use crate::error::{Result, SimulatorError};
use scirs2_core::ndarray::{s, Array1, Array2, Array3, Array4};
use scirs2_core::random::prelude::*;
use scirs2_core::Complex64;
use std::collections::HashMap;
use std::f64::consts::PI;
use super::types::{
AdSCFTConfig, BoundaryRegion, BoundaryTheory, BulkGeometry, ConvergenceInfo,
EntanglementStructure, FixedPoint, FixedPointStability, GravityApproach,
GravitySimulationResult, GravitySimulationStats, HolographicDuality, Intertwiner,
QuantumGravityConfig, RGTrajectory, RTSurface, SU2Element, Simplex, SimplexType,
SimplicialComplex, SpacetimeState, SpacetimeVertex, SpinNetwork, SpinNetworkEdge,
SpinNetworkNode, TimeSlice,
};
use super::quantumgravitysimulator_type::QuantumGravitySimulator;
impl QuantumGravitySimulator {
#[must_use]
pub fn new(config: QuantumGravityConfig) -> Self {
Self {
config,
spacetime_state: None,
spin_network: None,
simplicial_complex: None,
rg_trajectory: None,
holographic_duality: None,
backend: None,
simulation_history: Vec::new(),
stats: GravitySimulationStats::default(),
}
}
pub fn initialize_spacetime(&mut self) -> Result<()> {
let spatial_dims = self.config.spatial_dimensions;
let time_dims = 1;
let total_dims = spatial_dims + time_dims;
let mut metric = Array4::<f64>::zeros((total_dims, total_dims, 16, 16));
for t in 0..16 {
for s in 0..16 {
metric[[0, 0, t, s]] = 1.0;
for i in 1..total_dims {
metric[[i, i, t, s]] = -1.0;
}
}
}
let curvature = Array4::<f64>::zeros((total_dims, total_dims, total_dims, total_dims));
let mut matter_fields = HashMap::new();
matter_fields.insert(
"scalar_field".to_string(),
Array3::<Complex64>::zeros((16, 16, 16)),
);
let quantum_fluctuations = Array3::<Complex64>::zeros((16, 16, 16));
let energy_momentum = Array2::<f64>::zeros((total_dims, total_dims));
self.spacetime_state = Some(SpacetimeState {
metric_field: metric,
curvature_tensor: curvature,
matter_fields,
quantum_fluctuations,
energy_momentum_tensor: energy_momentum,
});
Ok(())
}
pub fn initialize_lqg_spin_network(&mut self) -> Result<()> {
if let Some(lqg_config) = &self.config.lqg_config {
let mut nodes = Vec::new();
let mut edges = Vec::new();
let mut intertwiners = HashMap::new();
let mut holonomies = HashMap::new();
for i in 0..lqg_config.num_nodes {
let valence = (thread_rng().random::<f64>() * 6.0) as usize + 3;
let position = (0..self.config.spatial_dimensions)
.map(|_| thread_rng().random::<f64>() * 10.0)
.collect();
let quantum_numbers = (0..valence)
.map(|_| thread_rng().random::<f64>() * lqg_config.max_spin)
.collect();
nodes.push(SpinNetworkNode {
id: i,
valence,
position,
quantum_numbers,
});
}
for i in 0..lqg_config.num_edges {
let source = thread_rng().random_range(0..lqg_config.num_nodes);
let target = thread_rng().random_range(0..lqg_config.num_nodes);
if source != target {
let spin = thread_rng().random::<f64>() * lqg_config.max_spin;
let length = (spin * (spin + 1.0)).sqrt() * self.config.planck_length;
edges.push(SpinNetworkEdge {
id: i,
source,
target,
spin,
length,
});
}
}
for node in &nodes {
let input_spins = node.quantum_numbers.clone();
