quantrs2_sim/quantum_gravity_simulation/
quantumgravitysimulator_new_group.rs

1//! # QuantumGravitySimulator - new_group Methods
2//!
3//! This module contains method implementations for `QuantumGravitySimulator`.
4//!
5//! 🤖 Generated with [SplitRS](https://github.com/cool-japan/splitrs)
6
7use crate::error::{Result, SimulatorError};
8use scirs2_core::ndarray::{s, Array1, Array2, Array3, Array4};
9use scirs2_core::random::prelude::*;
10use scirs2_core::Complex64;
11use std::collections::HashMap;
12use std::f64::consts::PI;
13
14use super::types::{
15    AdSCFTConfig, BoundaryRegion, BoundaryTheory, BulkGeometry, ConvergenceInfo,
16    EntanglementStructure, FixedPoint, FixedPointStability, GravityApproach,
17    GravitySimulationResult, GravitySimulationStats, HolographicDuality, Intertwiner,
18    QuantumGravityConfig, RGTrajectory, RTSurface, SU2Element, Simplex, SimplexType,
19    SimplicialComplex, SpacetimeState, SpacetimeVertex, SpinNetwork, SpinNetworkEdge,
20    SpinNetworkNode, TimeSlice,
21};
22
23use super::quantumgravitysimulator_type::QuantumGravitySimulator;
24
25impl QuantumGravitySimulator {
26    /// Create a new quantum gravity simulator
27    #[must_use]
28    pub fn new(config: QuantumGravityConfig) -> Self {
29        Self {
30            config,
31            spacetime_state: None,
32            spin_network: None,
33            simplicial_complex: None,
34            rg_trajectory: None,
35            holographic_duality: None,
36            backend: None,
37            simulation_history: Vec::new(),
38            stats: GravitySimulationStats::default(),
39        }
40    }
41    /// Initialize spacetime state
42    pub fn initialize_spacetime(&mut self) -> Result<()> {
43        let spatial_dims = self.config.spatial_dimensions;
44        let time_dims = 1;
45        let total_dims = spatial_dims + time_dims;
46        let mut metric = Array4::<f64>::zeros((total_dims, total_dims, 16, 16));
47        for t in 0..16 {
48            for s in 0..16 {
49                metric[[0, 0, t, s]] = 1.0;
50                for i in 1..total_dims {
51                    metric[[i, i, t, s]] = -1.0;
52                }
53            }
54        }
55        let curvature = Array4::<f64>::zeros((total_dims, total_dims, total_dims, total_dims));
56        let mut matter_fields = HashMap::new();
57        matter_fields.insert(
58            "scalar_field".to_string(),
59            Array3::<Complex64>::zeros((16, 16, 16)),
60        );
61        let quantum_fluctuations = Array3::<Complex64>::zeros((16, 16, 16));
62        let energy_momentum = Array2::<f64>::zeros((total_dims, total_dims));
63        self.spacetime_state = Some(SpacetimeState {
64            metric_field: metric,
65            curvature_tensor: curvature,
66            matter_fields,
67            quantum_fluctuations,
68            energy_momentum_tensor: energy_momentum,
69        });
70        Ok(())
71    }
72    /// Initialize Loop Quantum Gravity spin network
73    pub fn initialize_lqg_spin_network(&mut self) -> Result<()> {
74        if let Some(lqg_config) = &self.config.lqg_config {
75            let mut nodes = Vec::new();
76            let mut edges = Vec::new();
77            let mut intertwiners = HashMap::new();
78            let mut holonomies = HashMap::new();
79            for i in 0..lqg_config.num_nodes {
80                let valence = (thread_rng().random::<f64>() * 6.0) as usize + 3;
81                let position = (0..self.config.spatial_dimensions)
82                    .map(|_| thread_rng().random::<f64>() * 10.0)
83                    .collect();
84                let quantum_numbers = (0..valence)
85                    .map(|_| thread_rng().random::<f64>() * lqg_config.max_spin)
86                    .collect();
87                nodes.push(SpinNetworkNode {
88                    id: i,
89                    valence,
90                    position,
91                    quantum_numbers,
92                });
93            }
94            for i in 0..lqg_config.num_edges {
95                let source = thread_rng().random_range(0..lqg_config.num_nodes);
96                let target = thread_rng().random_range(0..lqg_config.num_nodes);
97                if source != target {
98                    let spin = thread_rng().random::<f64>() * lqg_config.max_spin;
99                    let length = (spin * (spin + 1.0)).sqrt() * self.config.planck_length;
100                    edges.push(SpinNetworkEdge {
101                        id: i,
102                        source,
