Optimal Effective Hamiltonian for Quantum Computing and Simulation

• URL: http://arxiv.org/abs/2602.03618v1
• Date: Tue, 03 Feb 2026 15:09:29 GMT
• Title: Optimal Effective Hamiltonian for Quantum Computing and Simulation
• Authors: Hao-Yu Guan, Xiao-Long Zhu, Yu-Hang Dang, Xiu-Hao Deng,
• Abstract summary: We establish the Least Action Unitary Transformation as the fundamental principle for effective models.<n>We validate this framework against experimental data from superconducting quantum processors.<n>This work provides a systematic, experimentally validated route for high-precision system learning and Hamiltonian engineering.
• Score: 1.0359978670015826
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The effective Hamiltonian serves as the conceptual pivot of quantum engineering, transforming physical complexity into programmable logic; yet, its construction remains compromised by the mathematical non-uniqueness of block diagonalization, which introduces an intrinsic "gauge freedom" that standard methods fail to resolve. We address this by establishing the Least Action Unitary Transformation (LAUT) as the fundamental principle for effective models. By minimizing geometric action, LAUT guarantees dynamical fidelity and inherently enforces the preservation of symmetries--properties frequently violated by conventional Schrieffer-Wolff and Givens rotation techniques. We identify the Bloch-Brandow formalism as the natural perturbative counterpart to this principle, yielding analytic expansions that preserve symmetries to high order. We validate this framework against experimental data from superconducting quantum processors, demonstrating that LAUT quantitatively reproduces interaction rates in driven entangling gates where standard approximations diverge. Furthermore, in tunable coupler architectures, we demonstrate that the LAUT approach captures essential non-rotating-wave contributions that standard models neglect; this inclusion is critical for quantitatively reproducing interaction rates and revealing physical multi-body interactions such as $XZX+YZY$, which are verified to be physical rather than gauge artifacts. By reconciling variational optimality with analytical tractability, this work provides a systematic, experimentally validated route for high-precision system learning and Hamiltonian engineering.

Related papers

• A Boundary Integral-based Neural Operator for Mesh Deformation [10.460831049056761]
  This paper presents an efficient mesh deformation method based on boundary integration and neural operators.<n>A key technical advantage of our framework is the mathematical decoupling of the physical integration process from the geometric representation.<n> Numerical experiments, including large deformations of flexible beams and rigid-body motions of NACA airfoils, confirm the model's high accuracy and strict adherence to the principles of linearity and superposition.
  arXiv  Detail & Related papers  (2026-02-27T06:09:07Z)
• Projection-Based Memory Kernel Coupling Theory for Quantum Dynamics: A Stable Framework for Non-Markovian Simulations [13.09851912426216]
  We present a projection-based, stability-preserving methodology for computing time correlation functions in open quantum systems.<n>This approach provides a versatile and reliable framework for non-Markovian dynamics in complex systems.
  arXiv  Detail & Related papers  (2026-02-11T08:22:00Z)
• Equivariant Evidential Deep Learning for Interatomic Potentials [55.6997213490859]
  Uncertainty quantification is critical for assessing the reliability of machine learning interatomic potentials in molecular dynamics simulations.<n>Existing UQ approaches for MLIPs are often limited by high computational cost or suboptimal performance.<n>We propose textitEquivariant Evidential Deep Learning for Interatomic Potentials ($texte2$IP), a backbone-agnostic framework that models atomic forces and their uncertainty jointly.
  arXiv  Detail & Related papers  (2026-02-11T02:00:25Z)
• Quantization of Physical Interaction Strengths via Singular Moduli [0.0]
  We introduce Interaction Metrology, a protocol that transforms the measurement of coupling strengths from an analog estimation into a topological counting problem.<n>We prove that the system's interaction moduli are topologically forced to take discrete, quantized values, forming a "Geometric $k$-Comb"<n>This discovery establishes a universal standard for force sensing and quantum logic gates, enabling the calibration of interaction strengths with topological certainty.
  arXiv  Detail & Related papers  (2025-12-25T15:54:48Z)
• Mixed Monotonicity Reachability Analysis of Neural ODE: A Trade-Off Between Tightness and Efficiency [1.7205106391379026]
  We propose a novel interval-based reachability method for neural ordinary differential equations (neural ODE)<n>We exploit the geometric structure of full initial sets and their boundaries via the homeomorphism property.<n>Our approach provides sound and computationally efficient over-approximations compared with CORA's zonotopes and NNV2.0 star set representations.
  arXiv  Detail & Related papers  (2025-10-15T10:25:32Z)
• Biorthogonal Neural Network Approach to Two-Dimensional Non-Hermitian Systems [5.513161407069216]
  Non-Hermitian quantum many-body systems exhibit a rich array of physical phenomena.<n>Non-Hermitian skin effects and exceptional points remain largely inaccessible to existing numerical techniques.
  arXiv  Detail & Related papers  (2025-08-01T21:02:41Z)
• Zassenhaus Expansion in Solving the Schrödinger Equation [0.0]
  A fundamental challenge lies in approximating the unitary evolution operator ( e-imathcalHt ) where ( mathcalH ) is a large, typically non-commuting, Hermitian operator.<n>We present a refinement of the fixed-depth simulation framework introduced by E. K"okc"u et al, incorporating the second-order Zassenhaus expansion.<n>This yields a controlled, non-unitary approximation with error scaling as ( mathcalO(t
  arXiv  Detail & Related papers  (2025-05-14T14:48:47Z)
• Intrinsic Regularization via Curved Momentum Space: A Geometric Solution to Divergences in Quantum Field Theory [0.0]
  UV divergences in quantum field theory (QFT) have long been a fundamental challenge.<n>We propose a novel and self-consistent approach in which UV regularization emerges naturally from the curved geometry of momentum space.<n>We show seamless extension to Minkowski space, maintainining regularization properties in relativistic QFT.
  arXiv  Detail & Related papers  (2025-02-20T10:49:26Z)
• 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.<n>We find sufficient conditions under which dynamical decoupling works for such systems.<n>Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution [50.13564338607482]
  We propose a novel optimization framework for the hyperspectral deconvolution problem, called DeepMix.<n>It consists of three distinct modules, namely, a data consistency module, a module that enforces the effect of the handcrafted regularizers, and a denoising module.<n>This work proposes a context aware denoising module designed to sustain the advancements achieved by the cooperative efforts of the other modules.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• 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)
• 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)
• On dissipative symplectic integration with applications to gradient-based optimization [77.34726150561087]
  We propose a geometric framework in which discretizations can be realized systematically. We show that a generalization of symplectic to nonconservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error.
  arXiv  Detail & Related papers  (2020-04-15T00:36:49Z)

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.