Enhancing Quantum Circuit Simulations through Structured Tensor Algebra Optimization

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In today's rapidly changing world, quantum computation is a game-changer, offering solutions to complex problems in various fields. It opens new doors to innovation and scientific progress, from enhancing data security to advancing drug discovery and improving computational efficiency. In parallel, quantum simulation on classical computers serves as a test lab for quantum ideas, ensuring they work correctly and aiding in learning about quantum science. These tools bridge two different worlds, making it easier to learn, discover, and innovate.Among the range of quantum simulation techniques, which include digital quantum simulations, variational quantum algorithms, quantum approximate optimization algorithms (QAOA), quantum annealing, and matrix product states, the latter appears as a notable option. They efficiently represent quantum states, particularly when dealing with highly complex systems. Their compact structure offers efficient storage and manipulation, making them a highly promising choice. However, challenges arise when optimizing the tensor network structure for different simulations, as finding the perfect configuration can be a computationally intensive task.This project addresses these challenges and boosts the efficiency of matrix product states in quantum simulations. We aim to develop techniques that can automatically identify and utilize optimal tensor network structures for different quantum tasks. This way, we can maximize the efficiency of matrix product states without dealing with the complexities often associated with manual optimization, as seen in existing quantum simulators. This approach has the potential to be a groundbreaking advancement in quantum simulation techniques, enabling us to tackle a wider range of complex problems more easily and quickly.Taking inspiration from the pioneering work by Ghorbani et al. on structured tensor algebra, as described in their paper "Compiling Structured Tensor Algebra," we plan to employ a symbolic computation framework called "StructTensor". This innovative approach will help us capture the structure, sparsity, and redundancy within quantum computations, leading to highly efficient simulations.Through a rigorous mathematical foundation, we will demonstrate the soundness of our symbolic structure computation and associated optimizations. We anticipate that this approach will outperform existing frameworks in various quantum computation workloads, ultimately accelerating quantum circuit simulations and advancing the field of quantum computing.