| 341 | } |
| 342 | |
| 343 | QMatrix getSwapMatrix(int qb1, int qb2, int numQb) { |
| 344 | DEMAND( numQb > 1 ); |
| 345 | DEMAND( (qb1 >= 0 && qb1 < numQb) ); |
| 346 | DEMAND( (qb2 >= 0 && qb2 < numQb) ); |
| 347 | |
| 348 | if (qb1 > qb2) |
| 349 | std::swap(qb1, qb2); |
| 350 | |
| 351 | if (qb1 == qb2) |
| 352 | return getIdentityMatrix(1 << numQb); |
| 353 | |
| 354 | QMatrix swap; |
| 355 | |
| 356 | if (qb2 == qb1 + 1) { |
| 357 | // qubits are adjacent |
| 358 | swap = QMatrix{{1,0,0,0},{0,0,1,0},{0,1,0,0},{0,0,0,1}}; |
| 359 | |
| 360 | } else { |
| 361 | // qubits are distant |
| 362 | int block = 1 << (qb2 - qb1); |
| 363 | swap = getZeroMatrix(block*2); |
| 364 | QMatrix iden = getIdentityMatrix(block/2); |
| 365 | |
| 366 | // Lemma 3.1 of arxiv.org/pdf/1711.09765.pdf |
| 367 | QMatrix p0{{1,0},{0,0}}; |
| 368 | QMatrix l0{{0,1},{0,0}}; |
| 369 | QMatrix l1{{0,0},{1,0}}; |
| 370 | QMatrix p1{{0,0},{0,1}}; |
| 371 | |
| 372 | /* notating a^(n+1) = identity(1<<n) (otimes) a, we construct the matrix |
| 373 | * [ p0^(N) l1^N ] |
| 374 | * [ l0^(N) p1^N ] |
| 375 | * where N = qb2 - qb1 */ |
| 376 | setSubMatrix(swap, getKroneckerProduct(iden, p0), 0, 0); |
| 377 | setSubMatrix(swap, getKroneckerProduct(iden, l0), block, 0); |
| 378 | setSubMatrix(swap, getKroneckerProduct(iden, l1), 0, block); |
| 379 | setSubMatrix(swap, getKroneckerProduct(iden, p1), block, block); |
| 380 | } |
| 381 | |
| 382 | // pad swap with outer identities |
| 383 | if (qb1 > 0) |
| 384 | swap = getKroneckerProduct(swap, getIdentityMatrix(1<<qb1)); |
| 385 | if (qb2 < numQb-1) |
| 386 | swap = getKroneckerProduct(getIdentityMatrix(1<<(numQb-qb2-1)), swap); |
| 387 | |
| 388 | return swap; |
| 389 | } |
| 390 | |
| 391 | /* (don't generate doxygen doc) |
| 392 | * |
no test coverage detected