Parallel-sequential circuits for ground states preparation

We introduce the parallel sequential (PS) circuit, an architecture that unifies and generalizes the brickwall and sequential circuits commonly used in quantum information science. By controlling the degree of parallelization, the PS circuit offers a flexible interpolation between these two types of circuits, allowing it to capture both the entanglement and correlation structures of the ground states of local gapped Hamiltonians with a circuit depth of T = O(log N) and a gate count of O(N). We numerically show the following results for the PS circuits: (1) A single-layer PS circuit efficiently prepares short-range correlated matrix product states with bond dimension D = 2 and correlation length ξ, with small error ε, using a circuit depth T~ξ log(N/ε). (2) The PS circuits' correct entanglement and correlation structure provides an advantage in finding ground states on noisy quantum devices. Specifically, compared to brickwall and sequential circuits, the PS circuit achieves lower ground-state energies in experimentally relevant regimes, where two-qubit gate noise typically exceeds idle noise. (3) The PS circuits with depth T~log N are free from (noise-induced) barren plateaus, leading to better trainability than brickwall and sequential circuits when used as variational circuit ansätze.