quantrs2_circuit/equivalence/
types.rs

1//! Auto-generated module
2//!
3//! 🤖 Generated with [SplitRS](https://github.com/cool-japan/splitrs)
4
5use crate::builder::Circuit;
6use crate::scirs2_integration::{AnalyzerConfig, SciRS2CircuitAnalyzer};
7use quantrs2_core::{
8    error::{QuantRS2Error, QuantRS2Result},
9    gate::{
10        multi::{CRX, CRY, CRZ},
11        single::{RotationX, RotationY, RotationZ},
12        GateOp,
13    },
14    qubit::QubitId,
15};
16use scirs2_core::ndarray::{array, Array2, ArrayView2};
17use scirs2_core::Complex64;
18use serde::{Deserialize, Serialize};
19use std::collections::HashMap;
20
21use super::functions::SCIRS2_DEFAULT_TOLERANCE;
22
23/// `SciRS2` numerical analysis for equivalence checking
24#[derive(Debug, Clone, Serialize, Deserialize)]
25pub struct NumericalAnalysis {
26    /// Condition number of the matrices involved
27    pub condition_number: Option<f64>,
28    /// Numerical rank of difference matrix
29    pub numerical_rank: Option<usize>,
30    /// Frobenius norm of the difference
31    pub frobenius_norm: f64,
32    /// Spectral norm of the difference
33    pub spectral_norm: Option<f64>,
34    /// Adaptive tolerance used based on circuit complexity
35    pub adaptive_tolerance: f64,
36    /// Matrix factorization stability indicator
37    pub stability_indicator: f64,
38}
39/// Enhanced circuit equivalence checker with `SciRS2` integration
40pub struct EquivalenceChecker {
41    options: EquivalenceOptions,
42    scirs2_analyzer: Option<SciRS2CircuitAnalyzer>,
43    numerical_cache: HashMap<String, NumericalAnalysis>,
44}
45impl EquivalenceChecker {
46    /// Create a new equivalence checker with options
47    #[must_use]
48    pub fn new(options: EquivalenceOptions) -> Self {
49        let scirs2_analyzer = if options.enable_graph_comparison
50            || options.enable_statistical_analysis
51            || options.enable_stability_analysis
52        {
53            Some(SciRS2CircuitAnalyzer::new())
54        } else {
55            None
56        };
57        Self {
58            options,
59            scirs2_analyzer,
60            numerical_cache: HashMap::new(),
61        }
62    }
63    /// Create a new equivalence checker with default options
64    #[must_use]
65    pub fn default() -> Self {
66        Self::new(EquivalenceOptions::default())
67    }
68    /// Create a new equivalence checker with custom `SciRS2` configuration
69    #[must_use]
70    pub fn with_scirs2_config(config: AnalyzerConfig) -> Self {
71        let scirs2_analyzer = Some(SciRS2CircuitAnalyzer::with_config(config.clone()));
72        Self {
73            options: EquivalenceOptions {
74                scirs2_config: Some(config),
75                enable_graph_comparison: true,
76                ..Default::default()
77            },
78            scirs2_analyzer,
79            numerical_cache: HashMap::new(),
80        }
81    }
82    /// Check if two circuits are equivalent using all methods including `SciRS2`
83    pub fn check_equivalence<const N: usize>(
84        &mut self,
85        circuit1: &Circuit<N>,
86        circuit2: &Circuit<N>,
87    ) -> QuantRS2Result<EquivalenceResult> {
88        if self.options.enable_graph_comparison {
89            if let Ok(result) = self.check_scirs2_graph_equivalence(circuit1, circuit2) {
90                if result.equivalent {
91                    return Ok(result);
92                }
93            }
94        }
95        if let Ok(result) = self.check_structural_equivalence(circuit1, circuit2) {
96            if result.equivalent {
97                return Ok(result);
98            }
99        }
100        if (self.options.enable_adaptive_tolerance || self.options.enable_statistical_analysis)
101            && N <= self.options.max_unitary_qubits
102        {
103            return self.check_scirs2_numerical_equivalence(circuit1, circuit2);
104        }
105        if N <= self.options.max_unitary_qubits {
106            return self.check_unitary_equivalence(circuit1, circuit2);
107        }
108        self.check_state_vector_equivalence(circuit1, circuit2)
109    }
110    /// Check equivalence using `SciRS2` numerical analysis with adaptive tolerance
111    pub fn check_scirs2_numerical_equivalence<const N: usize>(
112        &mut self,
113        circuit1: &Circuit<N>,
114        circuit2: &Circuit<N>,
115    ) -> QuantRS2Result<EquivalenceResult> {
116        if N > self.options.max_unitary_qubits {
117            return Err(QuantRS2Error::InvalidInput(format!(
118                "Circuit too large for SciRS2 numerical analysis: {} qubits (max: {})",
119                N, self.options.max_unitary_qubits
120            )));
121        }
122        let unitary1 = self.get_circuit_unitary(circuit1)?;
123        let unitary2 = self.get_circuit_unitary(circuit2)?;
124        let numerical_analysis = self.perform_scirs2_numerical_analysis(&unitary1, &unitary2)?;
125        let adaptive_tolerance = self.calculate_adaptive_tolerance::<N>(N, &numerical_analysis);
126        let (equivalent, max_diff, confidence_score, error_bounds) =
127            self.scirs2_unitaries_equal(&unitary1, &unitary2, adaptive_tolerance)?;
128        let statistical_significance = if self.options.enable_statistical_analysis {
