On The Study Of Partial Qubit Hamiltonian For Efficient Molecular Simulation Using Variational Quantum Eigensolvers

• URL: http://arxiv.org/abs/2308.12524v1
• Date: Thu, 24 Aug 2023 03:25:05 GMT
• Title: On The Study Of Partial Qubit Hamiltonian For Efficient Molecular Simulation Using Variational Quantum Eigensolvers
• Authors: Harshdeep Singh, Sabyashachi Mishra, Sonjoy Majumder
• Abstract summary: We present a new approach for extracting information from the partial qubit Hamiltonian of simple molecules to design more efficient variational quantum eigensolvers. The results of this study have the potential to demonstrate the potential advancement in the field of quantum computing and its implementation in quantum chemistry.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum computing is being extensively used in quantum chemistry, especially in simulating simple molecules and evaluating properties like the ground state energy, dipole moment, etc. The transformation of a molecular Hamiltonian from the fermionic space to the qubit space provides us with a series of Pauli strings and the energy calculation involves the evaluation of the expectation values of all these individual strings. This introduces a major bottleneck for applications of VQEs in quantum chemistry. Unlike the fermionic Hamiltonian, the terms in a qubit Hamiltonian are additive and the present paper exploits this property to describe a new approach for extracting information from the partial qubit Hamiltonian of simple molecules to design more efficient variational quantum eigensolvers. In the partial (qubit) Hamiltonian approach (PHA), the qubit Hamiltonian is studied term-by-term to understand their relative contributions to the overall energy and a partial Hamiltonian is constructed with fewer Pauli strings that can resolve the entire Hamiltonian. With PHA, we can simulate molecules at a much lower computational cost with a truncated Hamiltonian. Additionally, the outcomes of the measurements with PHA quench the error due to noise introduced by the quantum circuits. We have also demonstrated the application of PHA as an initialization technique, where the simple partial Hamiltonian can be used to find a suitable initial state for a more complex system. The results of this study have the potential to demonstrate the potential advancement in the field of quantum computing and its implementation in quantum chemistry.

Related papers

• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Ab initio extended Hubbard model of short polyenes for efficient quantum computing [0.0]
  We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method. The ab initio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers.
  arXiv  Detail & Related papers  (2024-04-02T04:13:09Z)
• Exactly solvable Hamiltonian fragments obtained from a direct sum of Lie algebras [0.0]
  Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. We apply more general classes of exactly solvable qubit Hamiltonians than previously considered to address the Hamiltonian measurement problem.
  arXiv  Detail & Related papers  (2024-02-14T18:22:45Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
  We introduce the Variational Adiabatic Gauge Transformation (VAGT) VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
  arXiv  Detail & Related papers  (2021-11-16T20:50:08Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• A Hybrid Quantum-Classical Hamiltonian Learning Algorithm [6.90132007891849]
  Hamiltonian learning is crucial to the certification of quantum devices and quantum simulators. We propose a hybrid quantum-classical Hamiltonian learning algorithm to find the coefficients of the Pauli operator of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-03-01T15:15:58Z)
• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices [69.50862982117127]
  We benchmark the working conditions of the numerically analog simulator and find less demanding experimental setups. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects.
  arXiv  Detail & Related papers  (2020-11-28T11:23:06Z)
• Dynamical Self-energy Mapping (DSEM) for quantum computing [0.0]
  For noisy intermediate-scale quantum (NISQ) devices only a moderate number of qubits with a limited coherence is available. We present how to bypass this challenge in practical molecular chemistry simulations on NISQ devices by employing a classical-quantum hybrid algorithm.
  arXiv  Detail & Related papers  (2020-10-12T04:12:21Z)
• Using Quantum Annealers to Calculate Ground State Properties of Molecules [0.0]
  We review two different methods for finding the ground state of molecular Hamiltonians using Ising model-based quantum annealers. We find that they are still outperformed by modern classical algorithms and that the scaling of the resource requirements remains a challenge.
  arXiv  Detail & Related papers  (2020-09-22T19:34:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.