Effects of Symmetry Breaking in Trotterized Real-Time Dynamics
By Ayla, Alexandra
EXTERNAL MENTOR: Dr. Bharath Sambasivam, Virginia Tech Center for Quantum Information Science and Engineering
The proposed research aims to develop symmetry-preserving algorithms for simulating time-dependent quantum dynamics on quantum computers. Building on foundational work in quantum simulation and the use of product-formula (Trotterization) methods to approximate complex Hamiltonians, we will investigate new approximation strategies that respect conserved quantities inherent to the target system, such as particle number or total spin projection for symmetry-aware simulation frameworks. Conventional Trotterization decomposes the full interaction into a sequence of simpler unitary operations that can be implemented on quantum hardware, but this process can break the exact symmetries of the system, therefore allowing the quantum state to leak into other irrelevant subspaces.
The intellectual merit of this project lies in advancing the theoretical and algorithmic foundations of quantum simulation by directly addressing one of its central limitations: the breaking of phys- ical symmetries during time-evolution approximations. Conventional product-formula (Trotter) methods decompose complex interactions into implementable unitary steps but can also violate conserved quantities such as particle number or spin projection. Recent theoretical proposals have emphasized the importance of symmetry-adapted bases and constrained dynamics for improving quantum-simulation fidelity; however, a systematic framework for constructing such approximations has not yet been developed.
Beyond its immediate scientific contributions, this project will broaden the impact of quantum simulation by making it more resource-efficient and physically accurate. Additionally, this will accelerate its application to problems of chemical reactivity, materials discovery, and energy conversion.