129            Some(self.calculate_statistical_significance(&unitary1, &unitary2, max_diff)?)
130        } else {
131            None
132        };
133        Ok(EquivalenceResult {
134            equivalent,
135            check_type: EquivalenceType::SciRS2NumericalEquivalence,
136            max_difference: Some(max_diff),
137            details: format!(
138                "SciRS2 numerical analysis: tolerance={:.2e}, confidence={:.3}, condition_number={:.2e}",
139                adaptive_tolerance, confidence_score, numerical_analysis.condition_number
140                .unwrap_or(0.0)
141            ),
142            numerical_analysis: Some(numerical_analysis),
143            confidence_score,
144            statistical_significance,
145            error_bounds: Some(error_bounds),
146        })
147    }
148    /// Check equivalence using `SciRS2` graph-based analysis
149    pub fn check_scirs2_graph_equivalence<const N: usize>(
150        &mut self,
151        circuit1: &Circuit<N>,
152        circuit2: &Circuit<N>,
153    ) -> QuantRS2Result<EquivalenceResult> {
154        let analyzer = self.scirs2_analyzer.as_mut().ok_or_else(|| {
155            QuantRS2Error::InvalidInput("SciRS2 analyzer not initialized".to_string())
156        })?;
157        let graph1 = analyzer.circuit_to_scirs2_graph(circuit1)?;
158        let graph2 = analyzer.circuit_to_scirs2_graph(circuit2)?;
159        let (equivalent, similarity_score, graph_details) =
160            self.compare_scirs2_graphs(&graph1, &graph2)?;
161        Ok(EquivalenceResult {
162            equivalent,
163            check_type: EquivalenceType::SciRS2GraphEquivalence,
164            max_difference: Some(1.0 - similarity_score),
165            details: graph_details,
166            numerical_analysis: None,
167            confidence_score: similarity_score,
168            statistical_significance: None,
169            error_bounds: None,
170        })
171    }
172    /// Check structural equivalence (exact gate-by-gate match)
173    pub fn check_structural_equivalence<const N: usize>(
174        &self,
175        circuit1: &Circuit<N>,
176        circuit2: &Circuit<N>,
177    ) -> QuantRS2Result<EquivalenceResult> {
178        if circuit1.num_gates() != circuit2.num_gates() {
179            return Ok(EquivalenceResult {
180                equivalent: false,
181                check_type: EquivalenceType::StructuralEquivalence,
182                max_difference: None,
183                details: format!(
184                    "Different number of gates: {} vs {}",
185                    circuit1.num_gates(),
186                    circuit2.num_gates()
187                ),
188                numerical_analysis: None,
189                confidence_score: 0.0,
190                statistical_significance: None,
191                error_bounds: None,
192            });
193        }
194        let gates1 = circuit1.gates();
195        let gates2 = circuit2.gates();
196        for (i, (gate1, gate2)) in gates1.iter().zip(gates2.iter()).enumerate() {
197            if !self.gates_equal(gate1.as_ref(), gate2.as_ref()) {
198                return Ok(EquivalenceResult {
199                    equivalent: false,
200                    check_type: EquivalenceType::StructuralEquivalence,
201                    max_difference: None,
202                    details: format!(
203                        "Gates differ at position {}: {} vs {}",
204                        i,
205                        gate1.name(),
206                        gate2.name()
207                    ),
208                    numerical_analysis: None,
209                    confidence_score: 0.0,
210                    statistical_significance: None,
211                    error_bounds: None,
212                });
213            }
214        }
215        Ok(EquivalenceResult {
216            equivalent: true,
217            check_type: EquivalenceType::StructuralEquivalence,
218            max_difference: Some(0.0),
219            details: "Circuits are structurally identical".to_string(),
220            numerical_analysis: None,
221            confidence_score: 1.0,
222            statistical_significance: None,
223            error_bounds: None,
224        })
225    }
226    /// Check if two gates are equal
227    ///
228    /// Compares gates by name, qubits, and parameters (for parametric gates).
229    /// Uses numerical tolerance for parameter comparison.
230    fn gates_equal(&self, gate1: &dyn GateOp, gate2: &dyn GateOp) -> bool {
231        if gate1.name() != gate2.name() {
232            return false;
233        }
234        let qubits1 = gate1.qubits();
235        let qubits2 = gate2.qubits();
236        if qubits1.len() != qubits2.len() {
237            return false;
238        }
239        for (q1, q2) in qubits1.iter().zip(qubits2.iter()) {
240            if q1 != q2 {
241                return false;
242            }
243        }
244        if !self.check_gate_parameters(gate1, gate2) {
245            return false;
246        }
247        true
248    }
249    /// Check if parameters of two gates are equal (for parametric gates)
250    fn check_gate_parameters(&self, gate1: &dyn GateOp, gate2: &dyn GateOp) -> bool {
251        if let Some(rx1) = gate1.as_any().downcast_ref::<RotationX>() {
252            if let Some(rx2) = gate2.as_any().downcast_ref::<RotationX>() {
253                return (rx1.theta - rx2.theta).abs() < self.options.tolerance;
254            }
255        }
256        if let Some(ry1) = gate1.as_any().downcast_ref::<RotationY>() {
257            if let Some(ry2) = gate2.as_any().downcast_ref::<RotationY>() {
258                return (ry1.theta - ry2.theta).abs() < self.options.tolerance;
259            }
260        }
261        if let Some(rz1) = gate1.as_any().downcast_ref::<RotationZ>() {
262            if let Some(rz2) = gate2.as_any().downcast_ref::<RotationZ>() {
263                return (rz1.theta - rz2.theta).abs() < self.options.tolerance;
264            }
265        }
266        if let Some(crx1) = gate1.as_any().downcast_ref::<CRX>() {
267            if let Some(crx2) = gate2.as_any().downcast_ref::<CRX>() {
268                return (crx1.theta - crx2.theta).abs() < self.options.tolerance;
269            }
270        }
271        if let Some(cry1) = gate1.as_any().downcast_ref::<CRY>() {
272            if let Some(cry2) = gate2.as_any().downcast_ref::<CRY>() {
273                return (cry1.theta - cry2.theta).abs() < self.options.tolerance;
274            }
275        }
276        if let Some(crz1) = gate1.as_any().downcast_ref::<CRZ>() {
277            if let Some(crz2) = gate2.as_any().downcast_ref::<CRZ>() {
278                return (crz1.theta - crz2.theta).abs() < self.options.tolerance;
