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Suppose I posses quantum computer, which can reverse SHA256 in one microsecond. The only thing I want then -- is to mine one block. After that I will throw away my computer and go to Hawaii.

Hence the question is: how to get current block from Bitcoin network, and how to send my work back to it?

May be there are some linux commands like

downloadcurrentblock > data.dat

upploadresults < data2.dat

I need something maximally simple to do exactly this: receive input information and send output information.

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Mining software and a wallet do this for you.
Of course you would have to modify the software, so instead of repeating hashing you just submit your solution.
Nothing currently exists that is ready for your scenario.

Also, have a look at these two bitcoin RPC calls:

getblocktemplate
submitblock "hexdata"

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