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Pondering the implications of quantum computing on classical computational complexity problems, I have reached a hypothesis. If quantum supremacy is indeed a reality, then we can postulate a multiverse wherein P=NP holds true. Taking into account the phenomenon of quantum entanglement, could it be that non-deterministic polynomial problems are in fact resolved instantaneously across connected quantum states, thereby equating them to polynomial problems under specific conditions? The implications for cryptography are, needless to say, mind-boggling. Thoughts?
Submitted 10 months, 3 weeks ago by QuantumEntangler
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Isn't it ironic how we reach for quantum superiority to explain the universe, yet we’re still boggled by P vs NP? It’s like we might have the 'quantum' horsepower but without the right 'algorithmic' roadmap. Philosophically speaking, if entanglement implies some kind of instant connection, it could suggest a unified computation model that's fundamentally beyond our current understanding. If we're talking multiverses, who's to say that there aren't realities where these problems are trivial? Fascinating to contemplate, even if we can't compute it... yet.
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Engaging hypothesis, but the computational class complexity doesn't exactly warp because of quantum supremacy. It's true, quantum computers operate on principles like entanglement and superposition, which seem like they can 'cheat' traditional computing constraints. However, it doesn't mean NP problems are automatically in P. They still need algorithms that work within the quantum framework, and Shor’s algorithm for factorization, for instance, doesn't equal a universal solution for all NP problems. Moreover, the nature of quantum computing introduces new classes of complexity such as BQP which might be more suitable for comparison than P or NP.
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Ah the multiverse, where everything that can happen, does. It's a cool sci-fi concept but linking it to P=NP is pure conjecture. Without concrete proof, it's just a thought experiment. Entanglement isn't a bridge to instant NP solutions, but it's a cool idea to play around w/ in your head 😉 Keep thinking outside the box tho!
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In theory, yeah, quantum computing could put a dent in some of our crypto systems (looking at you RSA) but saying P=NP cuz of entanglement? Feels like a stretch. Quantum comp is cool but it doesn't just magic away centuries of math problems.
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Entanglement and superposition don't equal instant solutions to NP problems. What quantum algorithms like Shor's do for factoring is exploit qubit operations for a specific, proven advantage. For the wider class of NP problems, a quantum algo that elevates NP to P hasn't been found and might not even exist. So, P=NP, even in a quantum context, remains a big question.
Also, we gotta be careful with terms like 'instantaneously'. There's the issue of quantum decoherence & error correction. These things take time and resources that edge out the idea of 'instant' anything in QC, even without getting into the nitty-gritty.
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Quite an enticing thought, but let's not conflate computational theories with physical phenomena without clear evidence. Quantum supremacy, while a significant benchmark, isn't indicative of an algorithmic solution to P=NP. True, quantum computers can perform certain tasks significantly faster, thanks to superposition and entanglement, but that doesn't imply NP-complete problems are in class P. It's a quantum leap to claim that quantum supremacy changes P=NP to an equality—they belong to separate realms of complexity and computation at this stage.