Towards Symmetry-Aware Efficient Simulation of Quantum Systems and Beyond
This work provides a unifying perspective for scalable approaches in quantum simulation, computation, and machine learning, though it is incremental as it builds on existing tensor network methods.
The paper addresses the challenge of efficiently simulating complex quantum systems by leveraging physics-informed priors, particularly symmetry, to enhance tensor network methods, enabling larger simulations through reduced computational costs.
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their efficiency can be further enhanced by incorporating physics-informed priors. A prominent example is symmetry: recent progress on $U(1)$-symmetric tensor networks, accelerated on GPUs and scaled to supercomputers, shows how conserved charges induce block-sparse structures that reduce computational cost and enable larger simulations. The same principle extends to general symmetries, inspiring equivariant neural networks in machine learning and guiding symmetry-preserving ansatze in variational quantum algorithms. Beyond symmetry, physics-informed design also includes strategies such as hybrid tensor networks and parallel sequential circuits, which pursue efficiency from complementary principles. This Perspective argues that physics-informed tensor networks, grounded in both symmetry and beyond-symmetry insights, provide unifying strategies for scalable approaches in quantum simulation, computation, and machine learning.