A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground state wavefunction on the quantum computer. This is used to compute the continued fraction representation of an interacting Green's function for use in condensed matter, particle physics, and other areas. The wavefunction does not need to be re-prepared at each iteration. The quantum algorithm represents an exponential reduction in memory over known classical methods. An extension of the method to determining the ground state is also discussed.
The method of quantum Lanczos recursion is extended to solve for multiple excitations on the quantum computer. While quantum Lanczos recursion is in principle capable of obtaining excitations, the extension to a block Lanczos routine can resolve degeneracies with better precision and only costs $\mathcal{O}(d^2)$ for $d$ excitations on top of the previously introduced quantum Lanczos recursion method. The formal complexity in applying all operators to the system at once with oblivious amplitude amplification is exponential, but this cost can be kept small to obtain the ground state by incremen…
Recursion method for quench dynamics: strengths and limitations
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Moscow State University, Faculty of Physics（莫斯科国立大学物理系）；HSE University（高等经济大学）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Wilczek Quantum Center, Shanghai Institute for Advanced Studies, University of Science and Technology of China（中国科学院大学上海高级研究院威尔切克量子中心）；Hefei National Laboratory（合肥国家实验室）；Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所量子技术数学方法系）；Russian Quantum Center（俄罗斯量子中心）
Symbolic operator growth and recursion method for spin-S Ising and q-states Potts models
Wilczek Quantum Center, Shanghai Institute for Advanced Studies, University of Science and Technology of China（上海高等研究院，中国科学院大学）；Hefei National Laboratory（合肥国家实验室）；Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所量子技术数学方法系）；Russian Quantum Center, Skolkovo（俄罗斯量子中心，斯科尔科沃）
Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step, especially for large systems, is the problem of calculating the inverse of a large sparse matrix to solve Dyson's equation and determine the local Green's function at each lattice site from the corresponding local self-energy. We present a new efficient algorithm, the Lanczos-based low-rank algorithm, for the calculation of the inverse of a large sparse matrix which…
We present an algorithm to compute Green's functions on quantum computers for interacting electron systems, which is a challenging task on conventional computers. It uses a continued fraction representation based on the Lanczos method, where the wave functions are expanded as linear combination of basis states within a quantum subspace. While on conventional computers the cost of the computation grows exponentially with system size, limiting the method to small systems, by representing the basis states on a quantum computer one may overcome this exponential scaling barrier. We propose a two-le…
We propose an algorithm to obtain Green's functions as a continued fraction on quantum computers, which is based on the construction of the Krylov basis using variational quantum algorithms, and included in a Lanczos iterative scheme. This allows the integration of quantum algorithms with first principles material science simulations, as we demonstrate within the dynamical mean-field theory (DMFT) framework. DMFT enables quantitative predictions for strongly correlated materials, and relies on the calculation of Green's functions. On conventional computers the exponential growth of the Hilbert…
Green's Functions from Sample-based Krylov Quantum Diagonalization: An Impurity Solver for Dynamical Mean-Field Theory
Center for Computation and Technology, Louisiana State University（路易斯安那州立大学计算与技术中心）；Department of Physics, The Pennsylvania State University（宾夕法尼亚州立大学物理系）；Department of Physics and Astronomy, Louisiana State University（路易斯安那州立大学物理与天文学系）
