Abstract
The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near future may enable us to compute energy spectra of classically-intractable systems, methods to simulate the Green's function with near-term quantum algorithms have not been proposed yet. Here, we propose two methods to calculate the Green's function of a given Hamiltonian on near-term quantum computers. The first one makes use of a variational dynamics simulation of quantum systems and computes the dynamics of the Green's function in real time directly. The second one utilizes the Lehmann representation of the Green's function and a method which calculates excited states of the Hamiltonian. Both methods require shallow quantum circuits and are compatible with near-term quantum computers. We numerically simulated the Green's function of the Fermi-Hubbard model and demonstrated the validity of our proposals.
Highlights
The advent of a primitive but still powerful form of quantum computers, called noisy intermediate-scale quantum (NISQ) devices, is approaching [1]
Many researchers expect that NISQ devices will exhibit supremacy over classical computers for some specific tasks, even though they cannot execute complicated quantum algorithms requiring a huge number of qubits and gate operations due to the erroneous nature of them [1]
We introduced a method for constructing a variational quantum circuit which acts as the time evolution operator for multiple initial states simultaneously, and makes the quantum circuit for computation of the Green’s function significantly shallower
Summary
The advent of a primitive but still powerful form of quantum computers, called noisy intermediate-scale quantum (NISQ) devices, is approaching [1]. Other important quantities to investigate quantum many-body systems other than eigenenergies and eigenstates have remained relatively disregarded in the recent development of near-term quantum algorithms, i.e., the Green’s function and the spectral function [18,19,20]. They are fundamental to study quantum many-body systems, especially strongly correlated systems; for example, in condensed matter physics, the spectral function tells us that the dispersion relation of quasiparticle excitations of a system, which gives crucial information on high-Tc superconductivity [21], magnetic materials [22], and topological insulators [23].
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