2021/04/14 by Trevor Keen, Bo Peng, Keen, Trevor +7 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Cluster (spacecraft) #Computational complexity theory #Computer science #Eigenvalues and eigenvectors #FOS: Physical sciences #Function (biology) #Geometry #Mathematics #Physics #Physics of Superconductivity and Magnetism #Product (mathematics) #Quantum #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum mechanics #Range (aeronautics) #Scaling #Spectroscopy and Quantum Chemical Studies #State (computer science) #Statistical physics #Time evolution #Unitary state #quant-ph
paper · pdf · doi:10.48550/arxiv.2104.06981
published in arXiv (Cornell University) (Cornell University) · 14 pages, 5 figures, 1 table
openalex publication_date 2021/04/14 · arxiv created 2022/03/22 · arxiv updated 2022/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of time evolution and measurements are well known, many state preparation methods are strongly system-dependent and require prior knowledge of the system's eigenvalue spectrum. Here, we report on a quantum-classical implementation of the coupled-cluster Green's function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state. While our approach is broadly applicable to many models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number of T gates that grows as O (N5 ) per time step to calculate the impurity Green's function in the time domain, where N is the total number of energy levels in the AIM. Since the number of T gates is analogous to the computational time complexity of a classical simulation, we achieve an order of magnitude improvement over a classical CCGF calculation of the same order, which requires O (N6 ) computational resources per time step.