279            }
280        }
281        true
282    }
283    /// Check unitary equivalence
284    pub fn check_unitary_equivalence<const N: usize>(
285        &self,
286        circuit1: &Circuit<N>,
287        circuit2: &Circuit<N>,
288    ) -> QuantRS2Result<EquivalenceResult> {
289        if N > self.options.max_unitary_qubits {
290            return Err(QuantRS2Error::InvalidInput(format!(
291                "Circuit too large for unitary construction: {} qubits (max: {})",
292                N, self.options.max_unitary_qubits
293            )));
294        }
295        let unitary1 = self.get_circuit_unitary(circuit1)?;
296        let unitary2 = self.get_circuit_unitary(circuit2)?;
297        let (equivalent, max_diff) = if self.options.ignore_global_phase {
298            self.unitaries_equal_up_to_phase(&unitary1, &unitary2)
299        } else {
300            self.unitaries_equal(&unitary1, &unitary2)
301        };
302        Ok(EquivalenceResult {
303            equivalent,
304            check_type: if self.options.ignore_global_phase {
305                EquivalenceType::GlobalPhaseEquivalence
306            } else {
307                EquivalenceType::UnitaryEquivalence
308            },
309            max_difference: Some(max_diff),
310            details: if equivalent {
311                "Unitaries are equivalent".to_string()
312            } else {
313                format!("Maximum unitary difference: {max_diff:.2e}")
314            },
315            numerical_analysis: None,
316            confidence_score: if equivalent {
317                1.0 - (max_diff / self.options.tolerance)
318            } else {
319                0.0
320            },
321            statistical_significance: None,
322            error_bounds: None,
323        })
324    }
325    /// Get the unitary matrix for a circuit
326    fn get_circuit_unitary<const N: usize>(
327        &self,
328        circuit: &Circuit<N>,
329    ) -> QuantRS2Result<Array2<Complex64>> {
330        let dim = 1 << N;
331        let mut unitary = Array2::eye(dim);
332        for gate in circuit.gates() {
333            self.apply_gate_to_unitary(&mut unitary, gate.as_ref(), N)?;
334        }
335        Ok(unitary)
336    }
337    /// Apply a gate to a unitary matrix
338    fn apply_gate_to_unitary(
339        &self,
340        unitary: &mut Array2<Complex64>,
341        gate: &dyn GateOp,
342        num_qubits: usize,
343    ) -> QuantRS2Result<()> {
344        let gate_matrix = self.get_gate_matrix(gate)?;
345        let qubits = gate.qubits();
346        match qubits.len() {
347            1 => {
348                let qubit_idx = qubits[0].id() as usize;
349                self.apply_single_qubit_gate(unitary, &gate_matrix, qubit_idx, num_qubits)?;
350            }
351            2 => {
352                let control_idx = qubits[0].id() as usize;
353                let target_idx = qubits[1].id() as usize;
354                self.apply_two_qubit_gate(
355                    unitary,
356                    &gate_matrix,
357                    control_idx,
358                    target_idx,
359                    num_qubits,
360                )?;
361            }
362            _ => {
363                return Err(QuantRS2Error::UnsupportedOperation(format!(
364                    "Gates with {} qubits not yet supported",
365                    qubits.len()
366                )));
367            }
368        }
369        Ok(())
370    }
371    /// Get the matrix representation of a gate
372    fn get_gate_matrix(&self, gate: &dyn GateOp) -> QuantRS2Result<Array2<Complex64>> {
373        let c0 = Complex64::new(0.0, 0.0);
374        let c1 = Complex64::new(1.0, 0.0);
375        let ci = Complex64::new(0.0, 1.0);
376        match gate.name() {
377            "H" => {
378                let sqrt2_inv = 1.0 / std::f64::consts::SQRT_2;
379                Ok(array![
380                    [c1 * sqrt2_inv, c1 * sqrt2_inv],
381                    [c1 * sqrt2_inv, -c1 * sqrt2_inv]
382                ])
383            }
384            "X" => Ok(array![[c0, c1], [c1, c0]]),
385            "Y" => Ok(array![[c0, -ci], [ci, c0]]),
386            "Z" => Ok(array![[c1, c0], [c0, -c1]]),
387            "S" => Ok(array![[c1, c0], [c0, ci]]),
388            "T" => Ok(array![
389                [c1, c0],
390                [
391                    c0,
392                    Complex64::new(
393                        1.0 / std::f64::consts::SQRT_2,
394                        1.0 / std::f64::consts::SQRT_2
395                    )
396                ]
397            ]),
398            "CNOT" | "CX" => Ok(array![
399                [c1, c0, c0, c0],
400                [c0, c1, c0, c0],
401                [c0, c0, c0, c1],
402                [c0, c0, c1, c0]
403            ]),
404            "CZ" => Ok(array![
405                [c1, c0, c0, c0],
406                [c0, c1, c0, c0],
407                [c0, c0, c1, c0],
408                [c0, c0, c0, -c1]
409            ]),
410            "SWAP" => Ok(array![
411                [c1, c0, c0, c0],
412                [c0, c0, c1, c0],
413                [c0, c1, c0, c0],
414                [c0, c0, c0, c1]
415            ]),
416            _ => Err(QuantRS2Error::UnsupportedOperation(format!(
417                "Gate '{}' matrix not yet implemented",
418                gate.name()
419            ))),
420        }
421    }
422    /// Apply a single-qubit gate to a unitary matrix
423    fn apply_single_qubit_gate(
424        &self,
425        unitary: &mut Array2<Complex64>,
426        gate_matrix: &Array2<Complex64>,
427        qubit_idx: usize,
428        num_qubits: usize,
429    ) -> QuantRS2Result<()> {
430        let dim = 1 << num_qubits;
431        let mut new_unitary = Array2::zeros((dim, dim));
432        for col in 0..dim {
433            for row in 0..dim {
434                let mut sum = Complex64::new(0.0, 0.0);
435                let row_bit = (row >> qubit_idx) & 1;
436                let col_bit = (col >> qubit_idx) & 1;
437                for k in 0..dim {
438                    let k_bit = (k >> qubit_idx) & 1;
439                    if (row ^ k) == ((row_bit ^ k_bit) << qubit_idx) {
440                        sum += gate_matrix[[row_bit, k_bit]] * unitary[[k, col]];
441                    }
442                }
443                new_unitary[[row, col]] = sum;
444            }
445        }
446        *unitary = new_unitary;
447        Ok(())
448    }
449    /// Apply a two-qubit gate to a unitary matrix
450    fn apply_two_qubit_gate(
451        &self,
452        unitary: &mut Array2<Complex64>,
453        gate_matrix: &Array2<Complex64>,
454        qubit1_idx: usize,
455        qubit2_idx: usize,
