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.is_empty() {
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).expect(
59            "Failed to apply CNOT from logical qubit to first ancilla in BitFlipCode encoding",
60        );
61        circuit.cnot(q0, q2).expect(
62            "Failed to apply CNOT from logical qubit to second ancilla in BitFlipCode encoding",
63        );
64
65        Ok(circuit)
66    }
67
68    fn decode_circuit(
69        &self,
70        encoded_qubits: &[QubitId],
71        syndrome_qubits: &[QubitId],
72    ) -> Result<Circuit<16>> {
73        let mut circuit = Circuit::<16>::new();
74
75        // Check if we have enough qubits
76        if encoded_qubits.len() < 3 {
77            return Err(SimulatorError::InvalidInput(
78                "BitFlipCode requires at least 3 encoded qubits".to_string(),
79            ));
80        }
81        if syndrome_qubits.len() < 2 {
82            return Err(SimulatorError::InvalidInput(
83                "BitFlipCode requires at least 2 syndrome qubits".to_string(),
84            ));
85        }
86
87        // Extract qubit IDs
88        let q0 = encoded_qubits[0];
89        let q1 = encoded_qubits[1];
90        let q2 = encoded_qubits[2];
91        let s0 = syndrome_qubits[0];
92        let s1 = syndrome_qubits[1];
93
94        // Syndrome extraction: CNOT from data qubits to syndrome qubits
95        circuit
96            .cnot(q0, s0)
97            .expect("Failed to apply CNOT from q0 to s0 in BitFlipCode syndrome extraction");
98        circuit
99            .cnot(q1, s0)
100            .expect("Failed to apply CNOT from q1 to s0 in BitFlipCode syndrome extraction");
101        circuit
102            .cnot(q1, s1)
103            .expect("Failed to apply CNOT from q1 to s1 in BitFlipCode syndrome extraction");
104        circuit
105            .cnot(q2, s1)
106            .expect("Failed to apply CNOT from q2 to s1 in BitFlipCode syndrome extraction");
107
108        // Apply corrections based on syndrome
109        // Syndrome 01 (s1=0, s0=1): bit flip on q0
110        circuit
111            .x(s1)
112            .expect("Failed to apply X to s1 before syndrome 01 correction in BitFlipCode");
113        circuit
114            .cx(s0, q0)
115            .expect("Failed to apply controlled-X for syndrome 01 correction in BitFlipCode");
116        circuit
117            .x(s1)
118            .expect("Failed to apply X to s1 after syndrome 01 correction in BitFlipCode");
119
120        // Syndrome 10 (s1=1, s0=0): bit flip on q1
121        circuit
122            .x(s0)
123            .expect("Failed to apply X to s0 before syndrome 10 correction in BitFlipCode");
124        circuit
125            .cx(s1, q1)
126            .expect("Failed to apply controlled-X for syndrome 10 correction in BitFlipCode");
127        circuit
128            .x(s0)
129            .expect("Failed to apply X to s0 after syndrome 10 correction in BitFlipCode");
130
131        // Syndrome 11 (s1=1, s0=1): bit flip on q2
132        circuit
133            .cx(s0, q2)
134            .expect("Failed to apply first controlled-X for syndrome 11 correction in BitFlipCode");
135        circuit.cx(s1, q2).expect(
136            "Failed to apply second controlled-X for syndrome 11 correction in BitFlipCode",
137        );
138
139        Ok(circuit)
140    }
141}
142
143/// The 3-qubit phase flip code
144///
145/// This code can detect and correct single phase flip errors.
146/// It encodes a single logical qubit into 3 physical qubits.
147#[derive(Debug, Clone, Copy)]
148pub struct PhaseFlipCode;
149
150impl ErrorCorrection for PhaseFlipCode {
151    fn physical_qubits(&self) -> usize {
152        3
153    }
154
155    fn logical_qubits(&self) -> usize {
156        1
157    }
158
159    fn distance(&self) -> usize {
160        3
161    }
162
163    fn encode_circuit(
164        &self,
165        logical_qubits: &[QubitId],
166        ancilla_qubits: &[QubitId],
167    ) -> Result<Circuit<16>> {
168        // We limit the circuit to 16 qubits maximum
169        let mut circuit = Circuit::<16>::new();
170
171        // Check if we have enough qubits
172        if logical_qubits.is_empty() {
173            return Err(SimulatorError::InvalidInput(
174                "PhaseFlipCode requires at least 1 logical qubit".to_string(),
175            ));
176        }
177        if ancilla_qubits.len() < 2 {
178            return Err(SimulatorError::InvalidInput(
179                "PhaseFlipCode requires at least 2 ancilla qubits".to_string(),
180            ));
181        }
182
183        // Extract qubit IDs
184        let q0 = logical_qubits[0];
185        let q1 = ancilla_qubits[0];
186        let q2 = ancilla_qubits[1];
187
188        // Apply Hadamard to all qubits
189        circuit
190            .h(q0)
191            .expect("Failed to apply first Hadamard to q0 in PhaseFlipCode encoding");
192        circuit
193            .h(q1)
194            .expect("Failed to apply first Hadamard to q1 in PhaseFlipCode encoding");
195        circuit
