Bqp Puns

import operator
from operator import mul
from functools import reduce

# Does "FACTOR" have a K_product that equals TARGET? 

factor = int(input('Enter your integer to factor: '))
target = int(input('Enter integer to see if a K_product exists for target: '))

factors = [];
for j in range(1, factor + 1):
  if factor % j == 0:
    factors.append(j)

total_product_of_factors = reduce(mul, factors)

# This statement WILL always work guaranteed.
# Because factors have ALL POSSIBLE DIVISORS.

if total_product_of_factors % target == 0:
  print('Yes, there is a subset product of', target)

Output

Enter your integer to factor: 4097
Enter integer to see if a K_product exists for target: 241
Yes, there is a subset product of 241

crosspost from reddit.com/r/math/comments/9m2ic0

What is your opinion and thoughts about possible ways to get an answer whether problems that are solvable on quantum computer within polynomial time (BQP) can be solved withing polynomial time on hypothetical machine that has discrete ontology? The latter means that it doesn't use continuous manifolds and such. It only uses discrete entities and maybe rational numbers as in discrete probability theory?

upd: by discrete I meant countable.

I was wondering, is the intersection of NP and coNP a subset of BQP, as in, is:

NP ∩ coNP ⊂ BQP ?

Hearthlytics Open #3

Date and Time:

3/28/2015

12:00 PM PDT

Tournament Style:

Best out of 5

Conquest

Server:

North America

Additional Comments:

Prizes:

35 USD and 10 “BQP” to 1st

15 USD and 5 “BQP” to 2nd

1 “BQP” to 3rd

1 “BQP” to 4th

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NP is the set of languages decidable by a Turing machine in nondeterministic polynomial time. An NP-complete language n is one such that given any language p in NP, the problem of recognizing p reduces to that of n. BQP is the set of languages decidable in bounded error polynomial time. One example of this seemingly being true is integer factorization.

Just to be clear, I do not believe this by any means. It's just a thought. I hope someone else has thoughts on it too.

本人本科和博士分别在中国和美国某大技校读理工科。对量子计算和半导体有一定了解。看了最近的一些新闻，想分享一下自己的看法。欢迎各位讨论以及提出不同的意见。

量子计算

量子计算是我相对比较了解的领域。想要严格讨论的话，要分成量子计算和量子通信两个子领域。

• 量子通信在技术上更成熟。虽然在技术细节上还有争议（比如完美单光子源），但距离现实世界已经很近。和传统的通信手段相比，无法被窃听（或者说任何窃听都一定会被检测到）。用学术界的语言，它可以实现“信息论安全性”（大致可以认为是理论上完美安全性）而不是传统的“计算安全性”（即想要破解加密信息原则上可能，但需要不切实际的计算量）。这一安全性的提升当然有价值。但是问题在于，虽然“计算安全性”并不完美，破解加密信息所需的计算量完全是天方夜谭。所以信息传递安全中最薄弱的一环从来不在于量子通信所提升的那个环节。因此这一技术对于通讯安全的边际价值微乎其微。
• 量子计算不仅在技术上离我们非常遥远，而且其理论价值也很有限。
  • 理论上，量子算法已经发展了二十多年了。当前真正有价值的量子算法其实只有两大类，一类衍生于 Grover 搜索算法，一类衍生于 Shor 算法。（还有一些两者的混合体比如 HHL 算法，在此暂且不表。）前者是一个搜索算法，在各种假定和前提下，可以用 O(sqrt(n)) 的时间搜索一个大小为 n 的“量子”数据库。这一加速并不能把一个指数加速到多项式，所以应用有限。后者则更激动人心，原则上可以把经典计算中指数复杂的质数分解问题加速到多项式复杂度，这直接威胁到 RSA 等广泛使用的加密算法。这也是量子计算这么受关注的最主要原因。但是问题在于，就算量子计算机被成功研制，“后量子”密码学早已蓬勃发展。相对于研发量子计算机的代价，人们可以用可以忽略不计的代价将当前的加密系统升级到对于量子计算机安全的版本，这使得量子计算机的意义大减。那么除了质数分解以外，量子计算机是不是还能解决其他经典计算机难以解决的问题？目前看来，答案是比较悲观的。在计算复杂性理论中，量子计算机能解决的问题的集合叫 BQP，经典计算机能解决的问题的集合叫 P（就是 P=NP 的那个 P）。除了质数分解这类问题，人们还没有发现在 BQP 但不在 P 中且有任何现实意义的问题。量子模拟或许是一个很有前景的应用，但它的应用场景很有限。
  • 实际上，量子计算机的研发还处于“宇宙大爆炸”的阶段。一个量子计算机想要破解2048位的 RSA，所需要的量子比特普遍认为在百万到千万的量级，这还不考虑在如此数量多量子比特时量子逻辑门的保真度难以维持。目前人们能造出的量子计算机只不过是一百的量级，这其中有好几个数量级的差距。（而且根据上文，就算这样的量子计算机被制造出来，人们只需要简单升级加密算法即可。）经常有人会将经典计算机中的摩尔定律类比到量子计算机的未来发展上去。但问题在于，量子计算机的研发不仅是一个工程问题。想要制备并且控制数百万量级量子比特，类似于制造一条“薛定谔的猫”（即宏观量子态）。有各种各样的证据表明这样的量子态是不稳定的。量子计算机大小的边界在哪里，学术界内部也众说纷纭。我个人持悲观态度。

