Exactly solvable Hamiltonian fragments obtained from a direct sum of Lie algebras

• URL: http://arxiv.org/abs/2402.09376v1
• Date: Wed, 14 Feb 2024 18:22:45 GMT
• Title: Exactly solvable Hamiltonian fragments obtained from a direct sum of Lie algebras
• Authors: Smik Patel, Artur F. Izmaylov
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for evaluation of the energies via repeated quantum measurements. In this work, we apply more general classes of exactly solvable qubit Hamiltonians than previously considered to address the Hamiltonian measurement problem. The most general exactly solvable Hamiltonians are defined by the condition that, within each simultaneous eigenspace of a set of Pauli symmetries, the Hamiltonian acts effectively as an element of a direct sum of so(N) Lie algebras, and can therefore be measured using a combination of unitaries in the associated Lie group, Clifford unitaries, and mid-circuit measurements. Application of such Hamiltonians to decomposing molecular electronic Hamiltonians via graph partitioning techniques shows a reduction in the total number of measurements required to estimate the expectation value compared with previously used exactly solvable qubit Hamiltonians.

Related papers

• Simulating NMR Spectra with a Quantum Computer [49.1574468325115]
  This paper provides a formalization of the complete procedure of the simulation of a spin system's NMR spectrum. We also explain how to diagonalize the Hamiltonian matrix with a quantum computer, thus enhancing the overall process's performance.
  arXiv  Detail & Related papers  (2024-10-28T08:43:40Z)
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Learning Symmetric Hamiltonian [9.79122046962129]
  Hamiltonian Learning is a process of recovering system Hamiltonian from measurements. In this study, we investigate the problem of learning the symmetric Hamiltonian from its eigenstate.
  arXiv  Detail & Related papers  (2024-04-09T01:38:32Z)
• Coherence generation with Hamiltonians [44.99833362998488]
  We explore methods to generate quantum coherence through unitary evolutions. This quantity is defined as the maximum derivative of coherence that can be achieved by a Hamiltonian. We identify the quantum states that lead to the largest coherence derivative induced by the Hamiltonian.
  arXiv  Detail & Related papers  (2024-02-27T15:06:40Z)
• On The Study Of Partial Qubit Hamiltonian For Efficient Molecular Simulation Using Variational Quantum Eigensolvers [0.0]
  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.
  arXiv  Detail & Related papers  (2023-08-24T03:25:05Z)
• Extension of exactly-solvable Hamiltonians using symmetries of Lie algebras [0.0]
  We show that a linear combination of operators forming a modest size Lie algebra can be substituted by determinants of the Lie algebra symmetries. The new class of solvable Hamiltonians can be measured efficiently using quantum circuits with gates that depend on the result of a mid-circuit measurement of the symmetries.
  arXiv  Detail & Related papers  (2023-05-29T17:19:56Z)
• 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)
• Simultaneous Stoquasticity [0.0]
  Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation.
  arXiv  Detail & Related papers  (2022-02-17T19:08:30Z)
• 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)
• Learning Quantum Hamiltonians from Single-qubit Measurements [5.609584942407068]
  We propose a recurrent neural network to learn the parameters of the target Hamiltonians from the temporal records of single-qubit measurements. It is applicable on both time-independent and time-dependent Hamiltonians.
  arXiv  Detail & Related papers  (2020-12-23T07:15:20Z)
• Stoquasticity in circuit QED [78.980148137396]
  We show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems. We corroborate the recent finding that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits.
  arXiv  Detail & Related papers  (2020-11-02T16:41:28Z)

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.