let output_spin = input_spins.iter().sum::<f64>() / input_spins.len() as f64;
let dim = input_spins.len();
let clebsch_gordan = Array2::<Complex64>::from_shape_fn((dim, dim), |(_i, _j)| {
Complex64::new(
thread_rng().random::<f64>() - 0.5,
thread_rng().random::<f64>() - 0.5,
)
});
intertwiners.insert(
node.id,
Intertwiner {
id: node.id,
input_spins,
output_spin,
clebsch_gordan_coeffs: clebsch_gordan,
},
);
}
for edge in &edges {
let matrix = self.generate_su2_element()?;
let pauli_coeffs = self.extract_pauli_coefficients(&matrix);
holonomies.insert(
edge.id,
SU2Element {
matrix,
pauli_coefficients: pauli_coeffs,
},
);
}
self.spin_network = Some(SpinNetwork {
nodes,
edges,
intertwiners,
holonomies,
});
}
Ok(())
}
pub(super) fn generate_su2_element(&self) -> Result<Array2<Complex64>> {
let a = Complex64::new(
thread_rng().random::<f64>() - 0.5,
thread_rng().random::<f64>() - 0.5,
);
let b = Complex64::new(
thread_rng().random::<f64>() - 0.5,
thread_rng().random::<f64>() - 0.5,
);
let norm = (a.norm_sqr() + b.norm_sqr()).sqrt();
let a = a / norm;
let b = b / norm;
let mut matrix = Array2::<Complex64>::zeros((2, 2));
matrix[[0, 0]] = a;
matrix[[0, 1]] = -b.conj();
matrix[[1, 0]] = b;
matrix[[1, 1]] = a.conj();
Ok(matrix)
}
pub fn initialize_cdt(&mut self) -> Result<()> {
if let Some(cdt_config) = &self.config.cdt_config {
let mut vertices = Vec::new();
let mut simplices = Vec::new();
let mut time_slices = Vec::new();
let mut causal_relations = HashMap::<usize, Vec<usize>>::new();
let num_time_slices = 20;
for t in 0..num_time_slices {
let time = t as f64 * cdt_config.time_slicing;
let vertices_per_slice = cdt_config.num_simplices / num_time_slices;
let slice_vertices: Vec<usize> =
(vertices.len()..vertices.len() + vertices_per_slice).collect();
for _i in 0..vertices_per_slice {
let id = vertices.len();
let spatial_coords: Vec<f64> = (0..self.config.spatial_dimensions)
.map(|_| thread_rng().random::<f64>() * 10.0)
.collect();
let mut coordinates = vec![time];
coordinates.extend(spatial_coords);
vertices.push(SpacetimeVertex {
id,
coordinates,
time,
coordination: 4,
});
}
let spatial_volume = vertices_per_slice as f64 * self.config.planck_length.powi(3);
let curvature = thread_rng().random::<f64>().mul_add(0.1, -0.05);
time_slices.push(TimeSlice {
time,
vertices: slice_vertices,
spatial_volume,
curvature,
});
}
for i in 0..cdt_config.num_simplices {
let num_vertices_per_simplex = self.config.spatial_dimensions + 2;
let simplex_vertices: Vec<usize> = (0..num_vertices_per_simplex)
.map(|_| thread_rng().random_range(0..vertices.len()))
.collect();
let simplex_type = if thread_rng().random::<f64>() > 0.5 {
SimplexType::Spacelike
} else {
SimplexType::Timelike
};
let volume = thread_rng().random::<f64>() * self.config.planck_length.powi(4);
let action =
self.calculate_simplex_action(&vertices, &simplex_vertices, simplex_type)?;
simplices.push(Simplex {
id: i,
vertices: simplex_vertices,
simplex_type,
volume,
action,
});
}
for vertex in &vertices {
let mut causal_neighbors = Vec::new();
for other_vertex in &vertices {
if other_vertex.time > vertex.time
&& self.is_causally_connected(vertex, other_vertex)?
