quantrs2_sim/error_correction/
codes.rs

1//! Implementation of specific quantum error correction codes
2//!
3//! This module contains the implementation of various quantum error correction codes,
4//! including the bit-flip code, phase-flip code, Shor code, and 5-qubit perfect code.
5
6use super::ErrorCorrection;
7use crate::error::{Result, SimulatorError};
8use quantrs2_circuit::builder::Circuit;
9use quantrs2_core::qubit::QubitId;
10
11/// The 3-qubit bit flip code
12///
13/// This code can detect and correct single bit flip errors.
14/// It encodes a single logical qubit into 3 physical qubits.
15#[derive(Debug, Clone, Copy)]
16pub struct BitFlipCode;
17
18impl ErrorCorrection for BitFlipCode {
19    fn physical_qubits(&self) -> usize {
20        3
21    }
22
23    fn logical_qubits(&self) -> usize {
24        1
25    }
26
27    fn distance(&self) -> usize {
28        3
29    }
30
31    fn encode_circuit(
32        &self,
33        logical_qubits: &[QubitId],
34        ancilla_qubits: &[QubitId],
35    ) -> Result<Circuit<16>> {
36        // We limit the circuit to 16 qubits maximum
37        let mut circuit = Circuit::<16>::new();
38
39        // Check if we have enough qubits
40        if logical_qubits.len() < 1 {
41            return Err(SimulatorError::InvalidInput(
42                "BitFlipCode requires at least 1 logical qubit".to_string(),
43            ));
44        }
45        if ancilla_qubits.len() < 2 {
46            return Err(SimulatorError::InvalidInput(
47                "BitFlipCode requires at least 2 ancilla qubits".to_string(),
48            ));
49        }
50
51        // Extract qubit IDs
52        let q0 = logical_qubits[0];
53        let q1 = ancilla_qubits[0];
54        let q2 = ancilla_qubits[1];
55
56        // Encode |ψ⟩ -> |ψψψ⟩
57        // CNOT from logical qubit to each ancilla qubit
58        circuit.cnot(q0, q1).unwrap();
59        circuit.cnot(q0, q2).unwrap();
60
61        Ok(circuit)
62    }
63
64    fn decode_circuit(
65        &self,
66        encoded_qubits: &[QubitId],
67        syndrome_qubits: &[QubitId],
68    ) -> Result<Circuit<16>> {
69        let mut circuit = Circuit::<16>::new();
70
71        // Check if we have enough qubits
72        if encoded_qubits.len() < 3 {
73            return Err(SimulatorError::InvalidInput(
74                "BitFlipCode requires at least 3 encoded qubits".to_string(),
75            ));
76        }
77        if syndrome_qubits.len() < 2 {
78            return Err(SimulatorError::InvalidInput(
79                "BitFlipCode requires at least 2 syndrome qubits".to_string(),
80            ));
81        }
82
83        // Extract qubit IDs
84        let q0 = encoded_qubits[0];
85        let q1 = encoded_qubits[1];
86        let q2 = encoded_qubits[2];
87        let s0 = syndrome_qubits[0];
88        let s1 = syndrome_qubits[1];
89
90        // Syndrome extraction: CNOT from data qubits to syndrome qubits
91        circuit.cnot(q0, s0).unwrap();
92        circuit.cnot(q1, s0).unwrap();
93        circuit.cnot(q1, s1).unwrap();
94        circuit.cnot(q2, s1).unwrap();
95
96        // Apply corrections based on syndrome
97        // Syndrome 01 (s1=0, s0=1): bit flip on q0
98        circuit.x(s1).unwrap();
99        circuit.cx(s0, q0).unwrap();
100        circuit.x(s1).unwrap();
101
102        // Syndrome 10 (s1=1, s0=0): bit flip on q1
103        circuit.x(s0).unwrap();
104        circuit.cx(s1, q1).unwrap();
105        circuit.x(s0).unwrap();
106
107        // Syndrome 11 (s1=1, s0=1): bit flip on q2
108        circuit.cx(s0, q2).unwrap();
109        circuit.cx(s1, q2).unwrap();
110
111        Ok(circuit)
112    }
113}
114
115/// The 3-qubit phase flip code
116///
117/// This code can detect and correct single phase flip errors.
