Preparing valence-bond-solid states on noisy intermediate-scale quantum computers

Quantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on gate-based computer general class of spin wave functions, the so-called valence-bond-solid (VBS) states, that are important for two reasons. First, VBS states exact ground interacting models introduced by Affleck, Kennedy, Lieb, and Tasaki (AKLT). Second, two-dimensional universal resource measurement-based computing. We find schemes prepare based their tensor-network representations yield circuits too deep be within reach noisy intermediate-scale (NISQ) computers. then apply nondeterministic method herein proposed spin-1 spin-$3/2$ AKLT defined one dimension honeycomb lattice, respectively. Shallow depth independent lattice size explicitly derived both cases, making use optimization outperform standard basis gate decomposition methods. The probabilistic nature routine translates into an average number repetitions successfully scales exponentially with sites $N$. However, strategies quadratically reduce this repetition overhead any bipartite devised. Our approach should permit NISQ processors explore model variants thereof, outperforming conventional numerical near future.