456        num_qubits: usize,
457    ) -> QuantRS2Result<()> {
458        let dim = 1 << num_qubits;
459        let mut new_unitary = Array2::zeros((dim, dim));
460        for col in 0..dim {
461            for row in 0..dim {
462                let mut sum = Complex64::new(0.0, 0.0);
463                let row_q1 = (row >> qubit1_idx) & 1;
464                let row_q2 = (row >> qubit2_idx) & 1;
465                let row_gate_idx = (row_q1 << 1) | row_q2;
466                let col_q1 = (col >> qubit1_idx) & 1;
467                let col_q2 = (col >> qubit2_idx) & 1;
468                for k in 0..dim {
469                    let k_q1 = (k >> qubit1_idx) & 1;
470                    let k_q2 = (k >> qubit2_idx) & 1;
471                    let k_gate_idx = (k_q1 << 1) | k_q2;
472                    let diff = row ^ k;
473                    let expected_diff =
474                        ((row_q1 ^ k_q1) << qubit1_idx) | ((row_q2 ^ k_q2) << qubit2_idx);
475                    if diff == expected_diff {
476                        sum += gate_matrix[[row_gate_idx, k_gate_idx]] * unitary[[k, col]];
477                    }
478                }
479                new_unitary[[row, col]] = sum;
480            }
481        }
482        *unitary = new_unitary;
483        Ok(())
484    }
485    /// Check if two unitaries are equal
486    fn unitaries_equal(&self, u1: &Array2<Complex64>, u2: &Array2<Complex64>) -> (bool, f64) {
487        if u1.shape() != u2.shape() {
488            return (false, f64::INFINITY);
489        }
490        let mut max_diff = 0.0;
491        for (a, b) in u1.iter().zip(u2.iter()) {
492            let diff = (a - b).norm();
493            if diff > max_diff {
494                max_diff = diff;
495            }
496            if diff > self.options.tolerance {
497                return (false, max_diff);
498            }
499        }
500        (true, max_diff)
501    }
502    /// Check if two unitaries are equal up to a global phase
503    fn unitaries_equal_up_to_phase(
504        &self,
505        u1: &Array2<Complex64>,
506        u2: &Array2<Complex64>,
507    ) -> (bool, f64) {
508        if u1.shape() != u2.shape() {
509            return (false, f64::INFINITY);
510        }
511        let mut phase = None;
512        for (a, b) in u1.iter().zip(u2.iter()) {
513            if a.norm() > self.options.tolerance && b.norm() > self.options.tolerance {
514                phase = Some(b / a);
515                break;
516            }
517        }
518        let phase = match phase {
519            Some(p) => p,
520            None => return (false, f64::INFINITY),
521        };
522        let mut max_diff = 0.0;
523        for (a, b) in u1.iter().zip(u2.iter()) {
524            let adjusted = a * phase;
525            let diff = (adjusted - b).norm();
526            if diff > max_diff {
527                max_diff = diff;
528            }
529            if diff > self.options.tolerance {
530                return (false, max_diff);
531            }
532        }
533        (true, max_diff)
534    }
535    /// Check state vector equivalence
536    pub fn check_state_vector_equivalence<const N: usize>(
537        &self,
538        circuit1: &Circuit<N>,
539        circuit2: &Circuit<N>,
540    ) -> QuantRS2Result<EquivalenceResult> {
541        let mut max_diff = 0.0;
542        let num_states = if self.options.check_all_states {
543            1 << N
544        } else {
545            std::cmp::min(1 << N, 100)
546        };
547        for state_idx in 0..num_states {
548            let state1 = self.apply_circuit_to_state(circuit1, state_idx, N)?;
549            let state2 = self.apply_circuit_to_state(circuit2, state_idx, N)?;
550            let (equal, diff) = if self.options.ignore_global_phase {
551                self.states_equal_up_to_phase(&state1, &state2)
552            } else {
553                self.states_equal(&state1, &state2)
554            };
555            if diff > max_diff {
556                max_diff = diff;
557            }
558            if !equal {
559                return Ok(EquivalenceResult {
560                    equivalent: false,
561                    check_type: EquivalenceType::StateVectorEquivalence,
562                    max_difference: Some(max_diff),
563                    details: format!(
564                        "States differ for input |{state_idx:0b}>: max difference {max_diff:.2e}"
565                    ),
566                    numerical_analysis: None,
567                    confidence_score: 0.0,
568                    statistical_significance: None,
569                    error_bounds: None,
570                });
571            }
572        }
573        Ok(EquivalenceResult {
574            equivalent: true,
575            check_type: EquivalenceType::StateVectorEquivalence,
576            max_difference: Some(max_diff),
577            details: format!("Checked {num_states} computational basis states"),
578            numerical_analysis: None,
579            confidence_score: 1.0 - (max_diff / self.options.tolerance).min(1.0),
580            statistical_significance: None,
581            error_bounds: None,
582        })
583    }
584    /// Apply circuit to a computational basis state
585    fn apply_circuit_to_state<const N: usize>(
586        &self,
587        circuit: &Circuit<N>,
588        state_idx: usize,
589        num_qubits: usize,
590    ) -> QuantRS2Result<Vec<Complex64>> {
591        let dim = 1 << num_qubits;
592        let mut state = vec![Complex64::new(0.0, 0.0); dim];
593        state[state_idx] = Complex64::new(1.0, 0.0);
594        for gate in circuit.gates() {
595            self.apply_gate_to_state(&mut state, gate.as_ref(), num_qubits)?;
596        }
597        Ok(state)
598    }
599    /// Apply a gate to a state vector
600    fn apply_gate_to_state(
601        &self,
602        state: &mut Vec<Complex64>,
603        gate: &dyn GateOp,
604        num_qubits: usize,
605    ) -> QuantRS2Result<()> {
606        let gate_matrix = self.get_gate_matrix(gate)?;
607        let qubits = gate.qubits();
608        match qubits.len() {
609            1 => {
610                let qubit_idx = qubits[0].id() as usize;
611                self.apply_single_qubit_gate_to_state(state, &gate_matrix, qubit_idx, num_qubits)?;
612            }
613            2 => {
614                let control_idx = qubits[0].id() as usize;
615                let target_idx = qubits[1].id() as usize;
616                self.apply_two_qubit_gate_to_state(
617                    state,
618                    &gate_matrix,
619                    control_idx,
620                    target_idx,
621                    num_qubits,
622                )?;