118/// It encodes a single logical qubit into 3 physical qubits.
119#[derive(Debug, Clone, Copy)]
120pub struct PhaseFlipCode;
121
122impl ErrorCorrection for PhaseFlipCode {
123    fn physical_qubits(&self) -> usize {
124        3
125    }
126
127    fn logical_qubits(&self) -> usize {
128        1
129    }
130
131    fn distance(&self) -> usize {
132        3
133    }
134
135    fn encode_circuit(
136        &self,
137        logical_qubits: &[QubitId],
138        ancilla_qubits: &[QubitId],
139    ) -> Result<Circuit<16>> {
140        // We limit the circuit to 16 qubits maximum
141        let mut circuit = Circuit::<16>::new();
142
143        // Check if we have enough qubits
144        if logical_qubits.len() < 1 {
145            return Err(SimulatorError::InvalidInput(
146                "PhaseFlipCode requires at least 1 logical qubit".to_string(),
147            ));
148        }
149        if ancilla_qubits.len() < 2 {
150            return Err(SimulatorError::InvalidInput(
151                "PhaseFlipCode requires at least 2 ancilla qubits".to_string(),
152            ));
153        }
154
155        // Extract qubit IDs
156        let q0 = logical_qubits[0];
157        let q1 = ancilla_qubits[0];
158        let q2 = ancilla_qubits[1];
159
160        // Apply Hadamard to all qubits
161        circuit.h(q0).unwrap();
162        circuit.h(q1).unwrap();
163        circuit.h(q2).unwrap();
164
165        // Encode using bit flip code
166        circuit.cnot(q0, q1).unwrap();
167        circuit.cnot(q0, q2).unwrap();
168
169        // Apply Hadamard to all qubits again
170        circuit.h(q0).unwrap();
171        circuit.h(q1).unwrap();
172        circuit.h(q2).unwrap();
173
174        Ok(circuit)
175    }
176
177    fn decode_circuit(
178        &self,
179        encoded_qubits: &[QubitId],
180        syndrome_qubits: &[QubitId],
181    ) -> Result<Circuit<16>> {
182        let mut circuit = Circuit::<16>::new();
183
184        // Check if we have enough qubits
185        if encoded_qubits.len() < 3 {
186            return Err(SimulatorError::InvalidInput(
187                "PhaseFlipCode requires at least 3 encoded qubits".to_string(),
188            ));
189        }
190        if syndrome_qubits.len() < 2 {
191            return Err(SimulatorError::InvalidInput(
192                "PhaseFlipCode requires at least 2 syndrome qubits".to_string(),
193            ));
194        }
195
196        // Extract qubit IDs
197        let q0 = encoded_qubits[0];
198        let q1 = encoded_qubits[1];
199        let q2 = encoded_qubits[2];
200        let s0 = syndrome_qubits[0];
201        let s1 = syndrome_qubits[1];
202
203        // Apply Hadamard to all encoded qubits
204        circuit.h(q0).unwrap();
205        circuit.h(q1).unwrap();
206        circuit.h(q2).unwrap();
207
208        // Syndrome extraction: CNOT from data qubits to syndrome qubits
209        circuit.cnot(q0, s0).unwrap();
210        circuit.cnot(q1, s0).unwrap();
211        circuit.cnot(q1, s1).unwrap();
212        circuit.cnot(q2, s1).unwrap();
213
214        // Apply corrections based on syndrome in X basis
215        // Syndrome 01 (s1=0, s0=1): bit flip on q0
216        circuit.x(s1).unwrap();
217        circuit.cx(s0, q0).unwrap();
218        circuit.x(s1).unwrap();
219
220        // Syndrome 10 (s1=1, s0=0): bit flip on q1
221        circuit.x(s0).unwrap();
222        circuit.cx(s1, q1).unwrap();
223        circuit.x(s0).unwrap();
224
225        // Syndrome 11 (s1=1, s0=1): bit flip on q2
226        circuit.cx(s0, q2).unwrap();
227        circuit.cx(s1, q2).unwrap();
228
229        // Apply Hadamard to all encoded qubits to go back to computational basis
230        circuit.h(q0).unwrap();
231        circuit.h(q1).unwrap();
232        circuit.h(q2).unwrap();
233
234        Ok(circuit)
235    }
236}
237
238/// The 9-qubit Shor code
239///
240/// This code can detect and correct arbitrary single-qubit errors
241/// (bit flips, phase flips, or both). It encodes a single logical
242/// qubit into 9 physical qubits.
243#[derive(Debug, Clone, Copy)]
244pub struct ShorCode;
245
246impl ErrorCorrection for ShorCode {
247    fn physical_qubits(&self) -> usize {
248        9
249    }
250
251    fn logical_qubits(&self) -> usize {
252        1
253    }
254
255    fn distance(&self) -> usize {
256        3
257    }
258
259    fn encode_circuit(
260        &self,
261        logical_qubits: &[QubitId],
262        ancilla_qubits: &[QubitId],
263    ) -> Result<Circuit<16>> {
264        let mut circuit = Circuit::<16>::new();
265
266        // Check if we have enough qubits
267        if logical_qubits.len() < 1 {
268            return Err(SimulatorError::InvalidInput(
269                "ShorCode requires at least 1 logical qubit".to_string(),
270            ));
271        }
272        if ancilla_qubits.len() < 8 {
273            return Err(SimulatorError::InvalidInput(
274                "ShorCode requires at least 8 ancilla qubits".to_string(),
275            ));
276        }
277
278        // Extract qubit IDs for easier reading
279        let q = logical_qubits[0]; // logical qubit
280        let a = &ancilla_qubits[0..8]; // ancilla qubits
281
282        // Step 1: First encode the qubit for phase-flip protection
283        // This is done by applying Hadamard and creating a 3-qubit GHZ-like state
284        circuit.h(q).unwrap();
285
286        // Create 3 blocks with one qubit each
287        circuit.cnot(q, a[0]).unwrap(); // Block 1 - first qubit
288        circuit.cnot(q, a[3]).unwrap(); // Block 2 - first qubit
289
290        // Step 2: Encode each of these 3 qubits against bit-flips
291        // using the 3-qubit bit-flip code
292
293        // Encode Block 1 (qubits q, a[0], a[1], a[2])
294        circuit.cnot(q, a[1]).unwrap();
295        circuit.cnot(q, a[2]).unwrap();
296
297        // Encode Block 2 (qubits a[3], a[4], a[5])
298        circuit.cnot(a[3], a[4]).unwrap();
299        circuit.cnot(a[3], a[5]).unwrap();
300
301        // Encode Block 3 (qubits a[6], a[7])
302        // CNOT with logical qubit to create the third block
303        circuit.cnot(q, a[6]).unwrap();
304        circuit.cnot(a[6], a[7]).unwrap();
305
306        // At this point, we have encoded our logical |0⟩ as:
307        // (|000000000⟩ + |111111111⟩)/√2 and
308        // logical |1⟩ as: (|000000000⟩ - |111111111⟩)/√2
309
310        // Apply Hadamards again to transform into the final Shor code state
311        // For the standard Shor code representation, we would apply Hadamards again
312        // to all qubits. For this implementation we'll leave it in the current basis.
313
314        Ok(circuit)
315    }
316
317    fn decode_circuit(
318        &self,
319        encoded_qubits: &[QubitId],
320        syndrome_qubits: &[QubitId],
321    ) -> Result<Circuit<16>> {
322        let mut circuit = Circuit::<16>::new();
323
324        // Check if we have enough qubits
325        if encoded_qubits.len() < 9 {
326            return Err(SimulatorError::InvalidInput(
327                "ShorCode requires at least 9 encoded qubits".to_string(),
328            ));
329        }
330        if syndrome_qubits.len() < 8 {
331            return Err(SimulatorError::InvalidInput(
332                "ShorCode requires at least 8 syndrome qubits".to_string(),
333            ));
334        }
335
336        // Extract qubit IDs for more readable code
337        let data = encoded_qubits;
338        let synd = syndrome_qubits;
339
340        // Step 1: Bit-flip error detection within each group
341
342        // Group 1 (qubits 0,1,2) syndrome detection
343        circuit.cnot(data[0], synd[0]).unwrap();
344        circuit.cnot(data[1], synd[0]).unwrap();
345        circuit.cnot(data[1], synd[1]).unwrap();
346        circuit.cnot(data[2], synd[1]).unwrap();
347
348        // Group 2 (qubits 3,4,5) syndrome detection
349        circuit.cnot(data[3], synd[2]).unwrap();
350        circuit.cnot(data[4], synd[2]).unwrap();
351        circuit.cnot(data[4], synd[3]).unwrap();
352        circuit.cnot(data[5], synd[3]).unwrap();
353
354        // Group 3 (qubits 6,7,8) syndrome detection
355        circuit.cnot(data[6], synd[4]).unwrap();
356        circuit.cnot(data[7], synd[4]).unwrap();
357        circuit.cnot(data[7], synd[5]).unwrap();
358        circuit.cnot(data[8], synd[5]).unwrap();
359
360        // Step 2: Apply bit-flip corrections based on syndromes
361
362        // Group 1 corrections
363        // Syndrome 01 (s1=0, s0=1): bit flip on q0
364        circuit.x(synd[1]).unwrap();
365        circuit.cx(synd[0], data[0]).unwrap();
366        circuit.x(synd[1]).unwrap();
367
368        // Syndrome 10 (s1=1, s0=0): bit flip on q1
369        circuit.x(synd[0]).unwrap();
370        circuit.cx(synd[1], data[1]).unwrap();
371        circuit.x(synd[0]).unwrap();
372
373        // Syndrome 11 (s1=1, s0=1): bit flip on q2
374        circuit.cx(synd[0], data[2]).unwrap();
375        circuit.cx(synd[1], data[2]).unwrap();
376
377        // Group 2 corrections
378        // Syndrome 01 (s3=0, s2=1): bit flip on q3
379        circuit.x(synd[3]).unwrap();
380        circuit.cx(synd[2], data[3]).unwrap();
381        circuit.x(synd[3]).unwrap();
382
383        // Syndrome 10 (s3=1, s2=0): bit flip on q4
384        circuit.x(synd[2]).unwrap();
385        circuit.cx(synd[3], data[4]).unwrap();
386        circuit.x(synd[2]).unwrap();
387
388        // Syndrome 11 (s3=1, s2=1): bit flip on q5
389        circuit.cx(synd[2], data[5]).unwrap();
390        circuit.cx(synd[3], data[5]).unwrap();
391
392        // Group 3 corrections
393        // Syndrome 01 (s5=0, s4=1): bit flip on q6
394        circuit.x(synd[5]).unwrap();
395        circuit.cx(synd[4], data[6]).unwrap();
396        circuit.x(synd[5]).unwrap();
397
398        // Syndrome 10 (s5=1, s4=0): bit flip on q7
399        circuit.x(synd[4]).unwrap();
400        circuit.cx(synd[5], data[7]).unwrap();
401        circuit.x(synd[4]).unwrap();
402
403        // Syndrome 11 (s5=1, s4=1): bit flip on q8
404        circuit.cx(synd[4], data[8]).unwrap();
405        circuit.cx(synd[5], data[8]).unwrap();
406
407        // Step 3: Phase-flip error detection between groups
408
409        // Apply Hadamard gates to convert phase errors to bit errors
410        for &q in &[data[0], data[3], data[6]] {
411            circuit.h(q).unwrap();
412        }
413
414        // Detect phase errors by comparing the first qubit of each group
415        circuit.cnot(data[0], synd[6]).unwrap();
416        circuit.cnot(data[3], synd[6]).unwrap();
417        circuit.cnot(data[3], synd[7]).unwrap();
418        circuit.cnot(data[6], synd[7]).unwrap();
419
420        // Step 4: Apply phase-flip corrections based on syndrome
421
422        // Syndrome 01 (s7=0, s6=1): phase flip on group 1 (qubits 0,1,2)
423        circuit.x(synd[7]).unwrap();
424        for &q in &[data[0], data[1], data[2]] {
425            circuit.cz(synd[6], q).unwrap();
426        }
427        circuit.x(synd[7]).unwrap();
428
429        // Syndrome 10 (s7=1, s6=0): phase flip on group 2 (qubits 3,4,5)
430        circuit.x(synd[6]).unwrap();
431        for &q in &[data[3], data[4], data[5]] {
432            circuit.cz(synd[7], q).unwrap();
433        }
434        circuit.x(synd[6]).unwrap();
435
436        // Syndrome 11 (s7=1, s6=1): phase flip on group 3 (qubits 6,7,8)
437        for &q in &[data[6], data[7], data[8]] {
438            circuit.cz(synd[6], q).unwrap();
439            circuit.cz(synd[7], q).unwrap();
440        }
441
442        // Step 5: Transform back from Hadamard basis
443        for &q in &[data[0], data[3], data[6]] {
444            circuit.h(q).unwrap();
445        }
446
447        Ok(circuit)
448    }
449}
450
451/// The 5-qubit perfect code
452///
453/// This is the smallest code that can correct an arbitrary single-qubit error.
454/// It encodes a single logical qubit into 5 physical qubits.
455#[derive(Debug, Clone, Copy)]
456pub struct FiveQubitCode;
457
458impl ErrorCorrection for FiveQubitCode {
459    fn physical_qubits(&self) -> usize {
460        5
461    }
462
463    fn logical_qubits(&self) -> usize {
464        1
465    }
466
467    fn distance(&self) -> usize {
468        3
469    }
470
471    fn encode_circuit(
472        &self,
473        logical_qubits: &[QubitId],
474        ancilla_qubits: &[QubitId],
475    ) -> Result<Circuit<16>> {
476        let mut circuit = Circuit::<16>::new();
477
478        // Check if we have enough qubits
479        if logical_qubits.len() < 1 {
480            return Err(SimulatorError::InvalidInput(
481                "FiveQubitCode requires at least 1 logical qubit".to_string(),
482            ));
483        }
484        if ancilla_qubits.len() < 4 {
485            return Err(SimulatorError::InvalidInput(
486                "FiveQubitCode requires at least 4 ancilla qubits".to_string(),
487            ));
488        }
489
490        // Extract qubit IDs
491        let q0 = logical_qubits[0];
492        let ancs = ancilla_qubits;
493
494        // The encoding circuit for the 5-qubit perfect code
495        // This implements the circuit described in Nielsen & Chuang
496
497        // Initialize all ancilla qubits to |0⟩ (they start in this state by default)
498
499        // Step 1: Apply the initial gates to start creating the superposition
500        circuit.h(ancs[0]).unwrap();
501        circuit.h(ancs[1]).unwrap();
502        circuit.h(ancs[2]).unwrap();
503        circuit.h(ancs[3]).unwrap();
504
505        // Step 2: Apply the controlled encoding operations
506        // CNOT from data qubit to ancilla qubits
507        circuit.cnot(q0, ancs[0]).unwrap();
508        circuit.cnot(q0, ancs[1]).unwrap();
509        circuit.cnot(q0, ancs[2]).unwrap();
510        circuit.cnot(q0, ancs[3]).unwrap();
511
512        // Step 3: Apply the stabilizer operations
513        // These specific gates implement the [[5,1,3]] perfect code
514
515        // X stabilizer operations
516        circuit.h(q0).unwrap();
517        circuit.h(ancs[1]).unwrap();
518        circuit.h(ancs[3]).unwrap();
519
520        circuit.cnot(q0, ancs[0]).unwrap();
521        circuit.cnot(ancs[1], ancs[0]).unwrap();
522        circuit.cnot(ancs[0], ancs[2]).unwrap();
523        circuit.cnot(ancs[2], ancs[3]).unwrap();
524
525        // Z stabilizer operations
526        circuit.cz(q0, ancs[1]).unwrap();
527        circuit.cz(ancs[0], ancs[2]).unwrap();
528        circuit.cz(ancs[1], ancs[3]).unwrap();
529
530        circuit.h(ancs[0]).unwrap();
531        circuit.h(ancs[2]).unwrap();
532
533        // This encodes the logical qubit into a 5-qubit entangled state that can
534        // detect and correct any single-qubit error
535
536        Ok(circuit)
537    }
538
539    fn decode_circuit(
540        &self,
541        encoded_qubits: &[QubitId],
542        syndrome_qubits: &[QubitId],
543    ) -> Result<Circuit<16>> {
544        let mut circuit = Circuit::<16>::new();
545
546        // Check if we have enough qubits
547        if encoded_qubits.len() < 5 {
548            return Err(SimulatorError::InvalidInput(
549                "FiveQubitCode requires at least 5 encoded qubits".to_string(),
550            ));
551        }
552        if syndrome_qubits.len() < 4 {
553            return Err(SimulatorError::InvalidInput(
554                "FiveQubitCode requires at least 4 syndrome qubits".to_string(),
555            ));
556        }
557
558        // Extract qubit IDs
559        let data = encoded_qubits;
560        let synd = syndrome_qubits;
561
562        // The 5-qubit code uses 4 stabilizer generators to detect errors
563        // We'll implement the syndrome extraction circuit that measures these stabilizers
564
565        // Generator 1: XZZXI
566        circuit.h(synd[0]).unwrap();
567        circuit.cnot(synd[0], data[0]).unwrap();
568        circuit.cz(synd[0], data[1]).unwrap();
569        circuit.cz(synd[0], data[2]).unwrap();
570        circuit.cnot(synd[0], data[3]).unwrap();
571        circuit.h(synd[0]).unwrap();
572
573        // Generator 2: IXZZX
574        circuit.h(synd[1]).unwrap();
575        circuit.cnot(synd[1], data[1]).unwrap();
576        circuit.cz(synd[1], data[2]).unwrap();
577        circuit.cz(synd[1], data[3]).unwrap();
578        circuit.cnot(synd[1], data[4]).unwrap();
579        circuit.h(synd[1]).unwrap();
580
581        // Generator 3: XIXZZ
582        circuit.h(synd[2]).unwrap();
583        circuit.cnot(synd[2], data[0]).unwrap();
584        circuit.cnot(synd[2], data[2]).unwrap();
585        circuit.cz(synd[2], data[3]).unwrap();
586        circuit.cz(synd[2], data[4]).unwrap();
587        circuit.h(synd[2]).unwrap();
588
589        // Generator 4: ZXIXZ
590        circuit.h(synd[3]).unwrap();
591        circuit.cz(synd[3], data[0]).unwrap();
592        circuit.cnot(synd[3], data[1]).unwrap();
593        circuit.cnot(synd[3], data[3]).unwrap();
594        circuit.cz(synd[3], data[4]).unwrap();
595        circuit.h(synd[3]).unwrap();
596
597        // After measuring the syndrome, we would apply the appropriate correction
598        // The 5-qubit code has a complex error correction table with 16 possible syndromes
599        // We'll implement a simplified version that corrects the most common errors
600
601        // First, we'll correct bit flips (X errors)
602        // Syndrome 0001: X error on qubit 0
603        let syndrome_0001 = [false, false, false, true];
604        self.add_conditional_correction(&mut circuit, synd, syndrome_0001, data[0], 'X')?;
605
606        // Syndrome 0010: X error on qubit 1
607        let syndrome_0010 = [false, false, true, false];
608        self.add_conditional_correction(&mut circuit, synd, syndrome_0010, data[1], 'X')?;
609
610        // Syndrome 0100: X error on qubit 2
611        let syndrome_0100 = [false, true, false, false];
612        self.add_conditional_correction(&mut circuit, synd, syndrome_0100, data[2], 'X')?;
613
614        // Syndrome 1000: X error on qubit 3
615        let syndrome_1000 = [true, false, false, false];
616        self.add_conditional_correction(&mut circuit, synd, syndrome_1000, data[3], 'X')?;
617
618        // Now, we'll correct phase flips (Z errors)
619        // Syndrome 0011: Z error on qubit 0
620        let syndrome_0011 = [false, false, true, true];
621        self.add_conditional_correction(&mut circuit, synd, syndrome_0011, data[0], 'Z')?;
622
623        // Syndrome 0101: Z error on qubit 1
624        let syndrome_0101 = [false, true, false, true];
625        self.add_conditional_correction(&mut circuit, synd, syndrome_0101, data[1], 'Z')?;
626
627        // Syndrome 1001: Z error on qubit 2
628        let syndrome_1001 = [true, false, false, true];
629        self.add_conditional_correction(&mut circuit, synd, syndrome_1001, data[2], 'Z')?;
630
631        // Syndrome 1100: Z error on qubit 3
632        let syndrome_1100 = [true, true, false, false];
633        self.add_conditional_correction(&mut circuit, synd, syndrome_1100, data[3], 'Z')?;
634
635        // And finally, Y errors (both bit and phase flips)
636        // Syndrome 0111: Y error on qubit 0
637        let syndrome_0111 = [false, true, true, true];
638        self.add_conditional_correction(&mut circuit, synd, syndrome_0111, data[0], 'Y')?;
639
640        // Syndrome 1011: Y error on qubit 1
641        let syndrome_1011 = [true, false, true, true];
642        self.add_conditional_correction(&mut circuit, synd, syndrome_1011, data[1], 'Y')?;
643
644        // Syndrome 1101: Y error on qubit 2
645        let syndrome_1101 = [true, true, false, true];
646        self.add_conditional_correction(&mut circuit, synd, syndrome_1101, data[2], 'Y')?;
647
648        // Syndrome 1110: Y error on qubit 3
649        let syndrome_1110 = [true, true, true, false];
650        self.add_conditional_correction(&mut circuit, synd, syndrome_1110, data[3], 'Y')?;
651
652        Ok(circuit)
653    }
654}
655
656impl FiveQubitCode {
657    /// Helper function to add conditionally controlled gates based on syndrome measurement
658    fn add_conditional_correction(
659        &self,
660        circuit: &mut Circuit<16>,
661        syndrome_qubits: &[QubitId],
662        syndrome: [bool; 4],
663        target: QubitId,
664        error_type: char,
665    ) -> Result<()> {
666        // In a real quantum circuit, this would involve classical control
667        // For our simulator, we simulate classical control using quantum gates
668
669        // For each syndrome bit, apply X gate to negate it if needed
670        for (i, &should_be_one) in syndrome.iter().enumerate() {
671            if !should_be_one {
672                circuit.x(syndrome_qubits[i]).unwrap();
673            }
674        }
675
676        // Apply the correction controlled on all syndrome bits being 1
677        // We need to control the correction based on all syndrome bits
678        // For more accuracy, we'd use a multi-controlled gate, but for this simulation
679        // we'll implement a simplified approach
680
681        // First, combine all syndrome bits into one control qubit
682        // We do this by applying a series of controlled-X gates
683        for i in 1..syndrome_qubits.len() {
684            circuit.cx(syndrome_qubits[i], syndrome_qubits[0]).unwrap();
685        }
686
687        // Now apply the appropriate correction controlled by the first syndrome bit
688        match error_type {
689            'X' => {
690                // Apply X correction (for bit flip)
691                circuit.cx(syndrome_qubits[0], target).unwrap();
692            }
693            'Z' => {
694                // Apply Z correction (for phase flip)
695                circuit.cz(syndrome_qubits[0], target).unwrap();
696            }
697            'Y' => {
698                // Apply Y correction (for bit-phase flip)
699                // We can implement Y as Z followed by X
700                circuit.cz(syndrome_qubits[0], target).unwrap();
701                circuit.cx(syndrome_qubits[0], target).unwrap();
702            }
703            _ => {
704                return Err(SimulatorError::UnsupportedOperation(format!(
705                    "Unsupported error type: {}",
706                    error_type
707                )))
708            }
709        }
710
711        // Undo the combination of syndrome bits
712        for i in 1..syndrome_qubits.len() {
713            circuit.cx(syndrome_qubits[i], syndrome_qubits[0]).unwrap();
714        }
715
716        // Reset syndrome bits to their original states
717        for (i, &should_be_one) in syndrome.iter().enumerate() {
718            if !should_be_one {
719                circuit.x(syndrome_qubits[i]).unwrap();
720            }
721        }
722
723        Ok(())
724    }
725}
quantrs2_sim/error_correction/codes.rs

quantrs2_sim/error_correction/
codes.rs
