Circuit complexity for coherent states

• Main Authors: Minyong Guo, Juan Hernandez, Robert C. Myers, Shan-Ming Ruan
• Format: Article
• Language: English
• Published: SpringerOpen 2018-10-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Black Holes in String Theory; Effective Field Theories; Lattice Quantum Field Theory
• Online Access: http://link.springer.com/article/10.1007/JHEP10(2018)011

Abstract We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen’s geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we consider the finite increase of the complexity of these states over the vacuum state. One observation is that generally, the optimal circuits introduce entanglement between the normal modes at intermediate stages even though our reference state and target states are not entangled in this basis. We also compare our results from Nielsen’s approach with those found using the Fubini-Study method of [2]. For general coherent states, we find that the complexities, as well as the optimal circuits, derived from these two approaches, are different.