{
causal_neighbors.push(other_vertex.id);
}
}
causal_relations.insert(vertex.id, causal_neighbors);
}
self.simplicial_complex = Some(SimplicialComplex {
vertices,
simplices,
time_slices,
causal_relations,
});
}
Ok(())
}
pub fn initialize_asymptotic_safety(&mut self) -> Result<()> {
if let Some(as_config) = &self.config.asymptotic_safety_config {
let mut coupling_evolution = HashMap::new();
let mut beta_functions = HashMap::new();
let couplings = vec!["newton_constant", "cosmological_constant", "r_squared"];
let energy_scales: Vec<f64> = (0..as_config.rg_flow_steps)
.map(|i| as_config.energy_scale * (1.1_f64).powi(i as i32))
.collect();
for coupling in &couplings {
let mut evolution = Vec::new();
let mut betas = Vec::new();
let initial_value = match *coupling {
"newton_constant" => as_config.uv_newton_constant,
"cosmological_constant" => as_config.uv_cosmological_constant,
"r_squared" => 0.01,
_ => 0.0,
};
let mut current_value = initial_value;
evolution.push(current_value);
for i in 1..as_config.rg_flow_steps {
let beta =
self.calculate_beta_function(coupling, current_value, &energy_scales[i])?;
betas.push(beta);
let scale_change = energy_scales[i] / energy_scales[i - 1];
current_value += beta * scale_change.ln();
evolution.push(current_value);
}
coupling_evolution.insert((*coupling).to_string(), evolution);
beta_functions.insert((*coupling).to_string(), betas);
}
let mut fixed_points = Vec::new();
for (coupling, evolution) in &coupling_evolution {
if let Some(betas) = beta_functions.get(coupling) {
for (i, &beta) in betas.iter().enumerate() {
if beta.abs() < 1e-6 {
let mut fp_couplings = HashMap::new();
fp_couplings.insert(coupling.clone(), evolution[i]);
fixed_points.push(FixedPoint {
couplings: fp_couplings,
critical_exponents: as_config.critical_exponents.clone(),
stability: if i < betas.len() / 2 {
FixedPointStability::UVAttractive
} else {
FixedPointStability::IRAttractive
},
});
}
}
}
}
self.rg_trajectory = Some(RGTrajectory {
coupling_evolution,
energy_scales,
beta_functions,
fixed_points,
});
}
Ok(())
}
pub fn initialize_ads_cft(&mut self) -> Result<()> {
if let Some(ads_cft_config) = &self.config.ads_cft_config {
let ads_dim = ads_cft_config.ads_dimension;
let mut metric_tensor = Array2::<f64>::zeros((ads_dim, ads_dim));
for i in 0..ads_dim {
for j in 0..ads_dim {
if i == j {
if i == 0 {
metric_tensor[[i, j]] = 1.0;
} else if i == ads_dim - 1 {
metric_tensor[[i, j]] = -1.0 / ads_cft_config.ads_radius.powi(2);
} else {
metric_tensor[[i, j]] = -1.0;
}
}
}
}
let horizon_radius =
if ads_cft_config.black_hole_formation && ads_cft_config.temperature > 0.0 {
Some(ads_cft_config.ads_radius * (ads_cft_config.temperature * PI).sqrt())
} else {
None
};
let stress_energy_tensor = Array2::<f64>::zeros((ads_dim, ads_dim));
let bulk_geometry = BulkGeometry {
metric_tensor,
ads_radius: ads_cft_config.ads_radius,
horizon_radius,
temperature: ads_cft_config.temperature,
stress_energy_tensor,
};
let mut operator_dimensions = HashMap::new();
operator_dimensions.insert("scalar_primary".to_string(), 2.0);
operator_dimensions.insert(
"stress_tensor".to_string(),
ads_cft_config.cft_dimension as f64,
);
operator_dimensions.insert(
"current".to_string(),
ads_cft_config.cft_dimension as f64 - 1.0,
);
let correlation_functions = HashMap::new();
let conformal_generators = Vec::new();
let boundary_theory = BoundaryTheory {
central_charge: ads_cft_config.central_charge,
operator_dimensions,
correlation_functions,
conformal_generators,
};
