Using measurements to reduce circuit depth: Deterministic preparation of the AKLT state in constant-time on an IBM Quantum processor

The ground state of the spin-1 AKLT model is a paradigmatic example of both a matrix product state and a symmetry protected topological phase, and additionally holds promise as a resource state for measurement-based quantum computation. However, because the AKLT state has a nonzero correlation length, its exact unitary preparation requires a circuit whose depth scales linearly with system size. In this talk, we show how to overcome this limitation by augmenting a finite-depth circuit with measurements, and ultimately present a recipe to prepare the spin-1 AKLT state in constant-time. Despite our scheme's reliance on measurements, we show that it can be made entirely deterministic by leveraging the Z2 x Z2 symmetry of the AKLT state.

We carry out our measurement-assisted scheme on an IBM Quantum processor and compare its performance with the purely unitary, sequential approach. Using the string order, entanglement spectrum, and quantum teleportation fidelity as metrics, we find that our measurement-assisted scheme outperforms its unitary counterpart. This work provides an efficient strategy to prepare a specific resource state, while more broadly serving as an experimental demonstration of the practical advantage afforded by measurement-based circuit depth reduction strategies on NISQ devices.