File size: 3,809 Bytes
80d7559 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 | // CARRY Fibonacci + Taylor Construction Braid (FTB) Research Module
// RESEARCH HYPOTHESIS: Evaluates mapping of Fibonacci recurrence + Taylor operator expansions to B3 braids.
//
// Formally labeled: RESEARCH_HYPOTHESIS (unproven quantum algorithm until validated).
use std::fmt;
use crate::quantum::core::Gate;
/// Research status tag for experimental constructions.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum ResearchStatus {
ResearchHypothesis,
ValidatedTheorem,
UnprovenCandidate,
}
impl fmt::Display for ResearchStatus {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
match self {
ResearchStatus::ResearchHypothesis => write!(f, "RESEARCH_HYPOTHESIS"),
ResearchStatus::ValidatedTheorem => write!(f, "VALIDATED_THEOREM"),
ResearchStatus::UnprovenCandidate => write!(f, "UNPROVEN_CANDIDATE"),
}
}
}
/// Fibonacci-Taylor Braid (FTB) Construction Object.
#[derive(Debug, Clone)]
pub struct FibonacciTaylorBraid {
pub order_n: usize,
pub time_t: f64,
pub status: ResearchStatus,
pub fibonacci_sequence: Vec<u64>,
pub taylor_coefficients: Vec<f64>,
pub braid_word: Vec<String>,
}
impl FibonacciTaylorBraid {
pub fn new(order_n: usize, time_t: f64) -> Self {
// 1. Compute Fibonacci recurrence F[n] = F[n-1] + F[n-2]
let mut fib = vec![1, 1];
for i in 2..order_n.max(2) {
let next = fib[i - 1] + fib[i - 2];
fib.push(next);
}
// 2. Compute Taylor expansion coefficients: c_k = t^k / k!
// CE-3 fix: stop accumulating once the term would overflow f64 or
// becomes negligible (|term| < 1e-15), to prevent Inf gate angles.
let mut taylor = Vec::new();
let mut factorial = 1.0f64;
let mut t_pow = 1.0f64;
for k in 0..order_n {
if k > 0 {
factorial *= k as f64;
t_pow *= time_t;
}
let term = t_pow / factorial;
if !term.is_finite() {
// Truncate series here; further terms would be Inf or NaN.
break;
}
taylor.push(term);
if term.abs() < 1e-15 {
// Series has converged; remaining terms are negligible.
break;
}
}
// 3. Construct braid generator sequence in B3 group: sigma_1, sigma_2
let mut braid_word = Vec::new();
for k in 0..order_n {
let fib_val = fib[k % fib.len()];
if fib_val % 2 == 0 {
braid_word.push(format!("sigma_1^{}", k + 1));
} else {
braid_word.push(format!("sigma_2^{}", k + 1));
}
}
Self {
order_n,
time_t,
status: ResearchStatus::ResearchHypothesis,
fibonacci_sequence: fib,
taylor_coefficients: taylor,
braid_word,
}
}
/// Map FTB braid word onto a sequence of single and two-qubit quantum gates.
pub fn synthesize_circuit_gates(&self, target_q1: usize, target_q2: usize) -> Vec<Gate> {
let mut gates = Vec::new();
for (k, coeff) in self.taylor_coefficients.iter().enumerate() {
let angle = coeff * (self.fibonacci_sequence[k % self.fibonacci_sequence.len()] as f64);
if k % 2 == 0 {
gates.push(Gate::rx(target_q1, angle));
gates.push(Gate::cnot(target_q1, target_q2));
} else {
gates.push(Gate::rz(target_q2, angle));
gates.push(Gate::cz(target_q1, target_q2));
}
}
gates
}
}
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