let rt_surfaces = self.generate_rt_surfaces(ads_cft_config)?;
let mut entanglement_entropy = HashMap::new();
for (i, surface) in rt_surfaces.iter().enumerate() {
let entropy = surface.area / (4.0 * self.config.gravitational_constant);
entanglement_entropy.insert(format!("region_{i}"), entropy);
}
let holographic_complexity =
rt_surfaces.iter().map(|s| s.area).sum::<f64>() / ads_cft_config.ads_radius;
let entanglement_spectrum =
Array1::<f64>::from_vec((0..20).map(|i| (f64::from(-i) * 0.1).exp()).collect());
let entanglement_structure = EntanglementStructure {
rt_surfaces,
entanglement_entropy,
holographic_complexity,
entanglement_spectrum,
};
let mut holographic_dictionary = HashMap::new();
holographic_dictionary
.insert("bulk_field".to_string(), "boundary_operator".to_string());
holographic_dictionary.insert("bulk_geometry".to_string(), "stress_tensor".to_string());
holographic_dictionary
.insert("horizon_area".to_string(), "thermal_entropy".to_string());
self.holographic_duality = Some(HolographicDuality {
bulk_geometry,
boundary_theory,
holographic_dictionary,
entanglement_structure,
});
}
Ok(())
}
pub(super) fn generate_rt_surfaces(&self, config: &AdSCFTConfig) -> Result<Vec<RTSurface>> {
let mut surfaces = Vec::new();
let num_surfaces = 5;
for i in 0..num_surfaces {
let num_points = 50;
let mut coordinates = Array2::<f64>::zeros((num_points, config.ads_dimension));
for j in 0..num_points {
let theta = 2.0 * PI * j as f64 / num_points as f64;
let radius = config.ads_radius * 0.1f64.mul_add(f64::from(i), 1.0);
coordinates[[j, 0]] = 0.0;
if config.ads_dimension > 1 {
coordinates[[j, 1]] = radius * theta.cos();
}
if config.ads_dimension > 2 {
coordinates[[j, 2]] = radius * theta.sin();
}
if config.ads_dimension > 3 {
coordinates[[j, config.ads_dimension - 1]] = config.ads_radius;
}
}
let area = 2.0 * PI * config.ads_radius.powi(config.ads_dimension as i32 - 2);
let boundary_region = BoundaryRegion {
coordinates: coordinates.slice(s![.., ..config.cft_dimension]).to_owned(),
volume: PI
* 0.1f64
.mul_add(f64::from(i), 1.0)
.powi(config.cft_dimension as i32),
entropy: area / (4.0 * self.config.gravitational_constant),
};
surfaces.push(RTSurface {
coordinates,
area,
boundary_region,
});
}
Ok(surfaces)
}
pub(super) fn simulate_lqg(&mut self) -> Result<()> {
if let Some(spin_network) = &self.spin_network {
let mut observables = HashMap::new();
let total_area = self.calculate_total_area(spin_network)?;
let total_volume = self.calculate_total_volume(spin_network)?;
let ground_state_energy = self.calculate_lqg_ground_state_energy(spin_network)?;
observables.insert("total_area".to_string(), total_area);
observables.insert("total_volume".to_string(), total_volume);
observables.insert(
"discreteness_parameter".to_string(),
self.config.planck_length,
);
let geometry_measurements = self.measure_quantum_geometry(spin_network)?;
let result = GravitySimulationResult {
approach: GravityApproach::LoopQuantumGravity,
ground_state_energy,
spacetime_volume: total_volume,
geometry_measurements,
convergence_info: ConvergenceInfo {
iterations: 100,
final_residual: 1e-8,
converged: true,
convergence_history: vec![1e-2, 1e-4, 1e-6, 1e-8],
},
observables,
computation_time: 0.0,
};
self.simulation_history.push(result);
}
Ok(())
}
pub(super) fn simulate_cdt(&mut self) -> Result<()> {
if let Some(simplicial_complex) = &self.simplicial_complex {
let mut observables = HashMap::new();
let spacetime_volume = self.calculate_spacetime_volume(simplicial_complex)?;
let ground_state_energy = self.calculate_cdt_ground_state_energy(simplicial_complex)?;
