Pymablock: an algorithm and a package for quasi-degenerate perturbation theory
- URL: http://arxiv.org/abs/2404.03728v1
- Date: Thu, 4 Apr 2024 18:00:08 GMT
- Title: Pymablock: an algorithm and a package for quasi-degenerate perturbation theory
- Authors: Isidora Araya Day, Sebastian Miles, Hugo K. Kerstens, Daniel Varjas, Anton R. Akhmerov,
- Abstract summary: We introduce an algorithm for constructing an effective Hamiltonian as well as a Python package, Pymablock, that implements it.
We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer--Wolff transformation achieves this and constructs an effective Hamiltonian, its scaling is suboptimal, and implementing it efficiently is both challenging and error-prone. We introduce an algorithm for constructing an equivalent effective Hamiltonian as well as a Python package, Pymablock, that implements it. Our algorithm combines an optimal asymptotic scaling with a range of other improvements. The package supports numerical and analytical calculations of any order and it is designed to be interoperable with any other packages for specifying the Hamiltonian. We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model. We also compare its performance with reference calculations and demonstrate its efficiency.
Related papers
- Quantum Maximum Entropy Inference and Hamiltonian Learning [4.9614587340495]
This work extends algorithms for maximum entropy inference and learning of graphical models to the quantum realm.
The generalization, known as quantum iterative scaling (QIS), is straightforward, but the key challenge lies in the non-commutative nature of quantum problem instances.
We explore quasi-Newton methods to enhance the performance of QIS and GD.
arXiv Detail & Related papers (2024-07-16T08:11:34Z) - Quantum walk informed variational algorithm design [0.0]
We present a theoretical framework for the analysis of amplitude transfer in Quantum Variational Algorithms (QVAs)
We develop algorithms for unconstrained and constrained novel optimisations.
We show significantly improved convergence over preexisting QVAs.
arXiv Detail & Related papers (2024-06-17T15:04:26Z) - Self-concordant Smoothing for Large-Scale Convex Composite Optimization [0.0]
We introduce a notion of self-concordant smoothing for minimizing the sum of two convex functions, one of which is smooth and the other may be nonsmooth.
We prove the convergence of two resulting algorithms: Prox-N-SCORE, a proximal Newton algorithm and Prox-GGN-SCORE, a proximal generalized Gauss-Newton algorithm.
arXiv Detail & Related papers (2023-09-04T19:47:04Z) - Sample Complexity for Quadratic Bandits: Hessian Dependent Bounds and
Optimal Algorithms [64.10576998630981]
We show the first tight characterization of the optimal Hessian-dependent sample complexity.
A Hessian-independent algorithm universally achieves the optimal sample complexities for all Hessian instances.
The optimal sample complexities achieved by our algorithm remain valid for heavy-tailed noise distributions.
arXiv Detail & Related papers (2023-06-21T17:03:22Z) - Quantum Goemans-Williamson Algorithm with the Hadamard Test and
Approximate Amplitude Constraints [62.72309460291971]
We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits.
Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit.
We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
arXiv Detail & Related papers (2022-06-30T03:15:23Z) - A quantum-inspired tensor network method for constrained combinatorial
optimization problems [5.904219009974901]
We propose a quantum-inspired tensor-network-based algorithm for general locally constrained optimization problems.
Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem.
Our results show the effectiveness of this construction and potential applications.
arXiv Detail & Related papers (2022-03-29T05:44:07Z) - Twisted hybrid algorithms for combinatorial optimization [68.8204255655161]
Proposed hybrid algorithms encode a cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity.
We show that for levels $p=2,ldots, 6$, the level $p$ can be reduced by one while roughly maintaining the expected approximation ratio.
arXiv Detail & Related papers (2022-03-01T19:47:16Z) - Non-perturbative analytical diagonalization of Hamiltonians with
application to coupling suppression and enhancement in cQED [0.0]
Deriving effective Hamiltonian models plays an essential role in quantum theory.
We present two symbolic methods for computing effective Hamiltonian models.
We study the ZZ and cross-resonance interactions of superconducting qubits systems.
arXiv Detail & Related papers (2021-11-30T19:01:44Z) - Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations.
Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff.
For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
arXiv Detail & Related papers (2021-09-07T20:01:22Z) - Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
We present a constructive algorithm for generating quantum circuits with time-independent depth.
We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model.
In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
arXiv Detail & Related papers (2021-04-01T19:06:00Z) - Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with
an artificial neural-network correlator ansatz [62.997667081978825]
We introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei.
We compute the binding energies and point-nucleon densities of $Aleq 4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian.
arXiv Detail & Related papers (2020-07-28T14:52:28Z)
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.