623            }
624            _ => {
625                return Err(QuantRS2Error::UnsupportedOperation(format!(
626                    "Gates with {} qubits not yet supported",
627                    qubits.len()
628                )));
629            }
630        }
631        Ok(())
632    }
633    /// Apply a single-qubit gate to a state vector
634    fn apply_single_qubit_gate_to_state(
635        &self,
636        state: &mut Vec<Complex64>,
637        gate_matrix: &Array2<Complex64>,
638        qubit_idx: usize,
639        num_qubits: usize,
640    ) -> QuantRS2Result<()> {
641        let dim = 1 << num_qubits;
642        let mut new_state = vec![Complex64::new(0.0, 0.0); dim];
643        for i in 0..dim {
644            let bit = (i >> qubit_idx) & 1;
645            for j in 0..2 {
646                let other_idx = i ^ ((bit ^ j) << qubit_idx);
647                new_state[i] += gate_matrix[[bit, j]] * state[other_idx];
648            }
649        }
650        *state = new_state;
651        Ok(())
652    }
653    /// Apply a two-qubit gate to a state vector
654    fn apply_two_qubit_gate_to_state(
655        &self,
656        state: &mut Vec<Complex64>,
657        gate_matrix: &Array2<Complex64>,
658        qubit1_idx: usize,
659        qubit2_idx: usize,
660        num_qubits: usize,
661    ) -> QuantRS2Result<()> {
662        let dim = 1 << num_qubits;
663        let mut new_state = vec![Complex64::new(0.0, 0.0); dim];
664        for i in 0..dim {
665            let bit1 = (i >> qubit1_idx) & 1;
666            let bit2 = (i >> qubit2_idx) & 1;
667            let gate_row = (bit1 << 1) | bit2;
668            for gate_col in 0..4 {
669                let new_bit1 = (gate_col >> 1) & 1;
670                let new_bit2 = gate_col & 1;
671                let j = i ^ ((bit1 ^ new_bit1) << qubit1_idx) ^ ((bit2 ^ new_bit2) << qubit2_idx);
672                new_state[i] += gate_matrix[[gate_row, gate_col]] * state[j];
673            }
674        }
675        *state = new_state;
676        Ok(())
677    }
678    /// Check if two state vectors are equal
679    fn states_equal(&self, s1: &[Complex64], s2: &[Complex64]) -> (bool, f64) {
680        if s1.len() != s2.len() {
681            return (false, f64::INFINITY);
682        }
683        let mut max_diff = 0.0;
684        for (a, b) in s1.iter().zip(s2.iter()) {
685            let diff = (a - b).norm();
686            if diff > max_diff {
687                max_diff = diff;
688            }
689            if diff > self.options.tolerance {
690                return (false, max_diff);
691            }
692        }
693        (true, max_diff)
694    }
695    /// Check if two state vectors are equal up to a global phase
696    fn states_equal_up_to_phase(&self, s1: &[Complex64], s2: &[Complex64]) -> (bool, f64) {
697        if s1.len() != s2.len() {
698            return (false, f64::INFINITY);
699        }
700        let mut phase = None;
701        for (a, b) in s1.iter().zip(s2.iter()) {
702            if a.norm() > self.options.tolerance && b.norm() > self.options.tolerance {
703                phase = Some(b / a);
704                break;
705            }
706        }
707        let phase = match phase {
708            Some(p) => p,
709            None => return (false, f64::INFINITY),
710        };
711        let mut max_diff = 0.0;
712        for (a, b) in s1.iter().zip(s2.iter()) {
713            let adjusted = a * phase;
714            let diff = (adjusted - b).norm();
715            if diff > max_diff {
716                max_diff = diff;
717            }
718            if diff > self.options.tolerance {
719                return (false, max_diff);
720            }
721        }
722        (true, max_diff)
723    }
724    /// Check probabilistic equivalence (measurement outcomes)
725    pub fn check_probabilistic_equivalence<const N: usize>(
726        &self,
727        circuit1: &Circuit<N>,
728        circuit2: &Circuit<N>,
729    ) -> QuantRS2Result<EquivalenceResult> {
730        let mut max_diff = 0.0;
731        for state_idx in 0..(1 << N) {
732            let probs1 = self.get_measurement_probabilities(circuit1, state_idx, N)?;
733            let probs2 = self.get_measurement_probabilities(circuit2, state_idx, N)?;
734            for (p1, p2) in probs1.iter().zip(probs2.iter()) {
735                let diff = (p1 - p2).abs();
736                if diff > max_diff {
737                    max_diff = diff;
738                }
739                if diff > self.options.tolerance {
740                    return Ok(EquivalenceResult {
741                        equivalent: false,
742                        check_type: EquivalenceType::ProbabilisticEquivalence,
743                        max_difference: Some(max_diff),
744                        details: format!(
745                            "Measurement probabilities differ for input |{state_idx:0b}>"
746                        ),
747                        numerical_analysis: None,
748                        confidence_score: 0.0,
749                        statistical_significance: None,
750                        error_bounds: None,
751                    });
752                }
753            }
754        }
755        Ok(EquivalenceResult {
756            equivalent: true,
757            check_type: EquivalenceType::ProbabilisticEquivalence,
758            max_difference: Some(max_diff),
759            details: "Measurement probabilities match for all inputs".to_string(),
760            numerical_analysis: None,
761            confidence_score: 1.0 - (max_diff / self.options.tolerance).min(1.0),
762            statistical_significance: None,
763            error_bounds: None,
764        })
765    }
766    /// Get measurement probabilities for a circuit and input state
767    fn get_measurement_probabilities<const N: usize>(
768        &self,
769        circuit: &Circuit<N>,
770        state_idx: usize,
771        num_qubits: usize,
772    ) -> QuantRS2Result<Vec<f64>> {
773        let final_state = self.apply_circuit_to_state(circuit, state_idx, num_qubits)?;
774        let probs: Vec<f64> = final_state
775            .iter()
776            .map(scirs2_core::Complex::norm_sqr)
777            .collect();
778        Ok(probs)
779    }
780    /// Perform comprehensive numerical analysis using `SciRS2` capabilities
781    fn perform_scirs2_numerical_analysis(
782        &self,
783        unitary1: &Array2<Complex64>,
784        unitary2: &Array2<Complex64>,
785    ) -> QuantRS2Result<NumericalAnalysis> {
786        let diff_matrix = unitary1 - unitary2;
787        let frobenius_norm = diff_matrix
788            .iter()
789            .map(scirs2_core::Complex::norm_sqr)
790            .sum::<f64>()
791            .sqrt();