碳基半导体

与量子计算机不同，碳基半导体更多的是一个工业问题而不是学术问题。

• 工业上，半导体工业自上世纪 60 年代以来有着多达半个世纪的积累。从仙童到英特尔台积电，其生产工艺以年为单位进行迭代，生产线不断扩大。这导致如今半导体产品质量稳定且价格极低。这就是所谓的经验学习曲线。假定基于碳纳米管的半导体器件在电学参数上可以与当前的硅基以及三五族半导体（下称“传统半导体”）相媲美，它还面临着如何大规模建厂生产，提高良品率和降低成本的问题。另一方面，传统半导体已经形成了非常成熟的产业链，每年都有大量资金和人才流入研发。这导致碳基半导体本来就输在了起跑线上，还跑得没有传统半导体快。除非传统半导体的发展陷入了严重的瓶颈，碳基半导体几乎没有可能取代传统半导体。一个类似的例子是光伏产业，即太阳能电池板。领域的领军人物之一 Yablonovitch 旗下公司生产的电池板效率（25-29%）远超传统的硅基太阳能电池板（15-23%），还具有柔性可折叠等特性。尽管如此，其成本完全无法与生产线反复迭代扩大的硅基太阳能电池板相比。类似摩尔定律，光伏领域内有所谓Swanson's law：太阳能电池板产量每扩大一倍，成本降低 20%。这导致 Yablonovitch 的产品只能应用在对效率极度敏感，但对成本不敏感的小众领域。其公司在 2019 年停止运营。值得一提的是，光伏领域内还有中国地方政府补贴建厂的现象，导致低效率的硅基太阳能电池板低于成本价销售。这一现象是否属于在政府影响下劣币驱逐良币，我认为也是值得思考的。（光伏产业还有其独有的一些特性，比如市场需求容易饱和，在此暂且不表。）
• 上面说到，除非传统半导体的发展陷入了严重的瓶颈，碳基半导体几乎没有可能取代传统半导体。在计算领域，普遍认为，传统半导体的制程低于 2nm 后会遇到各种各样的问题，比如短沟道效应和量子隧穿效应。一方面，半导体大厂如台积电和三星在全环绕栅（GAA）晶体管工艺的研发上有很大进展，从而给硅基半导体续命；另一方面，碳基半导体在 2nm 制程下能多大程度缓解短沟道和量子隧穿效应也未可知。本质上，短沟道和量子隧穿效应来源于晶体管的尺寸过小，将硅原子换成碳原子并不能避免这些问题。在显示领域，碳基半导体又具有能带带隙太小等问题，和传统材料比如 IGZO 相比优势有限。

结语

最后说一点私货。学术界在申请经费时常喜欢无节操夸大研究的影响力。

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Martin Freeman, and Andy Serkis.

They also play roles in Lord of the Rings.

I guess that makes them the Tolkien white guys.

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crosspost from reddit.com/r/math/comments/9m2ic0

What is your opinion and thoughts about possible ways to get an answer whether problems that are solvable on quantum computer within polynomial time (BQP) can be solved withing polynomial time on hypothetical machine that has discrete ontology? The latter means that it doesn't use continuous manifolds and such. It only uses discrete entities and maybe rational numbers as in discrete probability theory?

upd: by discrete I meant countable.

What is your opinion and thoughts about possible ways to get an answer whether problems that are solvable on quantum computer within polynomial time (BQP) can be solved within polynomial time on hypothetical machine that has discrete ontology? The latter means that it doesn't use continuous manifolds and such. It only uses discrete entities and maybe rational numbers as in discrete probability theory?

upd: by discrete I meant countable.

crosspost from reddit.com/r/math/comments/9m2ic0

What is your opinion and thoughts about possible ways to get an answer whether problems that are solvable on quantum computer within polynomial time (BQP) can be solved withing polynomial time on hypothetical machine that has discrete ontology? The latter means that it doesn't use continuous manifolds and such. It only uses discrete entities and maybe rational numbers as in discrete probability theory?

upd: by discrete I meant countable.

crosspost from reddit.com/r/math/comments/9m2ic0

What is your opinion and thoughts about possible ways to get an answer whether problems that are solvable on quantum computer within polynomial time (BQP) can be solved withing polynomial time on hypothetical machine that has discrete ontology? The latter means that it doesn't use continuous manifolds and such. It only uses discrete entities and maybe rational numbers as in discrete probability theory?

upd: by discrete I meant countable.