Quantum Algorithms and Simulation

Quantum Simulation of Physical Sciences

Theoretical physical sciences (chemistry, condensed matter physics, and biology) have made tremendous progress towards modeling physical processes, largely by relying on classical algorithms and computational resources. However, Nature is inherently quantum, and it is critical to harness quantum resources to simulate and understand physical processes. Quantum computers provide enormous computational power, while the best ways to use them for simulating physical sciences remain unclear. We develop novel paradigms to tackle both static problems such as electronic structure and dynamic problems such as real-time evolution of quantum systems, by combining the recent discovery of a powerful quantum singular value transformation (QSVT) algorithm and other quantum information concepts to fully unleash the power of quantum computers.

• Electronic Structure

Electronic structure theory studies the eigenstates and eigenenergies of many-electron interacting systems. Exact solutions of electronic structure on classical computers are intractable for large systems. We are interested in potential quantum advantages of quantum computers for such problems.



 

• Real-Time Dynamics

Real-time dynamics (Hamiltonian simulation) of interacting quantum systems are notoriously difficult on classical computers but they can be efficiently simulated on quantum computers. We are interested in developing efficient Hamiltonian simulation algorithms based on hybrid qubit-bosonic quantum resources to solve practical chemistry problems that are relevant to photosynthesis and catalysis, which often involve both electron and nuclei motion.



 

• Finite-Temperature and Extended Systems

We are also interested in simulating statistical properties of interacting quantum systems at a finite temperature. We aim to integrate state-of-the-art classical algorithms (such as quantum Monte Carlo) and quantum subroutines to enable efficient simulation of extended systems such as quantum materials with unprecedented accuracy and efficiency.

Robustness of Quantum Algorithms

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We are interested in exploring novel ways to build robustness into quantum algorithms at a coarse-grained or system level.