792        let condition_number = if self.options.enable_stability_analysis {
793            Some(self.estimate_condition_number(unitary1)?)
794        } else {
795            None
796        };
797        let spectral_norm = if self.options.enable_stability_analysis {
798            Some(self.calculate_spectral_norm(&diff_matrix)?)
799        } else {
800            None
801        };
802        let numerical_rank = self.estimate_numerical_rank(&diff_matrix);
803        let stability_indicator = if let Some(cond_num) = condition_number {
804            1.0 / (1.0 + (cond_num / self.options.max_condition_number).log10())
805        } else {
806            1.0
807        };
808        let adaptive_tolerance = self.calculate_adaptive_tolerance_internal(
809            unitary1.nrows(),
810            frobenius_norm,
811            condition_number.unwrap_or(1.0),
812        );
813        Ok(NumericalAnalysis {
814            condition_number,
815            numerical_rank: Some(numerical_rank),
816            frobenius_norm,
817            spectral_norm,
818            adaptive_tolerance,
819            stability_indicator,
820        })
821    }
822    /// Calculate adaptive tolerance based on circuit complexity and numerical properties
823    fn calculate_adaptive_tolerance<const N: usize>(
824        &self,
825        num_qubits: usize,
826        analysis: &NumericalAnalysis,
827    ) -> f64 {
828        let base_tolerance = if self.options.enable_adaptive_tolerance {
829            SCIRS2_DEFAULT_TOLERANCE
830        } else {
831            self.options.tolerance
832        };
833        let size_factor = (num_qubits as f64).powf(1.5).mul_add(1e-15, 1.0);
834        let condition_factor = if let Some(cond_num) = analysis.condition_number {
835            (cond_num / 1e12).log10().max(0.0).mul_add(1e-2, 1.0)
836        } else {
837            1.0
838        };
839        let norm_factor = analysis.frobenius_norm.mul_add(1e-3, 1.0);
840        base_tolerance * size_factor * condition_factor * norm_factor
841    }
842    /// Internal helper for adaptive tolerance calculation
843    fn calculate_adaptive_tolerance_internal(
844        &self,
845        matrix_size: usize,
846        frobenius_norm: f64,
847        condition_number: f64,
848    ) -> f64 {
849        let base_tolerance = SCIRS2_DEFAULT_TOLERANCE;
850        let size_factor = (matrix_size as f64).sqrt().mul_add(1e-15, 1.0);
851        let condition_factor = (condition_number / 1e12)
852            .log10()
853            .max(0.0)
854            .mul_add(1e-2, 1.0);
855        let norm_factor = frobenius_norm.mul_add(1e-3, 1.0);
856        base_tolerance * size_factor * condition_factor * norm_factor
857    }
858    /// Compare unitaries using `SciRS2` enhanced numerical analysis
859    fn scirs2_unitaries_equal(
860        &self,
861        u1: &Array2<Complex64>,
862        u2: &Array2<Complex64>,
863        adaptive_tolerance: f64,
864    ) -> QuantRS2Result<(bool, f64, f64, ErrorBounds)> {
865        if u1.shape() != u2.shape() {
866            return Ok((
867                false,
868                f64::INFINITY,
869                0.0,
870                ErrorBounds {
871                    lower_bound: f64::INFINITY,
872                    upper_bound: f64::INFINITY,
873                    confidence_level: 0.0,
874                    standard_deviation: None,
875                },
876            ));
877        }
878        let mut max_diff = 0.0;
879        let mut differences = Vec::new();
880        for (a, b) in u1.iter().zip(u2.iter()) {
881            let diff = if self.options.ignore_global_phase {
882                let phase = if a.norm() > adaptive_tolerance && b.norm() > adaptive_tolerance {
883                    b / a
884                } else {
885                    Complex64::new(1.0, 0.0)
886                };
887                (a * phase - b).norm()
888            } else {
889                (a - b).norm()
890            };
891            differences.push(diff);
892            if diff > max_diff {
893                max_diff = diff;
894            }
895        }
896        let mean_diff = differences.iter().sum::<f64>() / differences.len() as f64;
897        let variance = differences
898            .iter()
899            .map(|d| (d - mean_diff).powi(2))
900            .sum::<f64>()
901            / differences.len() as f64;
902        let std_dev = variance.sqrt();
903        let confidence_score = if max_diff <= adaptive_tolerance {
904            1.0 - (max_diff / adaptive_tolerance).min(1.0)
905        } else {
906            0.0
907        };
908        let error_bounds = ErrorBounds {
909            lower_bound: 2.0f64.mul_add(-std_dev, mean_diff).max(0.0),
910            upper_bound: 2.0f64.mul_add(std_dev, mean_diff),
911            confidence_level: self.options.confidence_level,
912            standard_deviation: Some(std_dev),
913        };
914        let equivalent = max_diff <= adaptive_tolerance;
915        Ok((equivalent, max_diff, confidence_score, error_bounds))
916    }
917    /// Compare `SciRS2` graphs for structural equivalence
918    fn compare_scirs2_graphs(
919        &self,
920        graph1: &crate::scirs2_integration::SciRS2CircuitGraph,
921        graph2: &crate::scirs2_integration::SciRS2CircuitGraph,
922    ) -> QuantRS2Result<(bool, f64, String)> {
923        if graph1.nodes.len() != graph2.nodes.len() {
924            return Ok((
925                false,
926                0.0,
927                format!(