103                        target,
104                        spin,
105                        length,
106                    });
107                }
108            }
109            for node in &nodes {
110                let input_spins = node.quantum_numbers.clone();
111                let output_spin = input_spins.iter().sum::<f64>() / input_spins.len() as f64;
112                let dim = input_spins.len();
113                let clebsch_gordan = Array2::<Complex64>::from_shape_fn((dim, dim), |(_i, _j)| {
114                    Complex64::new(
115                        thread_rng().random::<f64>() - 0.5,
116                        thread_rng().random::<f64>() - 0.5,
117                    )
118                });
119                intertwiners.insert(
120                    node.id,
121                    Intertwiner {
122                        id: node.id,
123                        input_spins,
124                        output_spin,
125                        clebsch_gordan_coeffs: clebsch_gordan,
126                    },
127                );
128            }
129            for edge in &edges {
130                let matrix = self.generate_su2_element()?;
131                let pauli_coeffs = self.extract_pauli_coefficients(&matrix);
132                holonomies.insert(
133                    edge.id,
134                    SU2Element {
135                        matrix,
136                        pauli_coefficients: pauli_coeffs,
137                    },
138                );
139            }
140            self.spin_network = Some(SpinNetwork {
141                nodes,
142                edges,
143                intertwiners,
144                holonomies,
145            });
146        }
147        Ok(())
148    }
149    /// Generate random SU(2) element
150    pub(super) fn generate_su2_element(&self) -> Result<Array2<Complex64>> {
151        let a = Complex64::new(
152            thread_rng().random::<f64>() - 0.5,
153            thread_rng().random::<f64>() - 0.5,
154        );
155        let b = Complex64::new(
156            thread_rng().random::<f64>() - 0.5,
157            thread_rng().random::<f64>() - 0.5,
158        );
159        let norm = (a.norm_sqr() + b.norm_sqr()).sqrt();
160        let a = a / norm;
161        let b = b / norm;
162        let mut matrix = Array2::<Complex64>::zeros((2, 2));
163        matrix[[0, 0]] = a;
164        matrix[[0, 1]] = -b.conj();
165        matrix[[1, 0]] = b;
166        matrix[[1, 1]] = a.conj();
167        Ok(matrix)
168    }
169    /// Initialize Causal Dynamical Triangulation
170    pub fn initialize_cdt(&mut self) -> Result<()> {
171        if let Some(cdt_config) = &self.config.cdt_config {
172            let mut vertices = Vec::new();
173            let mut simplices = Vec::new();
174            let mut time_slices = Vec::new();
175            let mut causal_relations = HashMap::<usize, Vec<usize>>::new();
176            let num_time_slices = 20;
177            for t in 0..num_time_slices {
178                let time = t as f64 * cdt_config.time_slicing;
179                let vertices_per_slice = cdt_config.num_simplices / num_time_slices;
180                let slice_vertices: Vec<usize> =
181                    (vertices.len()..vertices.len() + vertices_per_slice).collect();
182                for _i in 0..vertices_per_slice {
183                    let id = vertices.len();
184                    let spatial_coords: Vec<f64> = (0..self.config.spatial_dimensions)
185                        .map(|_| thread_rng().random::<f64>() * 10.0)
186                        .collect();
187                    let mut coordinates = vec![time];
188                    coordinates.extend(spatial_coords);
189                    vertices.push(SpacetimeVertex {
190                        id,
191                        coordinates,
192                        time,
193                        coordination: 4,
194                    });
195                }
196                let spatial_volume = vertices_per_slice as f64 * self.config.planck_length.powi(3);
197                let curvature = thread_rng().random::<f64>().mul_add(0.1, -0.05);
198                time_slices.push(TimeSlice {
199                    time,
200                    vertices: slice_vertices,
201                    spatial_volume,
202                    curvature,
203                });
204            }
205            for i in 0..cdt_config.num_simplices {
206                let num_vertices_per_simplex = self.config.spatial_dimensions + 2;
