-08T17:59:55Z) - Quantum Error Mitigation Relying on Permutation Filtering [84.66087478797475]
We propose a general framework termed as permutation filters, which includes the existing permutation-based methods as special cases.
We show that the proposed filter design algorithm always converges to the global optimum, and that the optimal filters can provide substantial improvements over the existing permutation-based methods.
arXiv Detail & Related papers (2021-07-03T16:07:30Z) - Facial Expression Recognition on a Quantum Computer [68.8204255655161]
We show a possible solution to facial expression recognition using a quantum machine learning approach.
We define a quantum circuit that manipulates the graphs adjacency matrices encoded into the amplitudes of some appropriately defined quantum states.
arXiv Detail & Related papers (2021-02-09T13:48:00Z) - Quantum Machine Learning for Particle Physics using a Variational
Quantum Classifier [0.0]
We propose a novel hybrid variational quantum classifier that combines the quantum gradient descent method with steepest gradient descent to optimise the parameters of the network.
We find that this algorithm has a better learning outcome than a classical neural network or a quantum machine learning method trained with a non-quantum optimisation method.
arXiv Detail & Related papers (2020-10-14T18:05:49Z) - Supervised Learning Using a Dressed Quantum Network with "Super
Compressed Encoding": Algorithm and Quantum-Hardware-Based Implementation [7.599675376503671]
Implementation of variational Quantum Machine Learning (QML) algorithms on Noisy Intermediate-Scale Quantum (NISQ) devices has issues related to the high number of qubits needed and the noise associated with multi-qubit gates.
We propose a variational QML algorithm using a dressed quantum network to address these issues.
Unlike in most other existing QML algorithms, our quantum circuit consists only of single-qubit gates, making it robust against noise.
arXiv Detail & Related papers (2020-07-20T16:29:32Z) - Permutation Matters: Anisotropic Convolutional Layer for Learning on
Point Clouds [145.79324955896845]
We propose a permutable anisotropic convolutional operation (PAI-Conv) that calculates soft-permutation matrices for each point.
Experiments on point clouds demonstrate that PAI-Conv produces competitive results in classification and semantic segmentation tasks.
arXiv Detail & Related papers (2020-05-27T02:42:29Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.