Gregory Nested Picard Iteration Schemes for Open Quantum Systems Governed by the Lindblad Equation

• URL: http://arxiv.org/abs/2606.29002v1
• Date: Sat, 27 Jun 2026 16:36:25 GMT
• Title: Gregory Nested Picard Iteration Schemes for Open Quantum Systems Governed by the Lindblad Equation
• Abstract summary: We develop Gregory NPI schemes constructed by Gregory-type quadrature on equispaced nodes.<n>We analyze the stability of the resulting scheme for a physics-based test equation.<n>We study the performance of a previously constructed CNOT gate for both closed and open quantum systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Numerical simulation of quantum computing hardware and open quantum systems governed by the Lindblad equation is challenging due to the high dimensionality of the density matrix and the need to preserve fundamental physical properties. In our previous work, we developed an arbitrary-order, low-rank, completely positive and trace preserving (CPTP) method for the Lindblad equation with time-dependent Hamiltonians by nested Picard iteration (NPI). In this work, we develop Gregory NPI schemes, which are CPTP schemes constructed by Gregory-type quadrature on equispaced nodes. The methods, which are of order up to nine, substantially reduce the computational cost compared to our previously proposed NPI schemes with Gaussian quadrature rules, while retaining high-order accuracy and structure preservation. We analyze the stability of the resulting scheme for a physics-based test equation. Numerical experiments verify the convergence of the method and demonstrate the effectiveness of the low-rank approximation. We study the performance of a previously constructed CNOT gate for both closed and open quantum systems.

Related papers

• Structure-Preserving Quantum Method of Lines for Evolutionary PDEs with Mixed Boundary Conditions [4.591453488105558]
  We give analysis and circuit design of structure-preserving quantum algorithms for second-order PDEs.<n>We implement our quantum algorithms with explicit block-encoding constructions and circuit implementations.<n>We conduct classical numerical experiments on the convection-diffusion equation, inhomogeneous heat equation, and Klein-Gordon equation.
  arXiv  Detail & Related papers  (2026-06-02T09:48:53Z)
• SpinGQE: A Generative Quantum Eigensolver for Spin Hamiltonians [42.007194397302825]
  Ground state search is central to quantum computing.<n>We present SpinGQE, an extension of the Generative Quantum Eigensolver framework to spin Hamiltonians.<n>We employ a transformer-based decoder to learn over quantum circuits that produce low-energy states.
  arXiv  Detail & Related papers  (2026-03-25T13:38:15Z)
• Full- and low-rank exponential midpoint schemes for forward and adjoint Lindblad equations [3.38220960870904]
  We develop full- and low-rank exponential midpoints for solving both the forward and adjoint Lindblad equations.<n>We show that the proposed schemes preserve positivity and trace unconditionally.<n> convergence of these numerical schemes is proved theoretically and verified numerically.
  arXiv  Detail & Related papers  (2025-05-31T02:15:00Z)
• Lindblad engineering for quantum Gibbs state preparation under the eigenstate thermalization hypothesis [1.0878042982949971]
  We show that a simplified protocol for quantum Gibbs state preparation algorithms is efficient under the eigenstate thermalization hypothesis (ETH)<n>We show that the realized Lindblad algorithm exhibits an inherent resilience against noise, opening up the path to a first demonstration on quantum computers.<n>This work bridges the gap between recent theoretical advances in dissipative Gibbs state preparation algorithms and their eventual quantum hardware implementation.
  arXiv  Detail & Related papers  (2024-12-23T16:35:12Z)
• Optimizing Unitary Coupled Cluster Wave Functions on Quantum Hardware: Error Bound and Resource-Efficient Optimizer [0.0]
  We study the projective quantum eigensolver (PQE) approach to optimizing unitary coupled cluster wave functions on quantum hardware.<n>We derive a bound relating off-diagonal coefficients (residues) of the Hamiltonian to the energy error of the algorithm and the overlap achieved by the obtained wavefunction.
  arXiv  Detail & Related papers  (2024-10-19T15:03:59Z)
• 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)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• 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)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• A Perturbation Algorithm for the Pointers of Franke-Gorini-Kossakowski-Lindblad-Sudarshan Equation [0.0]
  We focus on the quantum measurement operation which is determined by final stationary states of an open system. In seeking pointers, we have been able to propose a perturbative scheme of calculation, if we take the interaction components with an environment to be weak. The scheme we propose is different for the cases of non-degenerate and degenerate Hamiltonian.
  arXiv  Detail & Related papers  (2020-02-02T14:53:26Z)

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.