Abstract
Recently, there has been much interest in the efficient preparation of complex quantum states using low-depth quantum circuits, such as the quantum approximate optimization algorithm (QAOA). While it has been numerically shown that such algorithms prepare certain correlated states of quantum spins with surprising accuracy, a systematic way of quantifying the efficiency of the QAOA in general classes of models has been lacking. Here, we propose that the success of the QAOA in preparing ordered states is related to the interaction distance of the target state, which measures how close that state is to the manifold of all Gaussian states in an arbitrary basis of single-particle modes. We numerically verify this for several examples of nonintegrable quantum models, including Ising models with two- and three-spin interactions and the cluster model in an external field. Our results suggest that the structure of the entanglement spectrum, as witnessed by the interaction distance, correlates with the success of QAOA state preparation, and that this correlation also contains information about different phases present in the model. We conclude that the QAOA typically finds a solution that perturbs around the closest free-fermion state.2 MoreReceived 3 August 2020Accepted 8 December 2020DOI:https://doi.org/10.1103/PRXQuantum.2.010309Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement measuresOptimization problemsQuantum controlTechniquesIsing modelQuantum InformationCondensed Matter, Materials & Applied Physics
Highlights
In recent years, algorithms involving a hybrid quantumclassical procedure for cost function minimization have attracted much attention [1,2]
IV, we introduce an alternating operator protocol for the Ising model in transverse and longitudinal fields, and we demonstrate that the success of the quantum approximate optimization algorithm (QAOA) groundstate preparation correlates with its interaction distance
In this paper we investigate the preparation of ground states of nonintegrable quantum models using the QAOA
Summary
Algorithms involving a hybrid quantumclassical procedure for cost function minimization have attracted much attention [1,2] Among these is the quantum approximate optimization algorithm (QAOA), which employs an alternating operator ansatz for solving optimization problems that are mappable to the problem of finding the ground state of a classical Ising-type Hamiltonian [2]. Appendix B contains results for the model that realises the so-called cluster state [40], which is of importance in measurement-based quantum computation [41] and in symmetry-protected topological phases of matter [42,43,44,45] This model displays a critical line in its phase diagram when placed in an external magnetic field, similar to the antiferromagnetic model, and we demonstrate similar correlation between the interaction distance and QAOA preparation of its ground state
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call