207                let simplex_vertices: Vec<usize> = (0..num_vertices_per_simplex)
208                    .map(|_| thread_rng().random_range(0..vertices.len()))
209                    .collect();
210                let simplex_type = if thread_rng().random::<f64>() > 0.5 {
211                    SimplexType::Spacelike
212                } else {
213                    SimplexType::Timelike
214                };
215                let volume = thread_rng().random::<f64>() * self.config.planck_length.powi(4);
216                let action =
217                    self.calculate_simplex_action(&vertices, &simplex_vertices, simplex_type)?;
218                simplices.push(Simplex {
219                    id: i,
220                    vertices: simplex_vertices,
221                    simplex_type,
222                    volume,
223                    action,
224                });
225            }
226            for vertex in &vertices {
227                let mut causal_neighbors = Vec::new();
228                for other_vertex in &vertices {
229                    if other_vertex.time > vertex.time
230                        && self.is_causally_connected(vertex, other_vertex)?
231                    {
232                        causal_neighbors.push(other_vertex.id);
233                    }
234                }
235                causal_relations.insert(vertex.id, causal_neighbors);
236            }
237            self.simplicial_complex = Some(SimplicialComplex {
238                vertices,
239                simplices,
240                time_slices,
241                causal_relations,
242            });
243        }
244        Ok(())
245    }
246    /// Initialize Asymptotic Safety RG flow
247    pub fn initialize_asymptotic_safety(&mut self) -> Result<()> {
248        if let Some(as_config) = &self.config.asymptotic_safety_config {
249            let mut coupling_evolution = HashMap::new();
250            let mut beta_functions = HashMap::new();
251            let couplings = vec!["newton_constant", "cosmological_constant", "r_squared"];
252            let energy_scales: Vec<f64> = (0..as_config.rg_flow_steps)
253                .map(|i| as_config.energy_scale * (1.1_f64).powi(i as i32))
254                .collect();
255            for coupling in &couplings {
256                let mut evolution = Vec::new();
257                let mut betas = Vec::new();
258                let initial_value = match *coupling {
259                    "newton_constant" => as_config.uv_newton_constant,
260                    "cosmological_constant" => as_config.uv_cosmological_constant,
261                    "r_squared" => 0.01,
262                    _ => 0.0,
263                };
264                let mut current_value = initial_value;
265                evolution.push(current_value);
266                for i in 1..as_config.rg_flow_steps {
267                    let beta =
268                        self.calculate_beta_function(coupling, current_value, &energy_scales[i])?;
269                    betas.push(beta);
270                    let scale_change = energy_scales[i] / energy_scales[i - 1];
271                    current_value += beta * scale_change.ln();
272                    evolution.push(current_value);
273                }
274                coupling_evolution.insert((*coupling).to_string(), evolution);
275                beta_functions.insert((*coupling).to_string(), betas);
276            }
277            let mut fixed_points = Vec::new();
278            for (coupling, evolution) in &coupling_evolution {
279                if let Some(betas) = beta_functions.get(coupling) {
280                    for (i, &beta) in betas.iter().enumerate() {
281                        if beta.abs() < 1e-6 {
282                            let mut fp_couplings = HashMap::new();
283                            fp_couplings.insert(coupling.clone(), evolution[i]);
284                            fixed_points.push(FixedPoint {
285                                couplings: fp_couplings,
286                                critical_exponents: as_config.critical_exponents.clone(),
287                                stability: if i < betas.len() / 2 {
288                                    FixedPointStability::UVAttractive
289                                } else {
290                                    FixedPointStability::IRAttractive
291                                },
292                            });
293                        }
294                    }
295                }
296            }
