Can the XY+Z Heisenberg Model Be Compressed Using the Yang-Baxter Equation? An Exploration of the Compression of Quantum Time Dynamic Circuits Describing Heisenberg Spin Chains
Researcher ORCID Identifier
Open Access Senior Thesis
Bachelor of Arts
Dr. Niranjan Govind
Dr. Kevin Setter
Quantum computing is currently deployed on noisy intermediate-scale quantum (NISQ) devices, which are only able to simulate circuits reliably on shallow depth quantum circuits. A promising problem on near-term quantum computers is quantum time dynamics (QTD). However, QTD circuits grow with increasing time simulations making them difficult to simulate on NISQ devices. This thesis project explores QTD simulations in variations of 1D Heisenberg spin chains with nearest-neighbor and transverse external field interactions with an eye towards studying the dynamics in broader classes of spin models. I first study the quantum Yang-Baxter equation (YBE) and how it has been shown to compress simulations of QTD of spin models without external magnetic fields and its relationship to the free fermion model. I then combine this research with similar attempts at compressing QTD simulations of spin models that include an external field like the XY+Z model. I find that the XY+Z model cannot be compressed and deployed on a NISQ device because the YBE cannot be performed on the model perfectly, however, a more generalized transverse field model can be compressed.
Caron, Miriam; Peng, Bo Dr.; Gould, Scott Dr.; Setter, Kevin Dr.; and Govind, Niranjan Dr., "Can the XY+Z Heisenberg Model Be Compressed Using the Yang-Baxter Equation? An Exploration of the Compression of Quantum Time Dynamic Circuits Describing Heisenberg Spin Chains" (2023). Pitzer Senior Theses. 136.