VQE in the Early Fault-Tolerant Era

We examine the performance of the variational quantum eigensolver (VQE) on a small surface-code architecture. VQE and its variants are commonly considered for implementation on near-term hardware due to their ability to trade off shorter circuit depths for high sampling costs, making them less vulnerable to errors. In the early fault-tolerant era, where many errors may still escape undetected, this advantage may still be appealing; however, VQE also relies on rotations by small angles, which consume many T states. We show that even relatively low physical error rates, and correspondingly lower logical error rates, can still lead to significant degradations in performance, depending on what choices are made in how those rotations are approximated.