Abstract Variational quantum machine learning (VQML) models based on parameterized quantum circuits (PQC) have been expected to offer a potential quantum advantage for machine learning (ML) applications. However, comparison between VQML models and their classical counterparts is hard due to the lack of interpretability of VQML models. In this study, we introduce a graphical approach to analyze the PQC and the corresponding operation of VQML models to deal with this problem. In particular, we utilize the Stokes representation of quantum states to treat VQML models as network models based on the corresponding representations of basic gates. From this approach, we suggest the notion of active paths in the networks and relate the expressivity of VQML models with it. We investigate the growth of active paths in VQML models and observe that the expressivity of VQML models can be significantly limited for certain cases. Then we construct classical models inspired by our graphical interpretation of VQML models and show that they can emulate or outperform the outputs of VQML models for these cases. Our result provides a new way to interpret the operation of VQML models and facilitates the interconnection between quantum and classical ML areas.Abstract Variational quantum machine learning (VQML) models based on parameterized quantum circuits (PQC) have been expected to offer a potential quantum advantage for machine learning (ML) applications. However, comparison between VQML models and their classical counterparts is hard due to the lack of interpretability of VQML models. In this study, we introduce a graphical approach to analyze the PQC and the corresponding operation of VQML models to deal with this problem. In particular, we utilize the Stokes representation of quantum states to treat VQML models as network models based on the corresponding representations of basic gates. From this approach, we suggest the notion of active paths in the networks and relate the expressivity of VQML models with it. We investigate the growth of active paths in VQML models and observe that the expressivity of VQML models can be significantly limited for certain cases. Then we construct classical models inspired by our graphical interpretation of VQML models and show that they can emulate or outperform the outputs of VQML models for these cases. Our result provides a new way to interpret the operation of VQML models and facilitates the interconnection between quantum and classical ML areas.

Machine Learning Science and TechnologyJun 1, 20240 citations

Variational study of the one-dimensional t-J-V model

Gang Su

Physics Letters ADec 1, 20000 citations

Dynamical Properties of the t-J Model

C. Lavalle, Michael Brunner, Fakher F. Assaad +1 more

Springer eBooksJan 1, 20011 citation

Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm

Guillaume Verdon, Jacob A. Marks, Sasha Nanda +2 more

We introduce a new class of generative quantum-neural-network-based models called Quantum Hamiltonian-Based Models (QHBMs). In doing so, we establish a paradigmatic approach for quantum-probabilistic hybrid variational learning, where we efficiently decompose the tasks of learning classical and quantum correlations in a way which maximizes the utility of both classical and quantum processors. In addition, we introduce the Variational Quantum Thermalizer (VQT) for generating the thermal state of a given Hamiltonian and target temperature, a task for which QHBMs are naturally well-suited. The VQT can be seen as a generalization of the Variational Quantum Eigensolver (VQE) to thermal states: we show that the VQT converges to the VQE in the zero temperature limit. We provide numerical results demonstrating the efficacy of these techniques in illustrative examples. We use QHBMs and the VQT on Heisenberg spin systems, we apply QHBMs to learn entanglement Hamiltonians and compression codes in simulated free Bosonic systems, and finally we use the VQT to prepare thermal Fermionic Gaussian states for quantum simulation.We introduce a new class of generative quantum-neural-network-based models called Quantum Hamiltonian-Based Models (QHBMs). In doing so, we establish a paradigmatic approach for quantum-probabilistic hybrid variational learning, where we efficiently decompose the tasks of learning classical and quantum correlations in a way which maximizes the utility of both classical and quantum processors. In addition, we introduce the Variational Quantum Thermalizer (VQT) for generating the thermal state of a given Hamiltonian and target temperature, a task for which QHBMs are naturally well-suited. The VQT can be seen as a generalization of the Variational Quantum Eigensolver (VQE) to thermal states: we show that the VQT converges to the VQE in the zero temperature limit. We provide numerical results demonstrating the efficacy of these techniques in illustrative examples. We use QHBMs and the VQT on Heisenberg spin systems, we apply QHBMs to learn entanglement Hamiltonians and compression codes in simulated free Bosonic systems, and finally we use the VQT to prepare thermal Fermionic Gaussian states for quantum simulation.

arXiv:1910.02071Oct 4, 201944 citations

Numerical Study on the t-t′—J-J′ Model

Ken'ichi Takano, Kazuhiro Sano, Ippei Doi

Springer proceedings in physicsJan 1, 19920 citations

Estimation of the magnetic critical exponent by Tensor Product Variational Approach

Andrej Gendiar, Tomotoshi Nishino, René Derian

A variational problem for three-dimensional (3D) classical lattice models is considered with trial state given by two-dimensional (2D) uniform product of local variational weights. This approach, the tensor product variational approach (TPVA), has been applied to 3D classical models (the Ising and the Potts models). We consider a way of estimating the magnetic critical exponent $β$ for the simple 3D Ising model assuming a functional form of the spontaneous magnetization in the off critical region, where the TPVA provides reliable data.A variational problem for three-dimensional (3D) classical lattice models is considered with trial state given by two-dimensional (2D) uniform product of local variational weights. This approach, the tensor product variational approach (TPVA), has been applied to 3D classical models (the Ising and the Potts models). We consider a way of estimating the magnetic critical exponent $β$ for the simple 3D Ising model assuming a functional form of the spontaneous magnetization in the off critical region, where the TPVA provides reliable data.

arXiv:cond-mat/0412192Dec 8, 20042 citations

β

for the simple 3D Ising model assuming a functional form of the spontaneous magnetization in the off critical region, where the TPVA provides reliable data.