Efficient preparation of the AKLT ground state on a quantum computer

by Kevin Smith (BNL)

Monday 28 Mar 2022, 14:00 → 16:00 US/Eastern

The preparation and validation of physically interesting and useful quantum states and phases remains an important problem, particularly on modern NISQ devices. A prototypical example is the AKLT model which describes a novel, symmetry-protected topological phase of matter displaying fractionalized excitations at the edges, a finite energy gap in the bulk, and a hidden antiferromagnetic ordering. In this talk, I will describe an efficient algorithm to prepare the AKLT ground state on a quantum computer. I will begin by showing how its matrix product state representation naturally leads to a sequential algorithm with a circuit depth that is linear in the number of sites. I will then demonstrate how probabilistic measurements can be used to speed up this preparation scheme, leading to a constant time (and surprisingly deterministic) algorithm. Along the way, I will also show experimental results for small chains on an IBM device, showing good agreement with theoretical expectation.