297            self.rg_trajectory = Some(RGTrajectory {
298                coupling_evolution,
299                energy_scales,
300                beta_functions,
301                fixed_points,
302            });
303        }
304        Ok(())
305    }
306    /// Initialize AdS/CFT holographic duality
307    pub fn initialize_ads_cft(&mut self) -> Result<()> {
308        if let Some(ads_cft_config) = &self.config.ads_cft_config {
309            let ads_dim = ads_cft_config.ads_dimension;
310            let mut metric_tensor = Array2::<f64>::zeros((ads_dim, ads_dim));
311            for i in 0..ads_dim {
312                for j in 0..ads_dim {
313                    if i == j {
314                        if i == 0 {
315                            metric_tensor[[i, j]] = 1.0;
316                        } else if i == ads_dim - 1 {
317                            metric_tensor[[i, j]] = -1.0 / ads_cft_config.ads_radius.powi(2);
318                        } else {
319                            metric_tensor[[i, j]] = -1.0;
320                        }
321                    }
322                }
323            }
324            let horizon_radius =
325                if ads_cft_config.black_hole_formation && ads_cft_config.temperature > 0.0 {
326                    Some(ads_cft_config.ads_radius * (ads_cft_config.temperature * PI).sqrt())
327                } else {
328                    None
329                };
330            let stress_energy_tensor = Array2::<f64>::zeros((ads_dim, ads_dim));
331            let bulk_geometry = BulkGeometry {
332                metric_tensor,
333                ads_radius: ads_cft_config.ads_radius,
334                horizon_radius,
335                temperature: ads_cft_config.temperature,
336                stress_energy_tensor,
337            };
338            let mut operator_dimensions = HashMap::new();
339            operator_dimensions.insert("scalar_primary".to_string(), 2.0);
340            operator_dimensions.insert(
341                "stress_tensor".to_string(),
342                ads_cft_config.cft_dimension as f64,
343            );
344            operator_dimensions.insert(
345                "current".to_string(),
346                ads_cft_config.cft_dimension as f64 - 1.0,
347            );
348            let correlation_functions = HashMap::new();
349            let conformal_generators = Vec::new();
350            let boundary_theory = BoundaryTheory {
351                central_charge: ads_cft_config.central_charge,
352                operator_dimensions,
353                correlation_functions,
354                conformal_generators,
355            };
356            let rt_surfaces = self.generate_rt_surfaces(ads_cft_config)?;
357            let mut entanglement_entropy = HashMap::new();
358            for (i, surface) in rt_surfaces.iter().enumerate() {
359                let entropy = surface.area / (4.0 * self.config.gravitational_constant);
360                entanglement_entropy.insert(format!("region_{i}"), entropy);
361            }
362            let holographic_complexity =
363                rt_surfaces.iter().map(|s| s.area).sum::<f64>() / ads_cft_config.ads_radius;
364            let entanglement_spectrum =
365                Array1::<f64>::from_vec((0..20).map(|i| (f64::from(-i) * 0.1).exp()).collect());
366            let entanglement_structure = EntanglementStructure {
367                rt_surfaces,
368                entanglement_entropy,
369                holographic_complexity,
370                entanglement_spectrum,
371            };
372            let mut holographic_dictionary = HashMap::new();
373            holographic_dictionary
374                .insert("bulk_field".to_string(), "boundary_operator".to_string());
375            holographic_dictionary.insert("bulk_geometry".to_string(), "stress_tensor".to_string());
376            holographic_dictionary
377                .insert("horizon_area".to_string(), "thermal_entropy".to_string());
378            self.holographic_duality = Some(HolographicDuality {
379                bulk_geometry,
380                boundary_theory,
381                holographic_dictionary,
382                entanglement_structure,
383            });
384        }
385        Ok(())
386    }
387    /// Generate Ryu-Takayanagi surfaces
388    pub(super) fn generate_rt_surfaces(&self, config: &AdSCFTConfig) -> Result<Vec<RTSurface>> {
389        let mut surfaces = Vec::new();
390        let num_surfaces = 5;
391        for i in 0..num_surfaces {