928                    "Different number of nodes: {} vs {}",
929                    graph1.nodes.len(),
930                    graph2.nodes.len()
931                ),
932            ));
933        }
934        if graph1.edges.len() != graph2.edges.len() {
935            return Ok((
936                false,
937                0.0,
938                format!(
939                    "Different number of edges: {} vs {}",
940                    graph1.edges.len(),
941                    graph2.edges.len()
942                ),
943            ));
944        }
945        let node_similarity = self.calculate_node_similarity(graph1, graph2);
946        let edge_similarity = self.calculate_edge_similarity(graph1, graph2);
947        let topology_similarity = self.calculate_topology_similarity(graph1, graph2);
948        let overall_similarity = (node_similarity + edge_similarity + topology_similarity) / 3.0;
949        let equivalent = overall_similarity > 0.95;
950        let details = format!(
951            "Graph similarity analysis: nodes={node_similarity:.3}, edges={edge_similarity:.3}, topology={topology_similarity:.3}, overall={overall_similarity:.3}"
952        );
953        Ok((equivalent, overall_similarity, details))
954    }
955    /// Calculate node similarity between graphs
956    fn calculate_node_similarity(
957        &self,
958        graph1: &crate::scirs2_integration::SciRS2CircuitGraph,
959        graph2: &crate::scirs2_integration::SciRS2CircuitGraph,
960    ) -> f64 {
961        if graph1.nodes.is_empty() && graph2.nodes.is_empty() {
962            return 1.0;
963        }
964        let total_nodes = graph1.nodes.len().max(graph2.nodes.len());
965        let mut matching_nodes = 0;
966        for node1 in graph1.nodes.values() {
967            for node2 in graph2.nodes.values() {
968                if node1.node_type == node2.node_type {
969                    matching_nodes += 1;
970                    break;
971                }
972            }
973        }
974        f64::from(matching_nodes) / total_nodes as f64
975    }
976    /// Calculate edge similarity between graphs
977    fn calculate_edge_similarity(
978        &self,
979        graph1: &crate::scirs2_integration::SciRS2CircuitGraph,
980        graph2: &crate::scirs2_integration::SciRS2CircuitGraph,
981    ) -> f64 {
982        if graph1.edges.is_empty() && graph2.edges.is_empty() {
983            return 1.0;
984        }
985        let total_edges = graph1.edges.len().max(graph2.edges.len());
986        let mut matching_edges = 0;
987        for edge1 in graph1.edges.values() {
988            for edge2 in graph2.edges.values() {
989                if edge1.edge_type == edge2.edge_type {
990                    matching_edges += 1;
991                    break;
992                }
993            }
994        }
995        f64::from(matching_edges) / total_edges as f64
996    }
997    /// Calculate topology similarity using adjacency matrix comparison
998    fn calculate_topology_similarity(
999        &self,
1000        graph1: &crate::scirs2_integration::SciRS2CircuitGraph,
1001        graph2: &crate::scirs2_integration::SciRS2CircuitGraph,
1002    ) -> f64 {
1003        if graph1.adjacency_matrix.len() != graph2.adjacency_matrix.len() {
1004            return 0.0;
1005        }
1006        let mut total_elements = 0;
1007        let mut matching_elements = 0;
1008        for (row1, row2) in graph1
1009            .adjacency_matrix
1010            .iter()
1011            .zip(graph2.adjacency_matrix.iter())
1012        {
1013            if row1.len() != row2.len() {
1014                return 0.0;
1015            }
1016            for (elem1, elem2) in row1.iter().zip(row2.iter()) {
1017                total_elements += 1;
1018                if elem1 == elem2 {
1019                    matching_elements += 1;
1020                }
1021            }
1022        }
1023        if total_elements == 0 {
1024            1.0
1025        } else {
1026            f64::from(matching_elements) / f64::from(total_elements)
1027        }
1028    }
1029    /// Estimate condition number using power iteration method
1030    fn estimate_condition_number(&self, matrix: &Array2<Complex64>) -> QuantRS2Result<f64> {
1031        let n = matrix.nrows();
1032        if n == 0 {
1033            return Ok(1.0);
1034        }
1035        let mut v = vec![Complex64::new(1.0, 0.0); n];
1036        for _ in 0..10 {
1037            let mut new_v = vec![Complex64::new(0.0, 0.0); n];
1038            for i in 0..n {
1039                for j in 0..n {
1040                    for k in 0..n {
1041                        new_v[i] += matrix[[k, i]].conj() * matrix[[k, j]] * v[j];
1042                    }
1043                }
1044            }
1045            let norm = new_v
1046                .iter()
1047                .map(scirs2_core::Complex::norm_sqr)
1048                .sum::<f64>()
1049                .sqrt();
1050            if norm > 0.0 {
1051                for x in &mut new_v {
1052                    *x /= norm;
1053                }
1054            }
1055            v = new_v;
1056        }
1057        let estimated_largest_sv = v.iter().map(|x| x.norm()).sum::<f64>() / n as f64;
1058        let estimated_smallest_sv = 1.0 / estimated_largest_sv;
1059        Ok((estimated_largest_sv / estimated_smallest_sv.max(1e-16)).min(1e16))
1060    }
1061    /// Calculate spectral norm (largest singular value) of a matrix
1062    fn calculate_spectral_norm(&self, matrix: &Array2<Complex64>) -> QuantRS2Result<f64> {
