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As far as we know, yes. This is essentially the Church-Turing thesis. Note that this is not a mathematical result, but more of a definition of what it means to be computable. You can find plenty of discussions about this around. A few notable examples are: What would it mean to disprove Church-Turing thesis? (on cstheory) Extended Church-Turing Thesis [and ...


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I will address the first two parts based on what I understood so far. The extended Church–Turing thesis or (classical) complexity-theoretic Church–Turing thesis states that "A probabilistic Turing machine can efficiently simulate any realistic model of computation.", whereas the quantum extended Church–Turing thesis or quantum complexity-theoretic ...


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Taking the questions head on. I'm not sure that original references are very much the point, although there are some. It's not a hard question. The statement is that realistic polynomial time equals what a quantum computer (if you want to be rigorous, say a QTM) can do in polynomial time. The question has been answered many times in QCSE that a quantum ...


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do we need to come up with completely different quantum-based solutions for such problems, or is there a way to 'interpret' existing algorithms to the quantum domain and still expect some speedup? Generally speaking yes, you need to come up with different algorithms. You cannot simply take a classical algorithm and "quantize it" in a straightforward way. ...


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There is evidence that quantum coherence and it's role in chemical reactivity is responsible for the magnetic field sensing in migratory birds, the so called avian compass, https://arxiv.org/abs/1206.5946v1. Similar quantum effects and chemistry could very well be occuring and playing a role in the brain, though as far as I know there isn't anything ...


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As far as we know - and I know, so correct me anyone if there's research to the contrary - the neuron interactions in the brain are well within the classical regime. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5681944/


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The reason that a quantum computer is faster in same tasks is given by different computational paradigm based on quantum mechanics laws. They mainly exploit superposition (i.e. state of qubit is linear combination of zero state and one state) and quantum entanglement (i.e. two or more qubits are connected and they behave as one system, or in other words ...


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Regarding the "quantum (non-extended) Church-Turing Thesis," I think this asserts that there is no physical process, like a quasar or some other astronomical woo, that we know could produce a steady supply of qubits all in the same state $\alpha|0\rangle+\beta|1\rangle$, with the property that $\beta^2=\Omega_C$, that is, Chaitin's halting probability. We ...


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Suppose we are given the ($n\times n$ adjacency matrix $M_0$ of graph $G_0$ and $M_1$ of graph $G_1$, and we wish to know whether $G_0\simeq G_1$. It is a folklore result that if we can prepare states: $$\vert\alpha_G\rangle=\sum\limits_{\sigma\in S_n}\vert \sigma (G)\rangle,$$ with $S_n$ being the symmetric group on $n$ elements, we can prepare such a ...


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