Quantum computational advantage with symmetric quantum matter

April 26, 2021 - Austin Daniel and Akimasa Miyake

Advantage Setting
Austin Daniel and Akimasa Miyake have recently published a paper, Quantum Computational Advantage with String Order Parameters of One-Dimensional Symmetry-Protected Topological Order in Physical Review Letters.

This work relates the detection of a particular type of many-body quantum order to an unconditional demonstration of the superior power that quantum computers have over their classical counterparts.  Namely, they invent a Bell-type test to measure a macroscopic order parameter (called a string order parameter) for a particular class of symmetric quantum states, which produces highly correlated measurement outcomes.  Reproducing these correlations classically requires a circuit whose depth grows with the system size, whereas the quantum many-body states utilized can be prepared with constant-depth circuits.  

This work broadens the class of quantum states that are useful for demonstration of quantum computational advantage to a wide class of states in a symmetry-protected topological phase, which have been of interest in near-term experiments for simulating exotic phases of quantum matter.