392            let num_points = 50;
393            let mut coordinates = Array2::<f64>::zeros((num_points, config.ads_dimension));
394            for j in 0..num_points {
395                let theta = 2.0 * PI * j as f64 / num_points as f64;
396                let radius = config.ads_radius * 0.1f64.mul_add(f64::from(i), 1.0);
397                coordinates[[j, 0]] = 0.0;
398                if config.ads_dimension > 1 {
399                    coordinates[[j, 1]] = radius * theta.cos();
400                }
401                if config.ads_dimension > 2 {
402                    coordinates[[j, 2]] = radius * theta.sin();
403                }
404                if config.ads_dimension > 3 {
405                    coordinates[[j, config.ads_dimension - 1]] = config.ads_radius;
406                }
407            }
408            let area = 2.0 * PI * config.ads_radius.powi(config.ads_dimension as i32 - 2);
409            let boundary_region = BoundaryRegion {
410                coordinates: coordinates.slice(s![.., ..config.cft_dimension]).to_owned(),
411                volume: PI
412                    * 0.1f64
413                        .mul_add(f64::from(i), 1.0)
414                        .powi(config.cft_dimension as i32),
415                entropy: area / (4.0 * self.config.gravitational_constant),
416            };
417            surfaces.push(RTSurface {
418                coordinates,
419                area,
420                boundary_region,
421            });
422        }
423        Ok(surfaces)
424    }
425    /// Simulate Loop Quantum Gravity dynamics
426    pub(super) fn simulate_lqg(&mut self) -> Result<()> {
427        if let Some(spin_network) = &self.spin_network {
428            let mut observables = HashMap::new();
429            let total_area = self.calculate_total_area(spin_network)?;
430            let total_volume = self.calculate_total_volume(spin_network)?;
431            let ground_state_energy = self.calculate_lqg_ground_state_energy(spin_network)?;
432            observables.insert("total_area".to_string(), total_area);
433            observables.insert("total_volume".to_string(), total_volume);
434            observables.insert(
435                "discreteness_parameter".to_string(),
436                self.config.planck_length,
437            );
438            let geometry_measurements = self.measure_quantum_geometry(spin_network)?;
439            let result = GravitySimulationResult {
440                approach: GravityApproach::LoopQuantumGravity,
441                ground_state_energy,
442                spacetime_volume: total_volume,
443                geometry_measurements,
444                convergence_info: ConvergenceInfo {
445                    iterations: 100,
446                    final_residual: 1e-8,
447                    converged: true,
448                    convergence_history: vec![1e-2, 1e-4, 1e-6, 1e-8],
449                },
450                observables,
451                computation_time: 0.0,
452            };
453            self.simulation_history.push(result);
454        }
455        Ok(())
456    }
457    /// Simulate Causal Dynamical Triangulation
458    pub(super) fn simulate_cdt(&mut self) -> Result<()> {
459        if let Some(simplicial_complex) = &self.simplicial_complex {
460            let mut observables = HashMap::new();
461            let spacetime_volume = self.calculate_spacetime_volume(simplicial_complex)?;
462            let ground_state_energy = self.calculate_cdt_ground_state_energy(simplicial_complex)?;
463            let hausdorff_dimension = self.calculate_hausdorff_dimension(simplicial_complex)?;
464            observables.insert("spacetime_volume".to_string(), spacetime_volume);
465            observables.insert("hausdorff_dimension".to_string(), hausdorff_dimension);
466            observables.insert(
467                "average_coordination".to_string(),
468                simplicial_complex
469                    .vertices
470                    .iter()
471                    .map(|v| v.coordination as f64)
472                    .sum::<f64>()
473                    / simplicial_complex.vertices.len() as f64,
474            );
475            let geometry_measurements = self.measure_cdt_geometry(simplicial_complex)?;
476            let result = GravitySimulationResult {
477                approach: GravityApproach::CausalDynamicalTriangulation,
478                ground_state_energy,
479                spacetime_volume,
480                geometry_measurements,