196            .h(q2)
197            .expect("Failed to apply first Hadamard to q2 in PhaseFlipCode encoding");
198
199        // Encode using bit flip code
200        circuit
201            .cnot(q0, q1)
202            .expect("Failed to apply CNOT from q0 to q1 in PhaseFlipCode encoding");
203        circuit
204            .cnot(q0, q2)
205            .expect("Failed to apply CNOT from q0 to q2 in PhaseFlipCode encoding");
206
207        // Apply Hadamard to all qubits again
208        circuit
209            .h(q0)
210            .expect("Failed to apply second Hadamard to q0 in PhaseFlipCode encoding");
211        circuit
212            .h(q1)
213            .expect("Failed to apply second Hadamard to q1 in PhaseFlipCode encoding");
214        circuit
215            .h(q2)
216            .expect("Failed to apply second Hadamard to q2 in PhaseFlipCode encoding");
217
218        Ok(circuit)
219    }
220
221    fn decode_circuit(
222        &self,
223        encoded_qubits: &[QubitId],
224        syndrome_qubits: &[QubitId],
225    ) -> Result<Circuit<16>> {
226        let mut circuit = Circuit::<16>::new();
227
228        // Check if we have enough qubits
229        if encoded_qubits.len() < 3 {
230            return Err(SimulatorError::InvalidInput(
231                "PhaseFlipCode requires at least 3 encoded qubits".to_string(),
232            ));
233        }
234        if syndrome_qubits.len() < 2 {
235            return Err(SimulatorError::InvalidInput(
236                "PhaseFlipCode requires at least 2 syndrome qubits".to_string(),
237            ));
238        }
239
240        // Extract qubit IDs
241        let q0 = encoded_qubits[0];
242        let q1 = encoded_qubits[1];
243        let q2 = encoded_qubits[2];
244        let s0 = syndrome_qubits[0];
245        let s1 = syndrome_qubits[1];
246
247        // Apply Hadamard to all encoded qubits
248        circuit
249            .h(q0)
250            .expect("Failed to apply first Hadamard to q0 in PhaseFlipCode decoding");
251        circuit
252            .h(q1)
253            .expect("Failed to apply first Hadamard to q1 in PhaseFlipCode decoding");
254        circuit
255            .h(q2)
256            .expect("Failed to apply first Hadamard to q2 in PhaseFlipCode decoding");
257
258        // Syndrome extraction: CNOT from data qubits to syndrome qubits
259        circuit
260            .cnot(q0, s0)
261            .expect("Failed to apply CNOT from q0 to s0 in PhaseFlipCode syndrome extraction");
262        circuit
263            .cnot(q1, s0)
264            .expect("Failed to apply CNOT from q1 to s0 in PhaseFlipCode syndrome extraction");
265        circuit
266            .cnot(q1, s1)
267            .expect("Failed to apply CNOT from q1 to s1 in PhaseFlipCode syndrome extraction");
268        circuit
269            .cnot(q2, s1)
270            .expect("Failed to apply CNOT from q2 to s1 in PhaseFlipCode syndrome extraction");
271
272        // Apply corrections based on syndrome in X basis
273        // Syndrome 01 (s1=0, s0=1): bit flip on q0
274        circuit
275            .x(s1)
276            .expect("Failed to apply X to s1 before syndrome 01 correction in PhaseFlipCode");
277        circuit
278            .cx(s0, q0)
279            .expect("Failed to apply controlled-X for syndrome 01 correction in PhaseFlipCode");
280        circuit
281            .x(s1)
282            .expect("Failed to apply X to s1 after syndrome 01 correction in PhaseFlipCode");
283
284        // Syndrome 10 (s1=1, s0=0): bit flip on q1
285        circuit
286            .x(s0)
287            .expect("Failed to apply X to s0 before syndrome 10 correction in PhaseFlipCode");
288        circuit
289            .cx(s1, q1)
290            .expect("Failed to apply controlled-X for syndrome 10 correction in PhaseFlipCode");
291        circuit
292            .x(s0)
293            .expect("Failed to apply X to s0 after syndrome 10 correction in PhaseFlipCode");
294
295        // Syndrome 11 (s1=1, s0=1): bit flip on q2
296        circuit.cx(s0, q2).expect(
297            "Failed to apply first controlled-X for syndrome 11 correction in PhaseFlipCode",
298        );
299        circuit.cx(s1, q2).expect(
300            "Failed to apply second controlled-X for syndrome 11 correction in PhaseFlipCode",
301        );
302
303        // Apply Hadamard to all encoded qubits to go back to computational basis
304        circuit
305            .h(q0)
306            .expect("Failed to apply second Hadamard to q0 in PhaseFlipCode decoding");
307        circuit
308            .h(q1)
309            .expect("Failed to apply second Hadamard to q1 in PhaseFlipCode decoding");
310        circuit
311            .h(q2)
312            .expect("Failed to apply second Hadamard to q2 in PhaseFlipCode decoding");
313
314        Ok(circuit)
315    }
316}
317
318/// The 9-qubit Shor code
319///
320/// This code can detect and correct arbitrary single-qubit errors
321/// (bit flips, phase flips, or both). It encodes a single logical
322/// qubit into 9 physical qubits.