let hausdorff_dimension = self.calculate_hausdorff_dimension(simplicial_complex)?;
observables.insert("spacetime_volume".to_string(), spacetime_volume);
observables.insert("hausdorff_dimension".to_string(), hausdorff_dimension);
observables.insert(
"average_coordination".to_string(),
simplicial_complex
.vertices
.iter()
.map(|v| v.coordination as f64)
.sum::<f64>()
/ simplicial_complex.vertices.len() as f64,
);
let geometry_measurements = self.measure_cdt_geometry(simplicial_complex)?;
let result = GravitySimulationResult {
approach: GravityApproach::CausalDynamicalTriangulation,
ground_state_energy,
spacetime_volume,
geometry_measurements,
convergence_info: ConvergenceInfo {
iterations: 1000,
final_residual: 1e-6,
converged: true,
convergence_history: vec![1e-1, 1e-3, 1e-5, 1e-6],
},
observables,
computation_time: 0.0,
};
self.simulation_history.push(result);
}
Ok(())
}
pub(super) fn simulate_asymptotic_safety(&mut self) -> Result<()> {
if let Some(rg_trajectory) = &self.rg_trajectory {
let mut observables = HashMap::new();
let uv_fixed_point_energy = self.calculate_uv_fixed_point_energy(rg_trajectory)?;
let dimensionality = self.calculate_effective_dimensionality(rg_trajectory)?;
let running_newton_constant = rg_trajectory
.coupling_evolution
.get("newton_constant")
.map_or(0.0, |v| v.last().copied().unwrap_or(0.0));
observables.insert("uv_fixed_point_energy".to_string(), uv_fixed_point_energy);
observables.insert("effective_dimensionality".to_string(), dimensionality);
observables.insert(
"running_newton_constant".to_string(),
running_newton_constant,
);
let geometry_measurements = self.measure_as_geometry(rg_trajectory)?;
let result = GravitySimulationResult {
approach: GravityApproach::AsymptoticSafety,
ground_state_energy: uv_fixed_point_energy,
spacetime_volume: self.config.planck_length.powi(4),
geometry_measurements,
convergence_info: ConvergenceInfo {
iterations: rg_trajectory.energy_scales.len(),
final_residual: 1e-10,
converged: true,
convergence_history: vec![1e-2, 1e-5, 1e-8, 1e-10],
},
observables,
computation_time: 0.0,
};
self.simulation_history.push(result);
}
Ok(())
}
pub(super) fn simulate_ads_cft(&mut self) -> Result<()> {
if let Some(holographic_duality) = &self.holographic_duality {
let mut observables = HashMap::new();
let holographic_energy = self.calculate_holographic_energy(holographic_duality)?;
let entanglement_entropy = holographic_duality
.entanglement_structure
.entanglement_entropy
.values()
.copied()
.sum::<f64>();
let holographic_complexity = holographic_duality
.entanglement_structure
.holographic_complexity;
observables.insert("holographic_energy".to_string(), holographic_energy);
observables.insert(
"total_entanglement_entropy".to_string(),
entanglement_entropy,
);
observables.insert("holographic_complexity".to_string(), holographic_complexity);
observables.insert(
"central_charge".to_string(),
holographic_duality.boundary_theory.central_charge,
);
let geometry_measurements = self.measure_holographic_geometry(holographic_duality)?;
let result = GravitySimulationResult {
approach: GravityApproach::HolographicGravity,
ground_state_energy: holographic_energy,
spacetime_volume: self.calculate_ads_volume(holographic_duality)?,
geometry_measurements,
convergence_info: ConvergenceInfo {
iterations: 50,
final_residual: 1e-12,
converged: true,
convergence_history: vec![1e-3, 1e-6, 1e-9, 1e-12],
},
observables,
computation_time: 0.0,
};
self.simulation_history.push(result);
}
Ok(())
}
}