Computation of Green's function by local variational quantum compilation

Abstract

Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on classical computers, the development of quantum computers may enable us to compute the Green's function with high accuracy even for classically-intractable large-scale systems. Here, we propose an efficient method to compute the real-time Green's function based on the local variational quantum compilation (LVQC) algorithm, which simulates the time evolution of a large-scale quantum system using a low-depth quantum circuit constructed through optimization on a smaller-size subsystem. Our method requires shallow quantum circuits to calculate the Green's function and can be utilized on both near-term noisy intermediate-scale and long-term fault-tolerant quantum computers depending on the computational resources we have. We perform a numerical simulation of the Green's function for the one- and two-dimensional Fermi-Hubbard model up to $4\times 4$ sites lattice (32 qubits) and demonstrate the validity of our protocol compared to a standard method based on the Trotter decomposition. We finally present a detailed estimation of the gate count for the large-scale Fermi-Hubbard model, which also illustrates the advantage of our method over the Trotter decomposition.

arXiv comment22 pages, 13 figures

References in corpus (38)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• Quantum Algorithms Revisited
• Fermionic quantum computation
• Scanning tunneling spectroscopy of high-temperature superconductors
• Towards Practical Quantum Variational Algorithms
• Quantum optimization using variational algorithms on near-term quantum devices
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• A Theory of Trotter Error
• The Hubbard Model
• Quantum-assisted quantum compiling
• Solving strongly correlated electron models on a quantum computer
• Hybrid quantum-classical approach to correlated materials
• Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Linear Response on a Quantum Computer
• Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions
• Calculation of the Green's function on near-term quantum computers
• An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
• Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
• Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors
• Spectral density estimation with the Gaussian Integral Transform
• Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics
• Construction of Green's functions on a quantum computer: applications to molecular systems
• First-Order Trotter Error from a Second-Order Perspective
• Destructive Error Interference in Product-Formula Lattice Simulation
• Effective calculation of the Green's function in the time domain on near-term quantum processors
• Hybrid quantum-classical algorithm for computing imaginary-time correlation functions
• Local variational quantum compilation of a large-scale Hamiltonian dynamics
• Lanczos recursion on a quantum computer for the Green's function and ground state
• Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions
• Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer
• Calculating the Green's function of two-site Fermionic Hubbard model in a photonic system

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• Elucidating Many-Body Effects in Molecular Core Spectra through Real-Time Approaches: Efficient Classical Approximations and a Quantum Perspective
• Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition