Table 1 Simulated numbers of physical (memory and periphery) qubits and resource overheads (%) in the absence of a repair scheme (Original) and with 1, 2, 4, 8 redundant repair qubits (RR1, RR2, RR4, and RR8) respectively.
From: Enhancing the yield of bucket brigade quantum random access memory using redundancy repair
Code distance | Number of logical qubits | Number of physical qubits | Resource overhead (%) | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Original | RR1 | RR2 | RR4 | RR8 | RR1 | RR2 | RR4 | RR8 | |||||||||||
Mem | Peri | Mem | Peri | Mem | Peri | Mem | Peri | Mem | Peri | Mem | Peri | Mem | Peri | Mem | Peri | Mem | Peri | ||
QEC 3 | 16 | 272 | 374 | 289 | 544 | 306 | 544 | 340 | 544 | 408 | 595 | 6.25 | 45.45 | 12.5 | 45.5 | 25.0 | 45.5 | 50.0 | 59.1 |
32 | 544 | 663 | 561 | 867 | 578 | 867 | 612 | 867 | 680 | 901 | 3.13 | 30.77 | 6.25 | 30.77 | 12.5 | 30.8 | 25.0 | 35.9 | |
64 | 1,088 | 1,224 | 1,105 | 1,462 | 1,122 | 1,462 | 1,156 | 1,462 | 1,224 | 1,479 | 1.56 | 19.44 | 3.13 | 19.44 | 6.25 | 19.44 | 12.5 | 20.8 | |
128 | 2,176 | 2,329 | 2,193 | 2,601 | 2,210 | 2,601 | 2,244 | 2,601 | 2,312 | 2,601 | 0.78 | 11.68 | 1.56 | 11.68 | 3.13 | 11.68 | 6.25 | 11.68 | |
256 | 4,352 | 4,522 | 4,369 | 4,828 | 4,386 | 4,828 | 4,420 | 4,828 | 4,488 | 4,828 | 0.39 | 6.77 | 0.78 | 6.77 | 1.56 | 6.77 | 3.13 | 6.77 | |
512 | 8,704 | 8,891 | 8,721 | 9,231 | 8,738 | 9,231 | 8,772 | 9,231 | 8,840 | 9,231 | 0.20 | 3.82 | 0.39 | 3.82 | 0.78 | 3.82 | 1.56 | 3.82 | |
1,024 | 17,408 | 17,612 | 17,425 | 17,986 | 17,442 | 17,986 | 17,476 | 17,986 | 17,544 | 17,986 | 0.10 | 2.12 | 0.20 | 2.12 | 0.39 | 2.12 | 0.78 | 2.12 | |
QEC 5 | 16 | 784 | 1,078 | 833 | 1,568 | 882 | 1,568 | 980 | 1,568 | 1,176 | 1,715 | 6.25 | 45.45 | 12.5 | 45.5 | 25.0 | 45.5 | 50.0 | 59.1 |
32 | 1,568 | 1,911 | 1,617 | 2,499 | 1,666 | 2,499 | 1,764 | 2,499 | 1,960 | 2,597 | 3.13 | 30.77 | 6.25 | 30.77 | 12.5 | 30.8 | 25.0 | 35.9 | |
64 | 3,136 | 3,528 | 3,185 | 4,214 | 3,234 | 4,214 | 3,332 | 4,214 | 3,528 | 4,263 | 1.56 | 19.44 | 3.13 | 19.44 | 6.25 | 19.44 | 12.5 | 20.8 | |
128 | 6,272 | 6,713 | 6,321 | 7,497 | 6,370 | 7,497 | 6,468 | 7,497 | 6,664 | 7,497 | 0.78 | 11.68 | 1.56 | 11.68 | 3.13 | 11.68 | 6.25 | 11.68 | |
256 | 12,544 | 13,034 | 12,593 | 13,916 | 12,642 | 13,916 | 12,740 | 13,916 | 12,936 | 13,916 | 0.39 | 6.77 | 0.78 | 6.77 | 1.56 | 6.77 | 3.13 | 6.77 | |
