Bootstrapping Calabi-Yau Quantum Mechanics

• URL: http://arxiv.org/abs/2111.08442v1
• Date: Tue, 16 Nov 2021 13:20:38 GMT
• Title: Bootstrapping Calabi-Yau Quantum Mechanics
• Authors: Bao-ning Du, Min-xin Huang, Pei-xuan Zeng
• Abstract summary: We propose a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems. We find that the bootstrap method provides a promising alternative for the precision numerical calculations of the energy eigenvalues.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau geometries, where the exact quantization conditions have been conjecturally related to topological string theory. We find that the bootstrap method provides a promising alternative for the precision numerical calculations of the energy eigenvalues. An improvement in our approach is to use a larger set of two-dimensional operators instead of one-dimensional ones. We also apply our improved bootstrap methods to some non-relativistic models in the recent literature and demonstrate better numerical accuracies.

Related papers

• Variational quantum thermalizers based on weakly-symmetric nonunitary multi-qubit operations [0.0]
  Variational Quantum Thermalizers (VQTs) generate the thermal (Gibbs) state of a given Hamiltonian. Current algorithms struggle at intermediate temperatures, where the target state is nonpure but exhibits entanglement. We devise multi-qubit nonunitary operations that harness weak symmetries and thereby improve the performance of the algorithm.
  arXiv  Detail & Related papers  (2025-02-13T19:00:00Z)
• A Quantum-Centric Super-Krylov Diagonalization Method [0.562479170374811]
  We present a Krylov quantum diagonalization (KQD) method that uses only real-time evolutions and recovery probabilities.<n>We also propose a classical post-processing derivative estimation algorithm.
  arXiv  Detail & Related papers  (2024-12-23T05:21:43Z)
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions [39.58317527488534]
  We propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for extraction of low-lying energy states.<n>As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.
  arXiv  Detail & Related papers  (2024-11-25T20:33:47Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Truncation technique for variational quantum eigensolver for Molecular Hamiltonians [0.0]
  variational quantum eigensolver (VQE) is one of the most promising quantum algorithms for noisy quantum devices. We propose a physically intuitive truncation technique that starts the optimization procedure with a truncated Hamiltonian. This strategy allows us to reduce the required number of evaluations for the expectation value of Hamiltonian on a quantum computer.
  arXiv  Detail & Related papers  (2024-02-02T18:45:12Z)
• Higher-order topological kernels via quantum computation [68.8204255655161]
  Topological data analysis (TDA) has emerged as a powerful tool for extracting meaningful insights from complex data. We propose a quantum approach to defining Betti kernels, which is based on constructing Betti curves with increasing order.
  arXiv  Detail & Related papers  (2023-07-14T14:48:52Z)
• Generalization Metrics for Practical Quantum Advantage in Generative Models [68.8204255655161]
  Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
  arXiv  Detail & Related papers  (2022-01-21T16:35:35Z)
• Bootstrapping Bloch bands [0.0]
  We extend bootstrap methods to models with continuous Bloch band spectra. We find that the band structure can be obtained accurately provided the bootstrap uses moments involving both position and momentum variables. We also introduce several new techniques that can apply generally to other bootstrap studies.
  arXiv  Detail & Related papers  (2021-09-14T11:39:19Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Numerical Bootstrap in Quantum Mechanics [0.0]
  We study the effectiveness of the numerical bootstrap techniques recently developed in arXiv:2004.10212 for quantum mechanical systems. We find that for a double well potential the bootstrap method correctly captures non-perturbative aspects. We also study the singlet sector of O(N) vector model quantum mechanics, where we find that the bootstrap method yields results which in the large N agree with saddle point analysis.
  arXiv  Detail & Related papers  (2021-08-25T18:14:55Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation [7.620967781722716]
  We present a variational quantum algorithm for solving the Poisson equation. The proposed method defines the total potential energy of the Poisson equation as a Hamiltonian. Because the number of terms is independent of the size of the problem, this method requires relatively few quantum measurements.
  arXiv  Detail & Related papers  (2021-06-17T09:01:53Z)
• 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)
• Efficient construction of tensor-network representations of many-body Gaussian states [59.94347858883343]
  We present a procedure to construct tensor-network representations of many-body Gaussian states efficiently and with a controllable error. These states include the ground and thermal states of bosonic and fermionic quadratic Hamiltonians, which are essential in the study of quantum many-body systems.
  arXiv  Detail & Related papers  (2020-08-12T11:30:23Z)
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule [0.0]
  We study the problem of estimating the gradient of the function to be optimized directly from quantum measurements. We derive a mathematically exact formula that provides an algorithm for estimating the gradient of any multi-qubit parametric quantum evolution. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy.
  arXiv  Detail & Related papers  (2020-05-20T18:24:11Z)

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.