Random-matrix reduction in projective quantum mechanics: Numerical simulations

• URL: http://arxiv.org/abs/2606.19273v1
• Date: Wed, 17 Jun 2026 16:50:49 GMT
• Title: Random-matrix reduction in projective quantum mechanics: Numerical simulations
• Abstract summary: We present numerical simulations supporting the random-matrix state-reduction framework developed in the companion theoretical paper.<n>We compare GUE and GOE random Hamiltonians and show that GOE fails to produce the required isotropic complex projective diffusion.<n>The results show that microscopic state reduction, stable measurement records, effective irreversibility, and macroscopic classicality can be described as different coarse-grained manifestations of the same unitary mechanism.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present numerical simulations supporting the random-matrix state-reduction framework developed in the companion theoretical paper. The simulations test the main derived features of the model: isotropic diffusion generated by Gaussian Unitary Ensemble Hamiltonians in projective state space, the restriction of this diffusion to Brownian motion on the classical submanifold, Born-rule frequencies for detector-defined outcome classes, and stroboscopic Newtonian motion for macroscopic systems under repeated environmental monitoring. We also compare GUE and GOE random Hamiltonians and show that GOE fails to produce the required isotropic complex projective diffusion. Further simulations examine finite-resolution detector records in the double-slit experiment, Zeno stability of recorded equivalence classes, effective irreversibility from high-dimensional state-space dynamics and loss of path information, and tensor-product particle-device dynamics in the device limit. The results show that microscopic state reduction, stable measurement records, effective irreversibility, and macroscopic classicality can be described as different coarse-grained manifestations of the same stochastic unitary mechanism.

Related papers

• Precision quantum simulation of magnon spectra and interactions [94.30337065819249]
  We show high-precision simulation of both linear and non-linear response functions in a 2D XY spin-1/2 magnet using an analog-digital superconducting processor of up to 97 qubits.<n>Our results reveal stark variations in magnon decay rates across the Brillouin zone, with enhancement near van Hove singularities and suppression for edge-localized modes.
  arXiv  Detail & Related papers  (2026-07-14T22:11:22Z)
• Random-matrix reduction in projective quantum mechanics [0.0]
  We develop a state-space geometric framework for measurement, classicality, and quantum paradoxes, based on one dynamical conjecture.<n>Within this framework, interactions with measuring devices and environments are described by random-matrix dynamics on projective state space.<n>We show that this random-matrix dynamics yields isotropic diffusion, giving Born-rule transition probabilities in microscopic measurements.
  arXiv  Detail & Related papers  (2026-06-17T16:50:37Z)
• Quantum simulation of the Liouville equation in classical mechanics with discontinuous potential via Schrödingerization [42.22857110018992]
  We develop quantum simulation algorithms for the Liouville equation of classical mechanics with discontinuous potential.<n>We combine Hamiltonian-preserving schemes by Jin and Wen in Commun. Math. Sci. 3(3), 285-315 (2005) with the Schrdingerization method, which embeds the resulting nonunitary semi-discrete dynamics into a unitary Schrdinger type system.
  arXiv  Detail & Related papers  (2026-06-13T02:49:05Z)
• Quantum optomechanics of lossy bodies: general approach and structured squeezed vacuum effects [51.56484100374058]
  We investigate the overall optomechanical force experienced by a macroscopic lossy object in free space under external quantum illumination.<n>By driving the scattering field with an anisotropic, multimode squeezed vacuum state, the spatial profile of the electromagnetic quantum fluctuations can be engineered to exhibit broken rotational symmetry.<n>We establish a general formalism for macroscopic quantum optomechanics that operates beyond the constraints of thermal equilibrium.
  arXiv  Detail & Related papers  (2026-04-07T13:25:43Z)
• Exclusive Scattering Channels from Entanglement Structure in Real-Time Simulations [0.0]
  A scattering event in a quantum field theory is a coherent superposition of all processes consistent with its symmetries and kinematics.<n>This work introduces an experimentally inspired method to isolate scattering channels in Matrix Product State simulations.
  arXiv  Detail & Related papers  (2026-03-16T17:59:59Z)
• Physics-constrained Gaussian Processes for Predicting Shockwave Hugoniot Curves [39.92721695835137]
  A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states along the Hugoniot curve.<n>The framework reproduces the Hugoniot curve with satisfactory accuracy while also quantifying the uncertainty in the predictions.
  arXiv  Detail & Related papers  (2026-01-10T18:54:24Z)
• Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models [50.77646970127369]
  We propose an energy-based diffusion model with a Fokker--Planck-derived regularization term to enforce consistency.<n>We demonstrate our approach by sampling and simulating multiple biomolecular systems, including fast-folding proteins.
  arXiv  Detail & Related papers  (2025-06-20T16:38:29Z)
• Error mitigation of shot-to-shot fluctuations in analog quantum simulators [46.54051337735883]
  We introduce an error mitigation technique that addresses shot-to-shot fluctuations in the parameters for the Hamiltonian governing the system dynamics.<n>We rigorously prove that amplifying this shot-to-shot noise and extrapolating to the zero-noise limit recovers noiseless results for realistic noise distributions.<n> Numerically, we predict a significant enhancement in the effective many-body coherence time for Rydberg atom arrays under realistic conditions.
  arXiv  Detail & Related papers  (2025-06-19T18:00:00Z)
• High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED [0.0]
  We study the scattering dynamics of lattice quantum electrodynamics in 1+1 dimensions on quantum simulators. We construct multi-particle wave-packet states, evolve them in time, and detect outgoing particles post collision. This study highlights the role of classical and quantum simulation in enhancing our understanding of scattering processes in quantum field theories in real time.
  arXiv  Detail & Related papers  (2023-07-05T18:00:00Z)
• Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models [0.0]
  We introduce a hitherto unexplored family of kinetically constrained models featuring a conserved particle number. We reproduce the logarithmic dynamics observed in the quantum case using a classically simulable cellular automaton.
  arXiv  Detail & Related papers  (2022-10-27T16:50:27Z)
• Trapped-Ion Quantum Simulation of Collective Neutrino Oscillations [55.41644538483948]
  We study strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. We find that the gate complexity using second order Trotter- Suzuki formulae scales better with system size than with other decomposition methods such as Quantum Signal Processing.
  arXiv  Detail & Related papers  (2022-07-07T09:39:40Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy [62.997667081978825]
  We propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons.
  arXiv  Detail & Related papers  (2021-05-27T18:00:02Z)
• Scattering of mesons in quantum simulators [0.0]
  Cold-atom platforms stand as promising candidates to realize quantum simulations of non-perturbative phenomena in gauge theories. We demonstrate that present-day quantum simulators can imitate linear particle accelerators, giving access to S-matrix measurements of elastic and inelastic meson collisions.
  arXiv  Detail & Related papers  (2020-11-20T19:00:04Z)

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.