512 | 25,088 | 25,627 | 25,137 | 26,607 | 25,186 | 26,607 | 25,284 | 26,607 | 25,480 | 26,607 | 0.20 | 3.82 | 0.39 | 3.82 | 0.78 | 3.82 | 1.56 | 3.82 | |
1,024 | 50,176 | 50,764 | 50,225 | 51,842 | 50,274 | 51,842 | 50,372 | 51,842 | 50,568 | 51,842 | 0.10 | 2.12 | 0.20 | 2.12 | 0.39 | 2.12 | 0.78 | 2.12 | |
QEC 7 | 16 | 1,552 | 2,134 | 1,649 | 3,104 | 1,746 | 3,104 | 1,940 | 3,104 | 2,328 | 3,395 | 6.25 | 45.45 | 12.5 | 45.5 | 25.0 | 45.5 | 50.0 | 59.1 |
32 | 3,104 | 3,783 | 3,201 | 4,947 | 3,298 | 4,947 | 3,492 | 4,947 | 3,880 | 5,141 | 3.13 | 30.77 | 6.25 | 30.77 | 12.5 | 30.8 | 25.0 | 35.9 | |
64 | 6,208 | 6,984 | 6,305 | 8,342 | 6,402 | 8,342 | 6,596 | 8,342 | 6,984 | 8,439 | 1.56 | 19.44 | 3.13 | 19.44 | 6.25 | 19.44 | 12.5 | 20.8 | |
128 | 12,416 | 13,289 | 12,513 | 14,841 | 12,610 | 14,841 | 12,804 | 14,841 | 13,192 | 14,841 | 0.78 | 11.68 | 1.56 | 11.68 | 3.13 | 11.68 | 6.25 | 11.68 | |
256 | 24,832 | 25,802 | 24,929 | 27,548 | 25,026 | 27,548 | 25,220 | 27,548 | 25,608 | 27,548 | 0.39 | 6.77 | 0.78 | 6.77 | 1.56 | 6.77 | 3.13 | 6.77 | |
512 | 49,664 | 50,731 | 49,761 | 52,671 | 49,858 | 52,671 | 50,052 | 52,671 | 50,440 | 52,671 | 0.20 | 3.82 | 0.39 | 3.82 | 0.78 | 3.82 | 1.56 | 3.82 | |
1,024 | 99,328 | 100,492 | 99,425 | 102,626 | 99,522 | 102,626 | 99,716 | 102,626 | 100,104 | 102,626 | 0.10 | 2.12 | 0.20 | 2.12 | 0.39 | 2.12 | 0.78 | 2.12 | |
QEC 9 | 16 | 2,576 | 3,542 | 2,737 | 5,152 | 2,898 | 5,152 | 3,220 | 5,152 | 3,864 | 5,635 | 6.25 | 45.45 | 12.5 | 45.5 | 25.0 | 45.5 | 50.0 | 59.1 |
32 | 5,152 | 6,279 | 5,313 | 8,211 | 5,474 | 8,211 | 5,796 | 8,211 | 6,440 | 8,533 | 3.13 | 30.77 | 6.25 | 30.77 | 12.5 | 30.8 | 25.0 | 35.9 | |
64 | 10,304 | 11,592 | 10,465 | 13,846 | 10,626 | 13,846 | 10,948 | 13,846 | 11,592 | 14,007 | 1.56 | 19.44 | 3.13 | 19.44 | 19.44 | 12.66 | 12.5 | 20.8 | |
128 | 20,608 | 22,057 | 20,769 | 24,633 | 20,930 | 24,633 | 21,252 | 24,633 | 21,896 | 24,633 | 0.78 | 11.68 | 1.56 | 11.68 | 3.13 | 11.68 | 6.25 | 11.68 | |
256 | 41,216 | 42,826 | 41,377 | 45,724 | 41,538 | 45,724 | 41,860 | 45,724 | 42,504 | 45,724 | 0.39 | 6.77 | 0.78 | 6.77 | 1.56 | 6.77 | 3.13 | 6.77 | |
512 | 82,432 | 84,203 | 82,593 | 87,423 | 82,754 | 87,423 | 83,076 | 87,423 | 83,720 | 87,423 | 0.20 | 3.82 | 0.39 | 3.82 | 0.78 | 3.82 | 1.56 | 3.82 | |
1,024 | 164,864 | 166,796 | 165,025 | 170,338 | 165,186 | 170,338 | 165,508 | 170,338 | 166,152 | 170,338 | 0.10 | 2.12 | 0.20 | 2.12 | 0.39 | 2.12 | 0.78 | 2.12 | |