1063        Ok(matrix.iter().map(|x| x.norm()).fold(0.0, f64::max))
1064    }
1065    /// Estimate numerical rank of a matrix
1066    fn estimate_numerical_rank(&self, matrix: &Array2<Complex64>) -> usize {
1067        let tolerance = self.options.tolerance;
1068        let mut rank = 0;
1069        for row in matrix.rows() {
1070            let row_norm = row
1071                .iter()
1072                .map(scirs2_core::Complex::norm_sqr)
1073                .sum::<f64>()
1074                .sqrt();
1075            if row_norm > tolerance {
1076                rank += 1;
1077            }
1078        }
1079        rank
1080    }
1081    /// Calculate statistical significance of the difference
1082    fn calculate_statistical_significance(
1083        &self,
1084        u1: &Array2<Complex64>,
1085        u2: &Array2<Complex64>,
1086        max_difference: f64,
1087    ) -> QuantRS2Result<f64> {
1088        let n = u1.len();
1089        let degrees_of_freedom = n - 1;
1090        let differences: Vec<f64> = u1
1091            .iter()
1092            .zip(u2.iter())
1093            .map(|(a, b)| (a - b).norm())
1094            .collect();
1095        let mean_diff = differences.iter().sum::<f64>() / n as f64;
1096        let variance = differences
1097            .iter()
1098            .map(|d| (d - mean_diff).powi(2))
1099            .sum::<f64>()
1100            / degrees_of_freedom as f64;
1101        let std_error = (variance / n as f64).sqrt();
1102        let t_stat = if std_error > 0.0 {
1103            mean_diff / std_error
1104        } else {
1105            0.0
1106        };
1107        let p_value = 2.0 * (1.0 - (t_stat.abs() / (1.0 + t_stat.abs())));
1108        Ok(p_value.clamp(0.0, 1.0))
1109    }
1110}
1111/// Types of equivalence checks with `SciRS2` enhancements
1112#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
1113pub enum EquivalenceType {
1114    /// Check if circuits produce identical unitaries
1115    UnitaryEquivalence,
1116    /// Check if circuits produce same output states for all inputs
1117    StateVectorEquivalence,
1118    /// Check if measurement probabilities are identical
1119    ProbabilisticEquivalence,
1120    /// Check if circuits have identical gate structure
1121    StructuralEquivalence,
1122    /// Check if circuits are equivalent up to a global phase
1123    GlobalPhaseEquivalence,
1124    /// SciRS2-powered numerical equivalence with adaptive tolerance
1125    SciRS2NumericalEquivalence,
1126    /// `SciRS2` statistical equivalence with confidence intervals
1127    SciRS2StatisticalEquivalence,
1128    /// `SciRS2` graph-based structural equivalence
1129    SciRS2GraphEquivalence,
1130}
1131/// Error bounds and uncertainty quantification
1132#[derive(Debug, Clone, Serialize, Deserialize)]
1133pub struct ErrorBounds {
1134    /// Lower bound of the error estimate
1135    pub lower_bound: f64,
1136    /// Upper bound of the error estimate
1137    pub upper_bound: f64,
1138    /// Confidence interval level (e.g., 0.95 for 95%)
1139    pub confidence_level: f64,
1140    /// Standard deviation of error estimates
1141    pub standard_deviation: Option<f64>,
1142}
1143/// Enhanced options for equivalence checking with `SciRS2` features
1144#[derive(Debug, Clone, Serialize, Deserialize)]
1145pub struct EquivalenceOptions {
1146    /// Numerical tolerance for comparisons
1147    pub tolerance: f64,
1148    /// Whether to ignore global phase differences
1149    pub ignore_global_phase: bool,
1150    /// Whether to check all computational basis states
1151    pub check_all_states: bool,
1152    /// Maximum circuit size for unitary construction
1153    pub max_unitary_qubits: usize,
1154    /// Enable `SciRS2` adaptive tolerance
1155    pub enable_adaptive_tolerance: bool,
1156    /// Enable `SciRS2` statistical analysis
1157    pub enable_statistical_analysis: bool,
1158    /// Enable `SciRS2` numerical stability analysis
1159    pub enable_stability_analysis: bool,
1160    /// Enable `SciRS2` graph-based comparison
1161    pub enable_graph_comparison: bool,
1162    /// Confidence level for statistical tests (e.g., 0.95)
1163    pub confidence_level: f64,
1164    /// Maximum condition number for numerical stability
1165    pub max_condition_number: f64,
1166    /// `SciRS2` analyzer configuration
1167    pub scirs2_config: Option<AnalyzerConfig>,
1168    /// Complex number tolerance
1169    pub complex_tolerance: f64,
1170    /// Enable parallel computation for large circuits
1171    pub enable_parallel_computation: bool,
1172}
1173/// Enhanced result of equivalence check with `SciRS2` analysis
1174#[derive(Debug, Clone, Serialize, Deserialize)]
1175pub struct EquivalenceResult {
1176    /// Whether the circuits are equivalent
1177    pub equivalent: bool,
1178    /// Type of equivalence check performed
1179    pub check_type: EquivalenceType,
1180    /// Maximum difference found (for numerical checks)
1181    pub max_difference: Option<f64>,
1182    /// Additional details about the check
1183    pub details: String,
1184    /// `SciRS2` numerical analysis results
1185    pub numerical_analysis: Option<NumericalAnalysis>,
1186    /// Confidence score (0.0 to 1.0)
1187    pub confidence_score: f64,
1188    /// Statistical significance (p-value if applicable)
1189    pub statistical_significance: Option<f64>,
1190    /// Error bounds and uncertainty quantification
1191    pub error_bounds: Option<ErrorBounds>,
1192}
quantrs2_circuit/equivalence/types.rs

quantrs2_circuit/equivalence/
types.rs
