• Quantum algorithms for differential equations
• Quantum algorithms for machine learning
• Quantum sensing
• Continuous-variable quantum systems

Hi there! I'm Nana Liu, and I'm thrilled to be a tenure-track associate professor and principal investigator at Shanghai Jiao Tong University (SJTU). At my Quantum Information and Technologies (QIT) group, we dive into the fascinating worlds of continuous-variable quantum information, quantum algorithms for scientific computing, quantum machine learning, and the quantum internet.
Our research is incredibly diverse and interdisciplinary. Recently, we've developed innovative methods to transform time-dependent Hamiltonian problems into time-independent ones, which is also applicable to non-autonomous linear partial differential equations (PDEs). This breakthrough has significant implications for quantum simulation, offering new ways to tackle complex differential equations. I'm particularly excited about our work on analog quantum simulation of PDEs, showing the potential of continuous-variable systems for simulating classical physics problems.
We've also made strides in establishing the rigorous foundations of quantum simulation. Our work on the Schrodingerisation of differential equations provides an alternative demonstration of the Sz. Nagy dilation theorem and has broad applications, including the quantum simulation of Maxwell's equations with boundary conditions. This research opens up new perspectives on quantum thermodynamics through non-destructive probing techniques.
Our team is passionate about quantum-enhanced measurements and learning. We've advanced shadow tomography for continuous-variable quantum states and are developing quantum algorithms for linear and nonlinear ODEs and PDEs, focusing on time complexity and uncertainty quantification—key elements for practical quantum computing applications.
My journey in quantum science has been incredibly rewarding. Before joining SJTU, I was a postdoctoral researcher at the Center for Quantum Technologies (CQT) in Singapore. I earned my PhD from the University of Oxford as a Clarendon Scholar, and my academic interests span quantum mechanics, quantum process tomography, and high-energy particle physics. If you share any of these interests or just want to say hello, please drop me a line. We are always excited to connect with fellow enthusiasts and potential collaborators.

• Reinforcment Learning
• Quantum machine learning

• Numerical PDEs
• Quantum algorithms
• Quantum simulations

I am deeply interested in the numerical solutions of partial differential equations (PDEs). Solving differential equations numerically essentially involves simulating the real physical world on a computer. Traditional methods such as the finite element method and the finite difference method often face the curse of dimensionality when implemented on classical computers, with time complexity growing exponentially as the number of dimensions increases. Quantum computing algorithms, such as the Schrödingerisation method proposed by Professors Shi Jin, Nana Liu, and Yue Yu, provide an elegant solution to this problem. Their approach involves transforming PDEs into the Schrödinger equation, which can then be evolved over time through Hamiltonian simulation.
The concept of Hamiltonian simulation was introduced by Richard Feynman in 1982. He proposed the idea of using hardware based on the fundamental principles of quantum mechanics to construct a computer capable of efficiently simulating the evolution of quantum systems—what we now know as a quantum computer. Hamiltonian simulation allows us to leverage quantum computers to simulate quantum systems, thereby recreating the quantum physical world. This is an incredibly exciting development and represents the direction I am most passionate about pursuing in my research.

• Quantum machnie learning
• Schrodingerisation for PDE solving
• Continuous-variable quantum computing approach

My research interests primarily focus on quantum computing algorithms, their simulation, and evaluating the challenges associated with their physical implementation. Although I have some experience with digital quantum algorithms, I am currently more inclined toward exploring continuous-variable quantum computing algorithms.
Nana's work has demonstrated the potential of continuous-variable quantum computing algorithms in solving problems related to partial differential equations, including nonlinear partial differential equations. This has significant implications for a wide range of real-world applications. However, several areas still need further development in this field. These include the initial implementation using appropriate physical systems, efficiently extending these methods to more complex nonlinear problems, and the effective preparation of initial states.
I am keen to contribute to these areas by refining the current methodologies and exploring new applications for continuous-variable quantum algorithms. My goal is to develop more efficient and practical quantum computing solutions that can address valuable problems in various domains.

• Quantum algorithms
• Schrodingerisation for PDE solving
• Quantum simulations
• Continuous variable quantum computing

My scientific interest primarily revolves around the intersection of quantum computing and computational physics, particularly in the simulation of physical systems that challenge classical computational limits. The area of partial differential equations (PDEs), which are central to modeling phenomena in physics, engineering, and even finance, offers fertile ground for applying quantum computational techniques. My focus is on developing quantum algorithms that can efficiently handle these equations, especially those that scale poorly on classical computers due to high dimensionality or non-linearity.
The pursuit of quantum advantage in simulating PDEs is not merely academic but promises substantial practical implications. For instance, improved simulation of quantum systems could lead to breakthroughs in materials science or drug discovery, where understanding complex molecular structures and interactions is essential. Moreover, in the field of quantum mechanics itself, the ability to simulate large quantum systems accurately and efficiently could uncover new physical laws or refine existing theories.
I am also interested in exploring hybrid algorithms that combine classical and quantum computation to optimize performance and feasibility in near-term quantum devices. By advancing these methods, I aim to contribute to the foundational tools that enable quantum computers to solve real-world problems more effectively than classical counterparts.

• Quantum algorithms
• Quantum simulations
• Geometry
• Finite elements theory