Moment expansion method for composite open quantum systems including a damped oscillator mode

• URL: http://arxiv.org/abs/2311.06113v2
• Date: Sun, 30 Jun 2024 15:16:53 GMT
• Title: Moment expansion method for composite open quantum systems including a damped oscillator mode
• Authors: Masaaki Tokieda,
• Abstract summary: We develop a numerical method to compute the reduced density matrix of the target system and the low-order moments of the quadrature operators. The application to an optomechanical setting shows that the new method can compute the correlation functions accurately with a significant reduction in the computational cost.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a damped oscillator mode that is resonantly driven and is coupled to an arbitrary target system via the position quadrature operator. For such a composite open quantum system, we develop a numerical method to compute the reduced density matrix of the target system and the low-order moments of the quadrature operators. In this method, we solve the evolution equations for quantities related to moments of the quadrature operators, rather than for the density matrix elements as in the conventional approach. The application to an optomechanical setting shows that the new method can compute the correlation functions accurately with a significant reduction in the computational cost. Since the method does not involve any approximation in its abstract formulation itself, we investigate the numerical accuracy closely. This study reveals the numerical sensitivity of the new approach in certain parameter regimes. We find that this issue can be alleviated by using the position basis instead of the commonly used Fock basis.

Related papers

• Statistical Mechanics of Dynamical System Identification [3.1484174280822845]
  We develop a statistical mechanical approach to analyze sparse equation discovery algorithms. In this framework, statistical mechanics offers tools to analyze the interplay between complexity and fitness.
  arXiv  Detail & Related papers  (2024-03-04T04:32:28Z)
• Randomized semi-quantum matrix processing [0.0]
  We present a hybrid quantum-classical framework for simulating generic matrix functions. The method is based on randomization over the Chebyshev approximation of the target function. We prove advantages on average depths, including quadratic speed-ups on costly parameters.
  arXiv  Detail & Related papers  (2023-07-21T18:00:28Z)
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls [77.34726150561087]
  The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. We adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem.
  arXiv  Detail & Related papers  (2023-07-17T13:37:18Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Exploring the role of parameters in variational quantum algorithms [59.20947681019466]
  We introduce a quantum-control-inspired method for the characterization of variational quantum circuits using the rank of the dynamical Lie algebra. A promising connection is found between the Lie rank, the accuracy of calculated energies, and the requisite depth to attain target states via a given circuit architecture.
  arXiv  Detail & Related papers  (2022-09-28T20:24:53Z)
• A new method for directly computing reduced density matrices [0.0]
  We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system. The approach is based on techniques from non-equilibrium quantum field theory like thermo field dynamics, the Schwinger-Keldsyh formalism, and the Feynman-Vernon influence functional.
  arXiv  Detail & Related papers  (2022-04-19T11:58:36Z)
• 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)
• 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)
• Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models [0.0]
  We introduce a manifold learning-based method for uncertainty quantification (UQ) in describing systems. The proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.
  arXiv  Detail & Related papers  (2021-07-21T00:24:15Z)
• Circuit quantum electrodynamics (cQED) with modular quasi-lumped models [0.23624125155742057]
  Method partitions a quantum device into compact lumped or quasi-distributed cells. We experimentally validate the method on large-scale, state-of-the-art superconducting quantum processors.
  arXiv  Detail & Related papers  (2021-03-18T16:03:37Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)

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.