Quantum Resource Estimation for Simulating the SYK Model with Trotterization, qDRIFT, and Asymmetric Qubitization
The Sachdev-Ye-Kitaev (SYK) model has been identified as a promising candidate to run on early fault-tolerant quantum computers due to the relatively modest resources required to probe non-trivial physics (namely holographic duality and AdS/CFT correspondence). As such, it is crucial that the details of how to run such a simulation are well understood. Using PsiQuantum's Construct platform, we implement and analyze three different approaches to simulate the SYK model: Trotterization, qDRIFT, and asymmetric qubitization with Quantum Signal Processing. We provide an open-source library containing implementations for SYK simulation using all three methods, which we use to obtain quantum resource estimates for qubit and T gate count as functions of the number of Majorana modes and precision. We find that while qDRIFT and Trotterization benefit from a lower qubit count, the large number of T gates required lead to asymmetric qubitization being advantageous in most cases. This reinforces previous theoretical considerations. We intend both the implementations and the estimates to be useful for researchers to continue to study the SYK model and understand how the techniques and resources vary.