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Diagonal Adaptive Non-local Observables on Quantum Neural Networks

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Huan-Hsin Tseng, Yan Li, Hsin-Yi Lin, Samuel Yen-Chi Chen

๐Ÿ’ก ๊ฐœ์š”

๋ณธ ๋…ผ๋ฌธ์€ ๋ณ€๋ถ„ ์–‘์ž ์•Œ๊ณ ๋ฆฌ์ฆ˜(VQA)์˜ ํ•จ์ˆ˜ ๊ณต๊ฐ„์„ ํ™•์žฅํ•˜๋Š” ๋ฐ ํšจ๊ณผ์ ์ธ ์ ์‘ํ˜• ๋น„๊ตญ์†Œ ๊ด€์ธก๋Ÿ‰(ANO)์˜ ํŒŒ๋ผ๋ฏธํ„ฐ ๋ณต์žก์„ฑ๊ณผ ์ตœ์ ํ™” ๋น„์šฉ์„ ์ค„์ด๊ธฐ ์œ„ํ•ด ๋Œ€๊ฐ ๊ด€์ธก๋Ÿ‰๋งŒ์„ ์‚ฌ์šฉํ•˜๋Š” ์ƒˆ๋กœ์šด ํ˜•ํƒœ์˜ ANO๋ฅผ ์ œ์•ˆํ•ฉ๋‹ˆ๋‹ค. ์ œ์•ˆ๋œ ๋Œ€๊ฐ ANO๋Š” ๊ธฐ์กด์˜ ์ „์ฒด ANO์™€ ๋™์ผํ•œ ํ‘œํ˜„ ๋Šฅ๋ ฅ์„ ์œ ์ง€ํ•˜๋ฉด์„œ๋„ $k$-๊ตญ์†Œ ๊ด€์ธก๋Ÿ‰ ๋ณต์žก์„ฑ์„ $O(4^k)$์—์„œ $O(2^k)$๋กœ ํฌ๊ฒŒ ๊ฐ์†Œ์‹œํ‚ค๊ณ  ์ธก์ • ๊ด€๋ จ ๊ณ ์ „์  ๊ณ„์‚ฐ ๋น„์šฉ์„ ๋‚ฎ์ถฅ๋‹ˆ๋‹ค. ์ด๋Š” ๋Œ€๊ฐ ANO๊ฐ€ ๊ธฐ์กด VQC๋ฅผ ํฌํ•จํ•˜๋Š” ํŠน๋ณ„ํ•œ ๊ฒฝ์šฐ๋กœ์„œ ์ „์ฒด ANO์˜ ์ด์ ์„ ์ƒ๋‹น ๋ถ€๋ถ„ ๋ณด์กดํ•จ์„ ์˜๋ฏธํ•ฉ๋‹ˆ๋‹ค.

๐Ÿ”‘ ์‹œ์‚ฌ์  ๋ฐ ํ•œ๊ณ„

โ€ข
๋Œ€๊ฐ ํ•ญ๋งŒ ๊ณ ๋ คํ•˜๋Š” ANO๋Š” ํŒŒ๋ผ๋ฏธํ„ฐ ์ˆ˜๋ฅผ ์ค„์—ฌ VQA์˜ ํ•™์Šต ํšจ์œจ์„ฑ์„ ๋†’์ผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
โ€ข
์ธก์ • ์„ค๊ณ„์— ๋Œ€ํ•œ ํ•˜๋“œ์›จ์–ด ์š”๊ตฌ ์‚ฌํ•ญ์„ ์™„ํ™”ํ•˜๋ฉด์„œ๋„ VQA์˜ ํ‘œํ˜„ ๋Šฅ๋ ฅ์„ ์œ ์ง€ํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
โ€ข
๋ณธ ์—ฐ๊ตฌ์—์„œ ์ œ์‹œ๋œ ๋Œ€๊ฐ ANO์˜ ๊ตฌํ˜„ ๋ฐ ์‹ค์ œ ์–‘์ž ํ•˜๋“œ์›จ์–ด์—์„œ์˜ ์„ฑ๋Šฅ ๊ฒ€์ฆ์ด ํ•„์š”ํ•ฉ๋‹ˆ๋‹ค.
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