323#[derive(Debug, Clone, Copy)]
324pub struct ShorCode;
325
326impl ErrorCorrection for ShorCode {
327    fn physical_qubits(&self) -> usize {
328        9
329    }
330
331    fn logical_qubits(&self) -> usize {
332        1
333    }
334
335    fn distance(&self) -> usize {
336        3
337    }
338
339    fn encode_circuit(
340        &self,
341        logical_qubits: &[QubitId],
342        ancilla_qubits: &[QubitId],
343    ) -> Result<Circuit<16>> {
344        let mut circuit = Circuit::<16>::new();
345
346        // Check if we have enough qubits
347        if logical_qubits.is_empty() {
348            return Err(SimulatorError::InvalidInput(
349                "ShorCode requires at least 1 logical qubit".to_string(),
350            ));
351        }
352        if ancilla_qubits.len() < 8 {
353            return Err(SimulatorError::InvalidInput(
354                "ShorCode requires at least 8 ancilla qubits".to_string(),
355            ));
356        }
357
358        // Extract qubit IDs for easier reading
359        let q = logical_qubits[0]; // logical qubit
360        let a = &ancilla_qubits[0..8]; // ancilla qubits
361
362        // Step 1: First encode the qubit for phase-flip protection
363        // This is done by applying Hadamard and creating a 3-qubit GHZ-like state
364        circuit
365            .h(q)
366            .expect("Failed to apply Hadamard to logical qubit in ShorCode encoding");
367
368        // Create 3 blocks with one qubit each
369        circuit
370            .cnot(q, a[0])
371            .expect("Failed to apply CNOT to create Block 1 in ShorCode encoding"); // Block 1 - first qubit
372        circuit
373            .cnot(q, a[3])
374            .expect("Failed to apply CNOT to create Block 2 in ShorCode encoding"); // Block 2 - first qubit
375
376        // Step 2: Encode each of these 3 qubits against bit-flips
377        // using the 3-qubit bit-flip code
378
379        // Encode Block 1 (qubits q, a[0], a[1], a[2])
380        circuit
381            .cnot(q, a[1])
382            .expect("Failed to apply first CNOT for Block 1 bit-flip encoding in ShorCode");
383        circuit
384            .cnot(q, a[2])
385            .expect("Failed to apply second CNOT for Block 1 bit-flip encoding in ShorCode");
386
387        // Encode Block 2 (qubits a[3], a[4], a[5])
388        circuit
389            .cnot(a[3], a[4])
390            .expect("Failed to apply first CNOT for Block 2 bit-flip encoding in ShorCode");
391        circuit
392            .cnot(a[3], a[5])
393            .expect("Failed to apply second CNOT for Block 2 bit-flip encoding in ShorCode");
394
395        // Encode Block 3 (qubits a[6], a[7])
396        // CNOT with logical qubit to create the third block
397        circuit
398            .cnot(q, a[6])
399            .expect("Failed to apply CNOT to create Block 3 in ShorCode encoding");
400        circuit
401            .cnot(a[6], a[7])
402            .expect("Failed to apply CNOT for Block 3 bit-flip encoding in ShorCode");
403
404        // At this point, we have encoded our logical |0⟩ as:
405        // (|000_000_000⟩ + |111_111_111⟩)/√2 and
406        // logical |1⟩ as: (|000_000_000⟩ - |111_111_111⟩)/√2
407
408        // Apply Hadamards again to transform into the final Shor code state
409        // For the standard Shor code representation, we would apply Hadamards again
410        // to all qubits. For this implementation we'll leave it in the current basis.
411
412        Ok(circuit)
413    }
414
415    fn decode_circuit(
416        &self,
417        encoded_qubits: &[QubitId],
418        syndrome_qubits: &[QubitId],
419    ) -> Result<Circuit<16>> {
420        let mut circuit = Circuit::<16>::new();
421
422        // Check if we have enough qubits
423        if encoded_qubits.len() < 9 {
424            return Err(SimulatorError::InvalidInput(
425                "ShorCode requires at least 9 encoded qubits".to_string(),
426            ));
427        }
428        if syndrome_qubits.len() < 8 {
429            return Err(SimulatorError::InvalidInput(
430                "ShorCode requires at least 8 syndrome qubits".to_string(),
431            ));
432        }
433
434        // Extract qubit IDs for more readable code
435        let data = encoded_qubits;
436        let synd = syndrome_qubits;
437
438        // Step 1: Bit-flip error detection within each group
439
440        // Group 1 (qubits 0,1,2) syndrome detection
441        circuit.cnot(data[0], synd[0]).expect(
442            "Failed to apply CNOT from data[0] to synd[0] in ShorCode Group 1 syndrome detection",
443        );
444        circuit.cnot(data[1], synd[0]).expect(
445            "Failed to apply CNOT from data[1] to synd[0] in ShorCode Group 1 syndrome detection",
446        );
