Towards Perturbation Theory Methods on a Quantum Computer

Abstract

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today, techniques for PT are significantly lacking in quantum computing. Here we present a quantum circuit estimating both the energy and eigenstates corrections with PT methods, which we claim is far superior to the classical version when estimating the second order energy correction. Our approach is further demonstrated with an application on the extended Hubbard model, where numerical simulation based on qiskit is also presented. Unlike the popular quantum variational circuit, there is no training or optimizing process in our circuit, and all parameters are derived from the unperturbed Hamiltonian. Our work offers a new approach to studying complex systems with quantum devices, which might shed light on the quantum implementation of the more intricate methods based on PT.

arXiv commentMain: 16 pages, 4 figures; SM: 5 pages

References in corpus (20)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Elementary gates for quantum computation
• Quantum computational advantage using photons
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum Convolutional Neural Networks
• Error mitigation for short-depth quantum circuits
• Extending the computational reach of a noisy superconducting quantum processor
• Hartree-Fock on a superconducting qubit quantum computer
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Repeat-Until-Success Quantum Computing
• Generalized Jordan-Wigner Transformations
• Quantum circuits for strongly correlated quantum systems
• Doubling the size of quantum simulators by entanglement forging
• Quantum Machine Learning for Chemistry and Physics
• Quantum Machine Learning for Electronic Structure Calculations
• Universal simulation of Markovian quantum dynamics
• Doublon dynamics in the extended Fermi Hubbard model
• Minimal Effective Gibbs Ansatz (MEGA): A simple protocol for extracting an accurate thermal representation for quantum simulation

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• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations