Rivaling Near-Term Quantum Computers with Tensor Networks

by Miles Stoudenmire (Flatiron CCQ)

Friday Aug 6, 2021, 3:00 PM → 4:00 PM America/New_York

Quantum computing is currently generating great excitement and receiving large investments by major tech companies. One recent experiment by a group at Google specifically performed a task that would definitely be impossible for a regular, classical computer. But when taking into account the analog nature of Google's device, which incurs a small error at every step, is the real difficulty of the task unchanged?

Progress in simulations of quantum many-body systems have led to classical computing techniques with tradeoffs similar to Google's device. These techniques, based on tensor networks, can also run similar quantum programs or "circuits" efficiently as long as they make a small error at each step too. So in this more realistic comparison, does the quantum computer still beat the classical one?

After introducing the details of Google's experiment and quantum circuits, and the classical tensor network techniques we used to simulate them, I will unpack some conclusions from the comparisons we carried out. We find that in some regimes, tensor network methods set a very high bar for quantum computer hardware to clear, and that this bar may have a "universal" value in a specific sense. While Google's results still edge out our best classical results for now, the closeness of the competition suggests that this race is just beginning.