447        circuit.cnot(data[1], synd[1]).expect(
448            "Failed to apply CNOT from data[1] to synd[1] in ShorCode Group 1 syndrome detection",
449        );
450        circuit.cnot(data[2], synd[1]).expect(
451            "Failed to apply CNOT from data[2] to synd[1] in ShorCode Group 1 syndrome detection",
452        );
453
454        // Group 2 (qubits 3,4,5) syndrome detection
455        circuit.cnot(data[3], synd[2]).expect(
456            "Failed to apply CNOT from data[3] to synd[2] in ShorCode Group 2 syndrome detection",
457        );
458        circuit.cnot(data[4], synd[2]).expect(
459            "Failed to apply CNOT from data[4] to synd[2] in ShorCode Group 2 syndrome detection",
460        );
461        circuit.cnot(data[4], synd[3]).expect(
462            "Failed to apply CNOT from data[4] to synd[3] in ShorCode Group 2 syndrome detection",
463        );
464        circuit.cnot(data[5], synd[3]).expect(
465            "Failed to apply CNOT from data[5] to synd[3] in ShorCode Group 2 syndrome detection",
466        );
467
468        // Group 3 (qubits 6,7,8) syndrome detection
469        circuit.cnot(data[6], synd[4]).expect(
470            "Failed to apply CNOT from data[6] to synd[4] in ShorCode Group 3 syndrome detection",
471        );
472        circuit.cnot(data[7], synd[4]).expect(
473            "Failed to apply CNOT from data[7] to synd[4] in ShorCode Group 3 syndrome detection",
474        );
475        circuit.cnot(data[7], synd[5]).expect(
476            "Failed to apply CNOT from data[7] to synd[5] in ShorCode Group 3 syndrome detection",
477        );
478        circuit.cnot(data[8], synd[5]).expect(
479            "Failed to apply CNOT from data[8] to synd[5] in ShorCode Group 3 syndrome detection",
480        );
481
482        // Step 2: Apply bit-flip corrections based on syndromes
483
484        // Group 1 corrections
485        // Syndrome 01 (s1=0, s0=1): bit flip on q0
486        circuit.x(synd[1]).expect(
487            "Failed to apply X to synd[1] before Group 1 syndrome 01 correction in ShorCode",
488        );
489        circuit
490            .cx(synd[0], data[0])
491            .expect("Failed to apply controlled-X for Group 1 syndrome 01 correction in ShorCode");
492        circuit.x(synd[1]).expect(
493            "Failed to apply X to synd[1] after Group 1 syndrome 01 correction in ShorCode",
494        );
495
496        // Syndrome 10 (s1=1, s0=0): bit flip on q1
497        circuit.x(synd[0]).expect(
498            "Failed to apply X to synd[0] before Group 1 syndrome 10 correction in ShorCode",
499        );
500        circuit
501            .cx(synd[1], data[1])
502            .expect("Failed to apply controlled-X for Group 1 syndrome 10 correction in ShorCode");
503        circuit.x(synd[0]).expect(
504            "Failed to apply X to synd[0] after Group 1 syndrome 10 correction in ShorCode",
505        );
506
507        // Syndrome 11 (s1=1, s0=1): bit flip on q2
508        circuit.cx(synd[0], data[2]).expect(
509            "Failed to apply first controlled-X for Group 1 syndrome 11 correction in ShorCode",
510        );
511        circuit.cx(synd[1], data[2]).expect(
512            "Failed to apply second controlled-X for Group 1 syndrome 11 correction in ShorCode",
513        );
514
515        // Group 2 corrections
516        // Syndrome 01 (s3=0, s2=1): bit flip on q3
517        circuit.x(synd[3]).expect(
518            "Failed to apply X to synd[3] before Group 2 syndrome 01 correction in ShorCode",
519        );
520        circuit
521            .cx(synd[2], data[3])
522            .expect("Failed to apply controlled-X for Group 2 syndrome 01 correction in ShorCode");
523        circuit.x(synd[3]).expect(
524            "Failed to apply X to synd[3] after Group 2 syndrome 01 correction in ShorCode",
525        );
526
527        // Syndrome 10 (s3=1, s2=0): bit flip on q4
528        circuit.x(synd[2]).expect(
529            "Failed to apply X to synd[2] before Group 2 syndrome 10 correction in ShorCode",
530        );
531        circuit
532            .cx(synd[3], data[4])
533            .expect("Failed to apply controlled-X for Group 2 syndrome 10 correction in ShorCode");
534        circuit.x(synd[2]).expect(
535            "Failed to apply X to synd[2] after Group 2 syndrome 10 correction in ShorCode",
536        );
537
538        // Syndrome 11 (s3=1, s2=1): bit flip on q5
539        circuit.cx(synd[2], data[5]).expect(
540            "Failed to apply first controlled-X for Group 2 syndrome 11 correction in ShorCode",
541        );
542        circuit.cx(synd[3], data[5]).expect(
543            "Failed to apply second controlled-X for Group 2 syndrome 11 correction in ShorCode",
544        );
545
546        // Group 3 corrections
547        // Syndrome 01 (s5=0, s4=1): bit flip on q6
548        circuit.x(synd[5]).expect(
549            "Failed to apply X to synd[5] before Group 3 syndrome 01 correction in ShorCode",
550        );
551        circuit
552            .cx(synd[4], data[6])
553            .expect("Failed to apply controlled-X for Group 3 syndrome 01 correction in ShorCode");
554        circuit.x(synd[5]).expect(
555            "Failed to apply X to synd[5] after Group 3 syndrome 01 correction in ShorCode",
556        );
557
558        // Syndrome 10 (s5=1, s4=0): bit flip on q7
559        circuit.x(synd[4]).expect(
560            "Failed to apply X to synd[4] before Group 3 syndrome 10 correction in ShorCode",
561        );
562        circuit
563            .cx(synd[5], data[7])
564            .expect("Failed to apply controlled-X for Group 3 syndrome 10 correction in ShorCode");
565        circuit.x(synd[4]).expect(
566            "Failed to apply X to synd[4] after Group 3 syndrome 10 correction in ShorCode",
567        );
568
569        // Syndrome 11 (s5=1, s4=1): bit flip on q8
570        circuit.cx(synd[4], data[8]).expect(
571            "Failed to apply first controlled-X for Group 3 syndrome 11 correction in ShorCode",
572        );
573        circuit.cx(synd[5], data[8]).expect(
574            "Failed to apply second controlled-X for Group 3 syndrome 11 correction in ShorCode",
575        );
576
577        // Step 3: Phase-flip error detection between groups
578
579        // Apply Hadamard gates to convert phase errors to bit errors
580        for &q in &[data[0], data[3], data[6]] {
581            circuit
582                .h(q)
583                .expect("Failed to apply Hadamard for phase error detection in ShorCode");
584        }
585
586        // Detect phase errors by comparing the first qubit of each group
587        circuit.cnot(data[0], synd[6]).expect(
588            "Failed to apply CNOT from data[0] to synd[6] in ShorCode phase error detection",
589        );
590        circuit.cnot(data[3], synd[6]).expect(
591            "Failed to apply CNOT from data[3] to synd[6] in ShorCode phase error detection",
592        );
593        circuit.cnot(data[3], synd[7]).expect(
594            "Failed to apply CNOT from data[3] to synd[7] in ShorCode phase error detection",
595        );
596        circuit.cnot(data[6], synd[7]).expect(
597            "Failed to apply CNOT from data[6] to synd[7] in ShorCode phase error detection",
598        );
599
600        // Step 4: Apply phase-flip corrections based on syndrome
601
602        // Syndrome 01 (s7=0, s6=1): phase flip on group 1 (qubits 0,1,2)
603        circuit
604            .x(synd[7])
605            .expect("Failed to apply X to synd[7] before phase syndrome 01 correction in ShorCode");
606        for &q in &[data[0], data[1], data[2]] {
607            circuit.cz(synd[6], q).expect(
608                "Failed to apply controlled-Z for Group 1 phase syndrome 01 correction in ShorCode",
609            );
610        }
611        circuit
612            .x(synd[7])
613            .expect("Failed to apply X to synd[7] after phase syndrome 01 correction in ShorCode");
614
615        // Syndrome 10 (s7=1, s6=0): phase flip on group 2 (qubits 3,4,5)
616        circuit
617            .x(synd[6])
618            .expect("Failed to apply X to synd[6] before phase syndrome 10 correction in ShorCode");
619        for &q in &[data[3], data[4], data[5]] {
620            circuit.cz(synd[7], q).expect(
621                "Failed to apply controlled-Z for Group 2 phase syndrome 10 correction in ShorCode",
622            );
623        }
624        circuit
625            .x(synd[6])
626            .expect("Failed to apply X to synd[6] after phase syndrome 10 correction in ShorCode");
627
628        // Syndrome 11 (s7=1, s6=1): phase flip on group 3 (qubits 6,7,8)
629        for &q in &[data[6], data[7], data[8]] {
630            circuit
631                .cz(synd[6], q)
632                .expect("Failed to apply first controlled-Z for Group 3 phase syndrome 11 correction in ShorCode");
633            circuit
634                .cz(synd[7], q)
635                .expect("Failed to apply second controlled-Z for Group 3 phase syndrome 11 correction in ShorCode");
636        }
637
638        // Step 5: Transform back from Hadamard basis
639        for &q in &[data[0], data[3], data[6]] {
640            circuit.h(q).expect(
641                "Failed to apply Hadamard to transform back from phase error basis in ShorCode",
642            );
643        }
644
645        Ok(circuit)
646    }
647}
648
649/// The 5-qubit perfect code
650///
651/// This is the smallest code that can correct an arbitrary single-qubit error.
652/// It encodes a single logical qubit into 5 physical qubits.
653#[derive(Debug, Clone, Copy)]
654pub struct FiveQubitCode;
655
656impl ErrorCorrection for FiveQubitCode {
657    fn physical_qubits(&self) -> usize {
658        5
659    }
660
661    fn logical_qubits(&self) -> usize {
662        1
663    }
664
665    fn distance(&self) -> usize {
666        3
667    }
668
669    fn encode_circuit(
670        &self,
671        logical_qubits: &[QubitId],
672        ancilla_qubits: &[QubitId],
673    ) -> Result<Circuit<16>> {
674        let mut circuit = Circuit::<16>::new();
675
676        // Check if we have enough qubits
677        if logical_qubits.is_empty() {
678            return Err(SimulatorError::InvalidInput(
679                "FiveQubitCode requires at least 1 logical qubit".to_string(),
680            ));
681        }
682        if ancilla_qubits.len() < 4 {
683            return Err(SimulatorError::InvalidInput(
684                "FiveQubitCode requires at least 4 ancilla qubits".to_string(),
685            ));
686        }
687
688        // Extract qubit IDs
689        let q0 = logical_qubits[0];
690        let ancs = ancilla_qubits;
691
692        // The encoding circuit for the 5-qubit perfect code
693        // This implements the circuit described in Nielsen & Chuang
694
695        // Initialize all ancilla qubits to |0⟩ (they start in this state by default)
696
697        // Step 1: Apply the initial gates to start creating the superposition
698        circuit
699            .h(ancs[0])
700            .expect("Failed to apply Hadamard to ancs[0] in FiveQubitCode encoding initialization");
701        circuit
702            .h(ancs[1])
703            .expect("Failed to apply Hadamard to ancs[1] in FiveQubitCode encoding initialization");
704        circuit
705            .h(ancs[2])
706            .expect("Failed to apply Hadamard to ancs[2] in FiveQubitCode encoding initialization");
707        circuit
708            .h(ancs[3])
709            .expect("Failed to apply Hadamard to ancs[3] in FiveQubitCode encoding initialization");
710
711        // Step 2: Apply the controlled encoding operations
712        // CNOT from data qubit to ancilla qubits
713        circuit
714            .cnot(q0, ancs[0])
715            .expect("Failed to apply CNOT from q0 to ancs[0] in FiveQubitCode encoding");
716        circuit
717            .cnot(q0, ancs[1])
718            .expect("Failed to apply CNOT from q0 to ancs[1] in FiveQubitCode encoding");
719        circuit
720            .cnot(q0, ancs[2])
721            .expect("Failed to apply CNOT from q0 to ancs[2] in FiveQubitCode encoding");
722        circuit
723            .cnot(q0, ancs[3])
724            .expect("Failed to apply CNOT from q0 to ancs[3] in FiveQubitCode encoding");
725
726        // Step 3: Apply the stabilizer operations
727        // These specific gates implement the [[5,1,3]] perfect code
728
729        // X stabilizer operations
730        circuit
731            .h(q0)
732            .expect("Failed to apply Hadamard to q0 for X stabilizer in FiveQubitCode encoding");
733        circuit.h(ancs[1]).expect(
734            "Failed to apply Hadamard to ancs[1] for X stabilizer in FiveQubitCode encoding",
735        );
736        circuit.h(ancs[3]).expect(
737            "Failed to apply Hadamard to ancs[3] for X stabilizer in FiveQubitCode encoding",
738        );
739
740        circuit
741            .cnot(q0, ancs[0])
742            .expect("Failed to apply CNOT for X stabilizer step 1 in FiveQubitCode encoding");
743        circuit
744            .cnot(ancs[1], ancs[0])
745            .expect("Failed to apply CNOT for X stabilizer step 2 in FiveQubitCode encoding");
746        circuit
747            .cnot(ancs[0], ancs[2])
748            .expect("Failed to apply CNOT for X stabilizer step 3 in FiveQubitCode encoding");
749        circuit
750            .cnot(ancs[2], ancs[3])
751            .expect("Failed to apply CNOT for X stabilizer step 4 in FiveQubitCode encoding");
752
753        // Z stabilizer operations
754        circuit.cz(q0, ancs[1]).expect(
755            "Failed to apply controlled-Z for Z stabilizer step 1 in FiveQubitCode encoding",
756        );
757        circuit.cz(ancs[0], ancs[2]).expect(
758            "Failed to apply controlled-Z for Z stabilizer step 2 in FiveQubitCode encoding",
759        );
760        circuit.cz(ancs[1], ancs[3]).expect(
761            "Failed to apply controlled-Z for Z stabilizer step 3 in FiveQubitCode encoding",
762        );
763
764        circuit
765            .h(ancs[0])
766            .expect("Failed to apply final Hadamard to ancs[0] in FiveQubitCode encoding");
767        circuit
768            .h(ancs[2])
769            .expect("Failed to apply final Hadamard to ancs[2] in FiveQubitCode encoding");
770
771        // This encodes the logical qubit into a 5-qubit entangled state that can
772        // detect and correct any single-qubit error
773
774        Ok(circuit)
775    }
776
777    fn decode_circuit(
778        &self,
779        encoded_qubits: &[QubitId],
780        syndrome_qubits: &[QubitId],
781    ) -> Result<Circuit<16>> {
782        let mut circuit = Circuit::<16>::new();
783
784        // Check if we have enough qubits
785        if encoded_qubits.len() < 5 {
786            return Err(SimulatorError::InvalidInput(
787                "FiveQubitCode requires at least 5 encoded qubits".to_string(),
788            ));
789        }
790        if syndrome_qubits.len() < 4 {
791            return Err(SimulatorError::InvalidInput(
792                "FiveQubitCode requires at least 4 syndrome qubits".to_string(),
793            ));
794        }
795
796        // Extract qubit IDs
797        let data = encoded_qubits;
798        let synd = syndrome_qubits;
799
800        // The 5-qubit code uses 4 stabilizer generators to detect errors
801        // We'll implement the syndrome extraction circuit that measures these stabilizers
802
803        // Generator 1: XZZXI
804        circuit
805            .h(synd[0])
806            .expect("Failed to apply Hadamard to synd[0] before Generator 1 in FiveQubitCode syndrome extraction");
807        circuit
808            .cnot(synd[0], data[0])
809            .expect("Failed to apply CNOT for Generator 1 XZZXI at position 0 in FiveQubitCode");
810        circuit.cz(synd[0], data[1]).expect(
811            "Failed to apply controlled-Z for Generator 1 XZZXI at position 1 in FiveQubitCode",
812        );
813        circuit.cz(synd[0], data[2]).expect(
814            "Failed to apply controlled-Z for Generator 1 XZZXI at position 2 in FiveQubitCode",
815        );
816        circuit
817            .cnot(synd[0], data[3])
818            .expect("Failed to apply CNOT for Generator 1 XZZXI at position 3 in FiveQubitCode");
819        circuit
820            .h(synd[0])
821            .expect("Failed to apply Hadamard to synd[0] after Generator 1 in FiveQubitCode syndrome extraction");
822
823        // Generator 2: IXZZX
824        circuit
825            .h(synd[1])
826            .expect("Failed to apply Hadamard to synd[1] before Generator 2 in FiveQubitCode syndrome extraction");
827        circuit
828            .cnot(synd[1], data[1])
829            .expect("Failed to apply CNOT for Generator 2 IXZZX at position 1 in FiveQubitCode");
830        circuit.cz(synd[1], data[2]).expect(
831            "Failed to apply controlled-Z for Generator 2 IXZZX at position 2 in FiveQubitCode",
832        );
833        circuit.cz(synd[1], data[3]).expect(
834            "Failed to apply controlled-Z for Generator 2 IXZZX at position 3 in FiveQubitCode",
835        );
836        circuit
837            .cnot(synd[1], data[4])
838            .expect("Failed to apply CNOT for Generator 2 IXZZX at position 4 in FiveQubitCode");
839        circuit
840            .h(synd[1])
841            .expect("Failed to apply Hadamard to synd[1] after Generator 2 in FiveQubitCode syndrome extraction");
842
843        // Generator 3: XIXZZ
844        circuit
845            .h(synd[2])
846            .expect("Failed to apply Hadamard to synd[2] before Generator 3 in FiveQubitCode syndrome extraction");
847        circuit
848            .cnot(synd[2], data[0])
849            .expect("Failed to apply CNOT for Generator 3 XIXZZ at position 0 in FiveQubitCode");
850        circuit
851            .cnot(synd[2], data[2])
852            .expect("Failed to apply CNOT for Generator 3 XIXZZ at position 2 in FiveQubitCode");
853        circuit.cz(synd[2], data[3]).expect(
854            "Failed to apply controlled-Z for Generator 3 XIXZZ at position 3 in FiveQubitCode",
855        );
856        circuit.cz(synd[2], data[4]).expect(
857            "Failed to apply controlled-Z for Generator 3 XIXZZ at position 4 in FiveQubitCode",
858        );
859        circuit
860            .h(synd[2])
861            .expect("Failed to apply Hadamard to synd[2] after Generator 3 in FiveQubitCode syndrome extraction");
862
863        // Generator 4: ZXIXZ
864        circuit
865            .h(synd[3])
866            .expect("Failed to apply Hadamard to synd[3] before Generator 4 in FiveQubitCode syndrome extraction");
867        circuit.cz(synd[3], data[0]).expect(
868            "Failed to apply controlled-Z for Generator 4 ZXIXZ at position 0 in FiveQubitCode",
869        );
870        circuit
871            .cnot(synd[3], data[1])
872            .expect("Failed to apply CNOT for Generator 4 ZXIXZ at position 1 in FiveQubitCode");
873        circuit
874            .cnot(synd[3], data[3])
875            .expect("Failed to apply CNOT for Generator 4 ZXIXZ at position 3 in FiveQubitCode");
876        circuit.cz(synd[3], data[4]).expect(
877            "Failed to apply controlled-Z for Generator 4 ZXIXZ at position 4 in FiveQubitCode",
878        );
879        circuit
880            .h(synd[3])
881            .expect("Failed to apply Hadamard to synd[3] after Generator 4 in FiveQubitCode syndrome extraction");
882
883        // After measuring the syndrome, we would apply the appropriate correction
884        // The 5-qubit code has a complex error correction table with 16 possible syndromes
885        // We'll implement a simplified version that corrects the most common errors
886
887        // First, we'll correct bit flips (X errors)
888        // Syndrome 0001: X error on qubit 0
889        let syndrome_0001 = [false, false, false, true];
890        self.add_conditional_correction(&mut circuit, synd, syndrome_0001, data[0], 'X')?;
891
892        // Syndrome 0010: X error on qubit 1
893        let syndrome_0010 = [false, false, true, false];
894        self.add_conditional_correction(&mut circuit, synd, syndrome_0010, data[1], 'X')?;
895
896        // Syndrome 0100: X error on qubit 2
897        let syndrome_0100 = [false, true, false, false];
898        self.add_conditional_correction(&mut circuit, synd, syndrome_0100, data[2], 'X')?;
899
900        // Syndrome 1000: X error on qubit 3
901        let syndrome_1000 = [true, false, false, false];
902        self.add_conditional_correction(&mut circuit, synd, syndrome_1000, data[3], 'X')?;
903
904        // Now, we'll correct phase flips (Z errors)
905        // Syndrome 0011: Z error on qubit 0
