Symmetric Pruning in Quantum Neural Networks
- URL: http://arxiv.org/abs/2208.14057v1
- Date: Tue, 30 Aug 2022 08:17:55 GMT
- Title: Symmetric Pruning in Quantum Neural Networks
- Authors: Xinbiao Wang, Junyu Liu, Tongliang Liu, Yong Luo, Yuxuan Du, Dacheng
Tao
- Abstract summary: Quantum neural networks (QNNs) exert the power of modern quantum machines.
QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes.
We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
- Score: 111.438286016951
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Many fundamental properties of a quantum system are captured by its
Hamiltonian and ground state. Despite the significance of ground states
preparation (GSP), this task is classically intractable for large-scale
Hamiltonians. Quantum neural networks (QNNs), which exert the power of modern
quantum machines, have emerged as a leading protocol to conquer this issue. As
such, how to enhance the performance of QNNs becomes a crucial topic in GSP.
Empirical evidence showed that QNNs with handcraft symmetric ansatzes generally
experience better trainability than those with asymmetric ansatzes, while
theoretical explanations have not been explored. To fill this knowledge gap,
here we propose the effective quantum neural tangent kernel (EQNTK) and connect
this concept with over-parameterization theory to quantify the convergence of
QNNs towards the global optima. We uncover that the advance of symmetric
ansatzes attributes to their large EQNTK value with low effective dimension,
which requests few parameters and quantum circuit depth to reach the
over-parameterization regime permitting a benign loss landscape and fast
convergence. Guided by EQNTK, we further devise a symmetric pruning (SP) scheme
to automatically tailor a symmetric ansatz from an over-parameterized and
asymmetric one to greatly improve the performance of QNNs when the explicit
symmetry information of Hamiltonian is unavailable. Extensive numerical
simulations are conducted to validate the analytical results of EQNTK and the
effectiveness of SP.
Related papers
- Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks [0.0]
Quantum neural networks (QNNs) require an efficient training algorithm to achieve practical quantum advantages.
In this work, we prove a general trade-off between gradient measurement efficiency and expressivity in a wide class of deep QNNs.
We propose a general QNN ansatz called the stabilizer-logical product ansatz (SLPA) which can reach the upper limit of the trade-off inequality.
arXiv Detail & Related papers (2024-06-26T12:59:37Z) - Symmetry enhanced variational quantum imaginary time evolution [1.6872254218310017]
We provide guidance for constructing parameterized quantum circuits according to the locality and symmetries of the Hamiltonian.
Our approach can be used to implement the unitary and anti-unitary symmetries of a quantum system.
Numerical results confirm that the symmetry-enhanced circuits outperform the frequently-used parametrized circuits in the literature.
arXiv Detail & Related papers (2023-07-25T16:00:34Z) - Theory for Equivariant Quantum Neural Networks [0.0]
We present a theoretical framework to design equivariant quantum neural networks (EQNNs) for essentially any relevant symmetry group.
Our framework can be readily applied to virtually all areas of quantum machine learning.
arXiv Detail & Related papers (2022-10-16T15:42:21Z) - Adaptive construction of shallower quantum circuits with quantum spin
projection for fermionic systems [0.0]
Current devices only allow for hybrid quantum-classical algorithms with a shallow circuit depth, such as variational quantum eigensolver (VQE)
In this study, we report the importance of the Hamiltonian symmetry in constructing VQE circuits adaptively.
We demonstrate that symmetry-projection can provide a simple yet effective solution to this problem, by keeping the quantum state in the correct symmetry space, to reduce the overall gate operations.
arXiv Detail & Related papers (2022-05-14T17:08:18Z) - Theory of Quantum Generative Learning Models with Maximum Mean
Discrepancy [67.02951777522547]
We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs)
We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution.
Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
arXiv Detail & Related papers (2022-05-10T08:05:59Z) - On exploring practical potentials of quantum auto-encoder with
advantages [92.19792304214303]
Quantum auto-encoder (QAE) is a powerful tool to relieve the curse of dimensionality encountered in quantum physics.
We prove that QAE can be used to efficiently calculate the eigenvalues and prepare the corresponding eigenvectors of a high-dimensional quantum state.
We devise three effective QAE-based learning protocols to solve the low-rank state fidelity estimation, the quantum Gibbs state preparation, and the quantum metrology tasks.
arXiv Detail & Related papers (2021-06-29T14:01:40Z) - Chaos and Complexity from Quantum Neural Network: A study with Diffusion
Metric in Machine Learning [0.0]
We study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN)
We employ a statistical and differential geometric approach to study the learning theory of QNN.
arXiv Detail & Related papers (2020-11-16T10:41:47Z) - Quantum-optimal-control-inspired ansatz for variational quantum
algorithms [105.54048699217668]
A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form.
Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries.
This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
arXiv Detail & Related papers (2020-08-03T18:00:05Z) - On the learnability of quantum neural networks [132.1981461292324]
We consider the learnability of the quantum neural network (QNN) built on the variational hybrid quantum-classical scheme.
We show that if a concept can be efficiently learned by QNN, then it can also be effectively learned by QNN even with gate noise.
arXiv Detail & Related papers (2020-07-24T06:34:34Z) - Entanglement Classification via Neural Network Quantum States [58.720142291102135]
In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states.
We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine (RBM) architecture, known as Neural Network Quantum States (NNS)
arXiv Detail & Related papers (2019-12-31T07:40:23Z)
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.