Characterization of quantum circuit properties in hybrid quantum-classical algorithms

Recent advances in hybrid quantum-classical algorithms allow us to find the ground state of Hamiltonians for quantum chemistry and optimization problems. This can be achieved by searching the full Hilbert space via the sequential application of single-qubit rotations and entanglement blocks (multi-qubit gates). First results [Kandala et al., Nature 549, 242–246] indicate that the high dimensionality of the molecular Hilbert space enforces us to use a large number of entanglement blocks. In this way, we reach a critical circuit depth for state of the art quantum architectures with limited coherence times, which imposes important restrictions for near-term applications. In order to reduce the number of gate operations, we investigate different entanglement schemes and evaluate their properties by means of a set of descriptors that includes concurrence, site occupation, and convergence efficiency. We discuss the scalability of these approaches, the cost of their implementation in near future quantum devices, and the computational advantage of their application in variational quantum eigensolver optimizers.