906        let syndrome_0011 = [false, false, true, true];
907        self.add_conditional_correction(&mut circuit, synd, syndrome_0011, data[0], 'Z')?;
908
909        // Syndrome 0101: Z error on qubit 1
910        let syndrome_0101 = [false, true, false, true];
911        self.add_conditional_correction(&mut circuit, synd, syndrome_0101, data[1], 'Z')?;
912
913        // Syndrome 1001: Z error on qubit 2
914        let syndrome_1001 = [true, false, false, true];
915        self.add_conditional_correction(&mut circuit, synd, syndrome_1001, data[2], 'Z')?;
916
917        // Syndrome 1100: Z error on qubit 3
918        let syndrome_1100 = [true, true, false, false];
919        self.add_conditional_correction(&mut circuit, synd, syndrome_1100, data[3], 'Z')?;
920
921        // And finally, Y errors (both bit and phase flips)
922        // Syndrome 0111: Y error on qubit 0
923        let syndrome_0111 = [false, true, true, true];
924        self.add_conditional_correction(&mut circuit, synd, syndrome_0111, data[0], 'Y')?;
925
926        // Syndrome 1011: Y error on qubit 1
927        let syndrome_1011 = [true, false, true, true];
928        self.add_conditional_correction(&mut circuit, synd, syndrome_1011, data[1], 'Y')?;
929
930        // Syndrome 1101: Y error on qubit 2
931        let syndrome_1101 = [true, true, false, true];
932        self.add_conditional_correction(&mut circuit, synd, syndrome_1101, data[2], 'Y')?;
933
934        // Syndrome 1110: Y error on qubit 3
935        let syndrome_1110 = [true, true, true, false];
936        self.add_conditional_correction(&mut circuit, synd, syndrome_1110, data[3], 'Y')?;
937
938        Ok(circuit)
939    }
940}
941
942impl FiveQubitCode {
943    /// Helper function to add conditionally controlled gates based on syndrome measurement
944    fn add_conditional_correction(
945        &self,
946        circuit: &mut Circuit<16>,
947        syndrome_qubits: &[QubitId],
948        syndrome: [bool; 4],
949        target: QubitId,
950        error_type: char,
951    ) -> Result<()> {
952        // In a real quantum circuit, this would involve classical control
953        // For our simulator, we simulate classical control using quantum gates
954
955        // For each syndrome bit, apply X gate to negate it if needed
956        for (i, &should_be_one) in syndrome.iter().enumerate() {
957            if !should_be_one {
958                circuit
959                    .x(syndrome_qubits[i])
960                    .expect("Failed to apply X gate to negate syndrome bit in FiveQubitCode conditional correction");
961            }
962        }
963
964        // Apply the correction controlled on all syndrome bits being 1
965        // We need to control the correction based on all syndrome bits
966        // For more accuracy, we'd use a multi-controlled gate, but for this simulation
967        // we'll implement a simplified approach
968
969        // First, combine all syndrome bits into one control qubit
970        // We do this by applying a series of controlled-X gates
971        for i in 1..syndrome_qubits.len() {
972            circuit
973                .cx(syndrome_qubits[i], syndrome_qubits[0])
974                .expect("Failed to apply controlled-X to combine syndrome bits in FiveQubitCode conditional correction");
975        }
976
977        // Now apply the appropriate correction controlled by the first syndrome bit
978        match error_type {
979            'X' => {
980                // Apply X correction (for bit flip)
981                circuit.cx(syndrome_qubits[0], target).expect(
982                    "Failed to apply controlled-X correction for bit flip in FiveQubitCode",
983                );
984            }
985            'Z' => {
986                // Apply Z correction (for phase flip)
987                circuit.cz(syndrome_qubits[0], target).expect(
988                    "Failed to apply controlled-Z correction for phase flip in FiveQubitCode",
989                );
990            }
991            'Y' => {
992                // Apply Y correction (for bit-phase flip)
993                // We can implement Y as Z followed by X
994                circuit
995                    .cz(syndrome_qubits[0], target)
996                    .expect("Failed to apply controlled-Z for Y correction in FiveQubitCode");
997                circuit
998                    .cx(syndrome_qubits[0], target)
999                    .expect("Failed to apply controlled-X for Y correction in FiveQubitCode");
1000            }
1001            _ => {
1002                return Err(SimulatorError::UnsupportedOperation(format!(
1003                    "Unsupported error type: {error_type}"
1004                )))
1005            }
1006        }
1007
1008        // Undo the combination of syndrome bits
1009        for i in 1..syndrome_qubits.len() {
1010            circuit
1011                .cx(syndrome_qubits[i], syndrome_qubits[0])
1012                .expect("Failed to apply controlled-X to undo syndrome bit combination in FiveQubitCode conditional correction");
1013        }
1014
1015        // Reset syndrome bits to their original states
1016        for (i, &should_be_one) in syndrome.iter().enumerate() {
1017            if !should_be_one {
1018                circuit
1019                    .x(syndrome_qubits[i])
1020                    .expect("Failed to apply X gate to reset syndrome bit in FiveQubitCode conditional correction");
1021            }
1022        }
1023
1024        Ok(())
1025    }
1026}
quantrs2_sim/error_correction/codes.rs

quantrs2_sim/error_correction/
codes.rs
