my bidhday 2 day :| /s4s/ saved my life

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Congraz!!1!1!!

Happy birthday! I hope cool stuff happens to you today and always!

>>4619467
>>4619533
Thnx fam!

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88KB, 456x810px

>>4619235
Happy Birthday!

Here's some clown poop on your birthday cake.

Enjoy!

>>4619833
It's time to stop. I've seen this shit on r9k and s4s for far too long

>>4619235
Path integration has numerous applications including quantum mechanics, quantum chemistry, statistical mechanics, and computational finance. We want to compute an approximation to within error at most ε {\displaystyle \scriptstyle \varepsilon } \scriptstyle \varepsilon with probability, say, at least 3/4. Then the following was shown by Traub and Woźniakowski:

A quantum computer enjoys exponential speedup over the classical worst case and quadratic speedup over the classical randomized case.
The query complexity is of order ε − 1 {\displaystyle \scriptstyle \varepsilon ^{-1}} \scriptstyle\varepsilon^{-1}.
The qubit complexity is of order ε − 2 log ε − 1 {\displaystyle \scriptstyle \varepsilon ^{-2}\log \varepsilon ^{-1}} \scriptstyle\varepsilon^{-2}\log\varepsilon^{-1}.

Thus the qubit complexity of path integration is a second degree polynomial in ε − 1 {\displaystyle \scriptstyle \varepsilon ^{-1}} \scriptstyle\varepsilon^{-1}. That seems pretty good but we probably won't have enough qubits for a long time to do new science especially with error correction. Since this is a complexity result we can't do better by inventing a clever new algorithm. But perhaps we can do better by slightly modifying the queries.

In the standard model of quantum computation the probabilistic nature of quantum computation enters only through measurement; the queries are deterministic. In analogy with classical Monte Carlo Woźniakowski introduced the idea of a quantum setting with randomized queries. He showed that in this setting the qubit complexity is of order log ε − 1 {\displaystyle \scriptstyle \log \varepsilon ^{-1}} \scriptstyle \log\varepsilon^{-1}, thus achieving an exponential improvement over the qubit complexity in the standard quantum computing setting.

>>4619833
LOL

hapy bitdae

>>4620247
Thnx

>>4619235
Happy bday Jacques! Are you related to Gippo by chance?

>>4620309
Thnx
No, I'm not a Gippo Dudean
Lol