In this work, we present a general framework to calculate the lower bound for simulating a broad class of quantum Markov semigroups. Given a fixed accessible unitary set, we introduce the concept of convexified circuit depth to quantify the quantum simulation cost and analyze the necessary circuit depth to construct a quantum simulation scheme that achieves a specific order. Our framework can be applied to both unital and non-unital quantum dynamics, and the tightness of our lower bound technique is illustrated by showing that the upper and lower bounds coincide in several examples. The talk is based on arXiv:2303.11304 and arXiv:2407.15357.

Speaker Biography:

Peixue Wu got his Bachelor’s degree in mathematics at Fudan University. Later, he got his PhD in mathematics at University of Illinois at Urbana and Champaign under the supervision of Marius Junge and Renming Song. He is now a postdoctoral fellow at University of Waterloo and his research interest is quantum information theory.