Analytical approach to higher-order correlation functions in U(1) symmetric systems

• URL: http://arxiv.org/abs/2305.08923v2
• Date: Tue, 7 Nov 2023 03:38:02 GMT
• Title: Analytical approach to higher-order correlation functions in U(1) symmetric systems
• Authors: Zhi-Guang Lu, Cheng Shang, Ying Wu, and Xin-You L\"u
• Abstract summary: We derive a compact analytical solution of the $n$th-order equal-time correlation functions. Our solution applies to any dissipative quantum system that respects the U(1) symmetry. We have developed a user-friendly open-source library in Python known as the quantum correlation solver.
• Score: 5.760072408343651
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive a compact analytical solution of the $n$th-order equal-time correlation functions by using scattering matrix ($S$ matrix) under a weak coherent state input. Our solution applies to any dissipative quantum system that respects the U(1) symmetry. We further extend our analytical solution into two categories depending on whether the input and output channels are identical. The first category provides a different path for studying cross-correlation and multiple-drive cases, while the second category is instrumental in studying waveguide quantum electrodynamics systems. Our analytical solution allows for easy investigation of the statistical properties of multiple photons even in complex systems. Furthermore, we have developed a user-friendly open-source library in Python known as the quantum correlation solver, and this tool provides a convenient means to study various dissipative quantum systems that satisfy the above-mentioned criteria. Our study enables using $S$ matrix to study the photonic correlation and advance the possibilities for exploring complex systems.

Related papers

• Solving Dicke superradiance analytically: A compendium of methods [0.0]
  We present several analytical approaches to the Dicke superradiance problem. We explore multiple methods to tackle this problem, yielding a solution valid for any time and any number of spins.
  arXiv  Detail & Related papers  (2025-03-13T15:33:02Z)
• Revisiting Gaussian genuine entanglement witnesses with modern software [0.0]
  Continuous-variable Gaussian entanglement is an attractive concept in quantum information theory. We present several approaches to reconstruct the most probable physical covariance matrix from a measured non-physical one. We derive an explicit analytical expression for the symplectic trace of a positive definite matrix, which can serve as a simple witness of an entanglement witness.
  arXiv  Detail & Related papers  (2024-12-12T23:33:52Z)
• An efficient quantum algorithm for independent component analysis [3.400945485383699]
  Independent component analysis (ICA) is a fundamental data processing technique to decompose the captured signals into as independent as possible components. This paper presents a quantum ICA algorithm which focuses on computing a specified contrast function on a quantum computer.
  arXiv  Detail & Related papers  (2023-11-21T11:21:23Z)
• Unifying (Quantum) Statistical and Parametrized (Quantum) Algorithms [65.268245109828]
  We take inspiration from Kearns' SQ oracle and Valiant's weak evaluation oracle. We introduce an extensive yet intuitive framework that yields unconditional lower bounds for learning from evaluation queries.
  arXiv  Detail & Related papers  (2023-10-26T18:23:21Z)
• Analytic Evolution for Complex Coupled Tight-Binding Models: Applications to Quantum Light Manipulation [0.0]
  We present analytic solutions to the evolution in generalized tight-binding models. We apply our results to relevant examples in quantum light manipulation. Our study paves the way for a comprehensive mathematical framework describing the spatial evolution of quantum states.
  arXiv  Detail & Related papers  (2023-10-18T22:27:45Z)
• 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)
• Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
  Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
  arXiv  Detail & Related papers  (2022-10-12T06:46:38Z)
• Quantum Kernel Methods for Solving Differential Equations [21.24186888129542]
  We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are represented.
  arXiv  Detail & Related papers  (2022-03-16T18:56:35Z)
• The complexity of quantum support vector machines [1.7887848708497243]
  Quantum support vector machines employ quantum circuits to define the kernel function. We show that the dual problem can be solved in $O(M4.67/varepsilon2)$ quantum circuit evaluations.
  arXiv  Detail & Related papers  (2022-02-28T19:01:17Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
  We study two different methods to prepare excited states on a quantum computer. We benchmark these techniques on emulated and real quantum devices. These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
  arXiv  Detail & Related papers  (2020-09-28T17:21:25Z)
• Analysis of a density matrix renormalization group approach for transport in open quantum systems [0.0]
  Density matrix renormalization group-based tools have been widely used in the study of closed systems. We present an implementation based on state-of-the-art matrix product state (MPS) and tensor network methods. We show that this implementation is suited for studying thermal transport in one-dimensional systems.
  arXiv  Detail & Related papers  (2020-09-17T10:37:49Z)

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.