Local, Expressive, Quantum-Number-Preserving VQE Ansatze for Fermionic Systems

• URL: http://arxiv.org/abs/2104.05695v2
• Date: Mon, 10 May 2021 18:41:12 GMT
• Title: Local, Expressive, Quantum-Number-Preserving VQE Ansatze for Fermionic Systems
• Authors: Gian-Luca R. Anselmetti, David Wierichs, Christian Gogolin, and Robert M. Parrish
• Abstract summary: We propose VQE circuit fabrics with advantageous properties for the simulation of strongly correlated states of molecules and materials. We demonstrate that our entangler circuits are expressive already at low depth and parameter count, appear to become universal, and may be trainable without having to cross regions of vanishing regions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose VQE circuit fabrics with advantageous properties for the simulation of strongly correlated ground and excited states of molecules and materials under the Jordan-Wigner mapping that can be implemented linearly locally and preserve all relevant quantum numbers: the number of spin up ($\alpha$) and down ($\beta$) electrons and the total spin squared. We demonstrate that our entangler circuits are expressive already at low depth and parameter count, appear to become universal, and may be trainable without having to cross regions of vanishing gradient, when the number of parameters becomes sufficiently large and when these parameters are suitably initialized. One particularly appealing construction achieves this with just orbital rotations and pair exchange gates. We derive optimal four-term parameter shift rules for and provide explicit decompositions of our quantum number preserving gates and perform numerical demonstrations on highly correlated molecules on up to 20 qubits.

Related papers

• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer [0.0]
  We provide quantum circuits to perform ground and excited states calculations. We benchmark our approach on a chain with L=6 sites and periodic boundary conditions.
  arXiv  Detail & Related papers  (2024-10-10T10:19:02Z)
• 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)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Quantum simulation of Fermi-Hubbard model based on transmon qudit interaction [0.0]
  We introduce a novel quantum simulation approach utilizing qudits to overcome such complexities. We first demonstrate a Qudit Fermionic Mapping (QFM) that reduces the encoding cost associated with the qubit-based approach. We then describe the unitary evolution of the mapped Hamiltonian by interpreting the resulting Majorana operators in terms of physical single- and two-qudit gates.
  arXiv  Detail & Related papers  (2024-02-02T09:10:40Z)
• 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)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Improving the Accuracy of Variational Quantum Eigensolvers With Fewer Qubits Using Orbital Optimization [5.266892492931388]
  Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To-date, experimental demonstrations of algorithms such as the Variational Quantum Eigensolver (VQE) have been limited to small molecules using minimal basis sets. We propose incorporating an orbital optimization scheme into quantum eigensolvers wherein a parameterized partial unitary transformation is applied to the basis functions set.
  arXiv  Detail & Related papers  (2022-08-30T17:50:23Z)
• Gate-based spin readout of hole quantum dots with site-dependent $g-$factors [101.23523361398418]
  We experimentally investigate a hole double quantum dot in silicon by carrying out spin readout with gate-based reflectometry. We show that characteristic features in the reflected phase signal arising from magneto-spectroscopy convey information on site-dependent $g-$factors in the two dots.
  arXiv  Detail & Related papers  (2022-06-27T09:07:20Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Fast-forwarding quantum evolution [0.2621730497733946]
  We show that certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that considers the model of quantum computation, the Hamiltonians that induce the evolution, and the properties of the initial states.
  arXiv  Detail & Related papers  (2021-05-15T22:41:28Z)
• Efficient quantum circuits for quantum computational chemistry [0.0]
  Efficient ways to perform fermionic excitations are vital for the realization of the variational quantum eigensolver (VQE) on noisy intermediate-scale quantum computers. We demonstrate circuits that perform qubit excitations, excitations that do not account for fermionic anticommutation relations. Compared to circuits constructed with the standard use of "$CNOT$ staircases," our circuits offer a linear reduction in the number of $CNOT$ gates.
  arXiv  Detail & Related papers  (2020-05-29T09:46:23Z)

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.