481                convergence_info: ConvergenceInfo {
482                    iterations: 1000,
483                    final_residual: 1e-6,
484                    converged: true,
485                    convergence_history: vec![1e-1, 1e-3, 1e-5, 1e-6],
486                },
487                observables,
488                computation_time: 0.0,
489            };
490            self.simulation_history.push(result);
491        }
492        Ok(())
493    }
494    /// Simulate Asymptotic Safety
495    pub(super) fn simulate_asymptotic_safety(&mut self) -> Result<()> {
496        if let Some(rg_trajectory) = &self.rg_trajectory {
497            let mut observables = HashMap::new();
498            let uv_fixed_point_energy = self.calculate_uv_fixed_point_energy(rg_trajectory)?;
499            let dimensionality = self.calculate_effective_dimensionality(rg_trajectory)?;
500            let running_newton_constant = rg_trajectory
501                .coupling_evolution
502                .get("newton_constant")
503                .map_or(0.0, |v| v.last().copied().unwrap_or(0.0));
504            observables.insert("uv_fixed_point_energy".to_string(), uv_fixed_point_energy);
505            observables.insert("effective_dimensionality".to_string(), dimensionality);
506            observables.insert(
507                "running_newton_constant".to_string(),
508                running_newton_constant,
509            );
510            let geometry_measurements = self.measure_as_geometry(rg_trajectory)?;
511            let result = GravitySimulationResult {
512                approach: GravityApproach::AsymptoticSafety,
513                ground_state_energy: uv_fixed_point_energy,
514                spacetime_volume: self.config.planck_length.powi(4),
515                geometry_measurements,
516                convergence_info: ConvergenceInfo {
517                    iterations: rg_trajectory.energy_scales.len(),
518                    final_residual: 1e-10,
519                    converged: true,
520                    convergence_history: vec![1e-2, 1e-5, 1e-8, 1e-10],
521                },
522                observables,
523                computation_time: 0.0,
524            };
525            self.simulation_history.push(result);
526        }
527        Ok(())
528    }
529    /// Simulate AdS/CFT correspondence
530    pub(super) fn simulate_ads_cft(&mut self) -> Result<()> {
531        if let Some(holographic_duality) = &self.holographic_duality {
532            let mut observables = HashMap::new();
533            let holographic_energy = self.calculate_holographic_energy(holographic_duality)?;
534            let entanglement_entropy = holographic_duality
535                .entanglement_structure
536                .entanglement_entropy
537                .values()
538                .copied()
539                .sum::<f64>();
540            let holographic_complexity = holographic_duality
541                .entanglement_structure
542                .holographic_complexity;
543            observables.insert("holographic_energy".to_string(), holographic_energy);
544            observables.insert(
545                "total_entanglement_entropy".to_string(),
546                entanglement_entropy,
547            );
548            observables.insert("holographic_complexity".to_string(), holographic_complexity);
549            observables.insert(
550                "central_charge".to_string(),
551                holographic_duality.boundary_theory.central_charge,
552            );
553            let geometry_measurements = self.measure_holographic_geometry(holographic_duality)?;
554            let result = GravitySimulationResult {
555                approach: GravityApproach::HolographicGravity,
556                ground_state_energy: holographic_energy,
557                spacetime_volume: self.calculate_ads_volume(holographic_duality)?,
558                geometry_measurements,
559                convergence_info: ConvergenceInfo {
560                    iterations: 50,
561                    final_residual: 1e-12,
562                    converged: true,
563                    convergence_history: vec![1e-3, 1e-6, 1e-9, 1e-12],
564                },
565                observables,
566                computation_time: 0.0,
567            };
568            self.simulation_history.push(result);
569        }
570        Ok(())
571    }
572}
quantrs2_sim/quantum_gravity_simulation/quantumgravitysimulator_new_group.rs

quantrs2_sim/quantum_gravity_simulation/
quantumgravitysimulator_new_group.rs
