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Quantum Computing since Democritus by Scott Aaronson

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13 Proofs

We're going to start by beating a retreat from QuantumLand, back onto the safe territory of computational complexity. In particular, we're going to see how, in the 1980s and 1990s, computational complexity theory reinvented the millennia-old concept of mathematical proof – making it probabilistic, interactive, and cryptographic. But then, having fashioned our new pruning-hooks (proving-hooks?), we're going to return to QuantumLand and reap the harvest. In particular, I’ll show you why, if you could see the entire trajectory of a hidden variable, then you could efficiently solve any problem that admits a “statistical zero-knowledge proof protocol,” including problems like Graph Isomorphism for which no efficient quantum algorithm is yet ...

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