Constant-depth preparation of matrix product states with adaptive quantum circuits*

Matrix product states comprise a broad class of physically interesting entangled states highly relevant to condensed matter physics, quantum chemistry, and quantum machine learning. While it is well known that any matrix product state can be exactly prepared using a linear-depth circuit, decoherence limits current NISQ-era processors to fairly shallow-depth circuits, inhibiting the preparation of matrix product states larger than a few sites. In this talk, I will present a general method capable of deterministically preparing a wide variety of matrix product states in constant depth, including paradigmatic examples such as the AKLT state, the GHZ state, and the Majumdar-Ghosh state. I will show how the core ingredients of this algorithm -- unitary gates, midcircuit measurements, classical feedforward, and symmetries of the target state -- can be blended to produce a completely deterministic protocol, despite the use of non-unitary circuit components. Finally, I will show that our constant-depth, measurement-assisted approach experimentally outperforms its unitary linear-depth counterpart in the prepartion of the AKLT state on an IBM Quantum processor.