Verifiably Exact Solution of the Electronic Schr\"odinger Equation on Quantum Devices

• URL: http://arxiv.org/abs/2303.00758v1
• Date: Wed, 1 Mar 2023 19:00:00 GMT
• Title: Verifiably Exact Solution of the Electronic Schr\"odinger Equation on Quantum Devices
• Authors: Scott E. Smart and David A. Mazziotti
• Abstract summary: We present an algorithm that yields verifiably exact solutions of the many-electron Schr"odinger equation. We demonstrate the algorithm on both quantum simulators and noisy quantum computers.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum computers have the potential for an exponential speedup of classical molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) algorithms are intractable on current hardware while variational quantum eigensolvers (VQE) are dependent upon approximate wave functions without guaranteed convergence. In this Article we present an algorithm that yields verifiably exact solutions of the many-electron Schr\"odinger equation. Rather than solve the Schr\"odinger equation directly, we solve its contraction over all electrons except two, known as the contracted Schr\"odinger equation (CSE). The CSE generates an exact wave function ansatz, constructed from a product of two-body-based non-unitary transformations, that scales polynomially with molecular size and hence, provides a potentially exponential acceleration of classical molecular electronic structure calculations on ideal quantum devices. We demonstrate the algorithm on both quantum simulators and noisy quantum computers with applications to H$_{2}$ dissociation and the rectangle-to-square transition in H$_{4}$. The CSE quantum algorithm, which is a type of contracted quantum eigensolver (CQE), provides a significant step towards realizing verifiably accurate but scalable molecular simulations on quantum devices.

Related papers

• Quantum computation of conical intersections on a programmable superconducting quantum processor [10.064448021157139]
  Conical intersections (CIs) are pivotal in many photochemical processes. We present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent method.
  arXiv  Detail & Related papers  (2024-02-20T04:12:40Z)
• Electronic Excited States from a Variance-Based Contracted Quantum Eigensolver [6.5460423831540275]
  We leverage the advantages of quantum computers to develop an algorithm for the highly accurate calculation of excited states. We apply the algorithm in a classical simulation without noise to computing the ground and excited states of H$_4$ and BH.
  arXiv  Detail & Related papers  (2023-05-04T17:59:05Z)
• 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)
• Recompilation-enhanced simulation of electron-phonon dynamics on IBM Quantum computers [62.997667081978825]
  We consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems. We perform experiments on IBM quantum hardware for both weak and strong electron-phonon coupling. Despite significant device noise, through the use of approximate circuit recompilation we obtain electron-phonon dynamics on current quantum computers comparable to exact diagonalisation.
  arXiv  Detail & Related papers  (2022-02-16T19:00:00Z)
• Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation [5.188498150496968]
  We present a quantum kernel function (QKFE) algorithm for solving thermodynamic properties of quantum many-body systems. As compared to its classical counterpart, namely the kernel method (KPM), QKFE has an exponential advantage in the cost of both time and memory. We demonstrate its efficiency with applications to one and two-dimensional quantum spin models, and a fermionic lattice.
  arXiv  Detail & Related papers  (2022-02-02T18:00:04Z)
• Computing molecular excited states on a D-Wave quantum annealer [52.5289706853773]
  We demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience.
  arXiv  Detail & Related papers  (2021-07-01T01:02:17Z)
• Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation [58.720142291102135]
  We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer. We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
  arXiv  Detail & Related papers  (2021-06-22T18:00:00Z)
• VQE Method: A Short Survey and Recent Developments [5.9640499950316945]
  The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been successfully applied to solve the electronic Schr"odinger equation for a variety of small molecules. Modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze.
  arXiv  Detail & Related papers  (2021-03-15T16:25:36Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Electronic structure with direct diagonalization on a D-Wave quantum annealer [62.997667081978825]
  This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
  arXiv  Detail & Related papers  (2020-09-02T22:46:47Z)
• Gate-free state preparation for fast variational quantum eigensolver simulations: ctrl-VQE [0.0]
  VQE is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. We propose an alternative algorithm where the quantum circuit used for state preparation is removed entirely and replaced by a quantum control routine. As with VQE, the objective function optimized is the expectation value of the qubit-mapped molecular Hamiltonian.
  arXiv  Detail & Related papers  (2020-08-10T17:53:09Z)

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.