If it start solving hashes that would be a problem to the double spending feature of Bitcoin
No, it woudn't, because then miners would also start mining using QCs. Difficulty would skyrocket, ASICs would go to scrapyards and network would continue to be secure - you'd still need more compute power to make a 51% attack and double-spend.
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That would require all miners to buy a bunch of QCs. Maybe they won't be available that fast to everyone.
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