Research

As we approach the limitations of classical hardware scaling, the development of quantum computing provides the next leap in computational capability. Quantum linear algebra explores efficient methods based on the principles of quantum mechanics, which is intrinsically linear, and applies them to real-world applications, like machine learning, optimization, and chemistry. My works have provided efficient methods for element-wise operations of matrices on quantum computers, and explored quantum advantage for transformer inference and kernel methods.

Selected works:

• N. Guo, etc., Quantum linear algebra is all you need for Transformer architectures, arXiv:2402.16714
• N. Guo, K. Mitarai, K. Fujii, Nonlinear transformation of complex amplitudes via quantum singular value transformation, Phys. Rev. Research (2024)
• S. Yang, N. Guo, M. Santha, P. Rebentrost, Quantum Alphatron: quantum advantage for learning with kernels and noise, Quantum (2023)

As classical and closed-system quantum models face scaling challenges, open-system approaches offer a new paradigm for quantum algorithms. By leveraging the natural non-unitary dynamics of Lindbladian evolution, this framework transforms environmental interactions from obstacles into computational resources. My works have introduced methods to encode and solve linear ordinary differential equations within density matrices, demonstrating how dissipation and decoherence can be harnessed as fundamental tools for quantum computation.

Selected works:

• ZX Shang, N Guo, D An, Q Zhao, Design nearly optimal quantum algorithm for linear differential equations via Lindbladians, Physical Review Letters (2025)

As we confront the immense complexity and environmental sensitivity of near-term quantum processors, the field of AI for Quantum provides a critical pathway toward practical quantum advantage. This discipline leverages powerful classical machine learning methods to address fundamental challenges in building and operating quantum computers. This also includes the theoretical analysis of the learnability of quantum states and the training of machine learning models for quantum systems.

Selected works:

• L. Ming, N. Guo, M. Luo, P. Rebentrost, Provable learning of quantum states with graphical models, arXiv:2309.09235