Say NO to Optimization: A Non-Orthogonal Quantum Eigensolver

• URL: http://arxiv.org/abs/2205.09039v1
• Date: Wed, 18 May 2022 16:20:36 GMT
• Title: Say NO to Optimization: A Non-Orthogonal Quantum Eigensolver
• Authors: Unpil Baek, Diptarka Hait, James Shee, Oskar Leimkuhler, William J. Huggins, Torin F. Stetina, Martin Head-Gordon, K. Birgitta Whaley
• Abstract summary: A balanced description of both static and dynamic correlations in electronic systems with nearly degenerate low-lying states presents a challenge for multi-configurational methods on classical computers. We present here a quantum algorithm utilizing the action of correlating cluster operators to provide high-quality wavefunction ans"atze.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A balanced description of both static and dynamic correlations in electronic systems with nearly degenerate low-lying states presents a challenge for multi-configurational methods on classical computers. We present here a quantum algorithm utilizing the action of correlating cluster operators to provide high-quality wavefunction ans\"atze employing a non-orthogonal multireference basis that captures a significant portion of the exact wavefunction in a highly compact manner, and that allows computation of the resulting energies and wavefunctions at polynomial cost with a quantum computer. This enables a significant improvement over the corresponding classical non-orthogonal solver, which incurs an exponential cost when evaluating off-diagonal matrix elements between the ansatz states, and is therefore intractable. We implement the non-orthogonal quantum eigensolver (NOQE) here with an efficient ansatz parameterization inspired by classical quantum chemistry methods that succeed in capturing significant amounts of electronic correlation accurately. By taking advantage of classical methods for chemistry, NOQE provides a flexible, compact, and rigorous description of both static and dynamic electronic correlation, making it an attractive method for the calculation of electronic states of a wide range of molecular systems.

Related papers

• Projective Quantum Eigensolver with Generalized Operators [0.0]
  We develop a methodology for determining the generalized operators in terms of a closed form residual equations in the PQE framework. With the application on several molecular systems, we have demonstrated our ansatz achieves similar accuracy to the (disentangled) UCC with singles, doubles and triples.
  arXiv  Detail & Related papers  (2024-10-21T15:40:22Z)
• Quantum algorithms for the variational optimization of correlated electronic states with stochastic reconfiguration and the linear method [0.0]
  We present quantum algorithms for the variational optimization of wavefunctions correlated by products of unitary operators. While an implementation on classical computing hardware would require exponentially growing compute cost, the cost (number of circuits and shots) of our quantum algorithms is in system size.
  arXiv  Detail & Related papers  (2024-08-03T17:53:35Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Orders of magnitude reduction in the computational overhead for quantum many-body problems on quantum computers via an exact transcorrelated method [0.0]
  We show that the Hamiltonian becomes non-Hermitian, posing problems for quantum algorithms based on the variational principle. We overcome these limitations with the ansatz-based quantum imaginary time evolution algorithm. Our work paves the way for the use of exact transcorrelated methods for the simulations of ab initio systems on quantum computers.
  arXiv  Detail & Related papers  (2022-01-09T16:37:32Z)
• 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)
• 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)
• Optimized Low-Depth Quantum Circuits for Molecular Electronic Structure using a Separable Pair Approximation [0.0]
  We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the long term, provide significantly improved initial states for quantum algorithms.
  arXiv  Detail & Related papers  (2021-05-09T05:10:59Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• 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)

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.