What is the correct picture of our world? Are noise and errors part of the essence of matters, and the beautiful perfect patterns we see around us, as well as the notions of information and computation, are just derived concepts in a noisy world? Or do noise and errors just express our imperfect perception of otherwise perfect laws of nature? Talking about an inherently noisy reality may well reflect a better understanding across various scales and areas.
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While reading Gregory Chaitin’s MetaMath I jotted down some notes:
“Randomness is irreducible, incompressible.
Pattern stems from a subset of randomness.”
I’d consider noise as a subset of randomness containing compressible pattern. As for errors: some – like the halting problem – are unpredictable.
I note that you and most people use laws (plural) of nature.
For laws to be perfect, predictable and without error, I’ve been wondering if that implies irreducibility hence randomness.
Irreducible laws of nature.
I somehow feel happy with this answer, despite the paradox it implies.
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“Are noise and errors part of the essence of matters, and the beautiful perfect patterns we see around us, as well as the notions of information and computation, are just derived concepts in a noisy world? Or do noise and errors just express our imperfect perception of otherwise perfect laws of nature?”
I hate to have to choose. Perhaps it can be both.
Gil,
A bit off topic, but have you seen:
Phys. Rev. A 79, 012332 (2009)
Fibonacci scheme for fault-tolerant quantum computation
by Panos Aliferis and John Preskill?
Given your skepticism regarding error correction in connection with Quantum Computation (I believe my assumption is correct), I was curious what you thought of the article.
Dear Michael, fualt-tolerance quantum computation is based on a remarkable theorem called the “threshold theorem” which was proved by several groups of researchers in the mid 90s. Since then there have been significant progress in extending the scope of the theorem in terms of the type of noise it can handle, and reducing the numerical value of the threshold.
A breakthrough work by Knill uses error-detection codes rather than error-correction codes and massive post-selection. This allows one to raise the value of the threshold (based on numerical simulations) to 0.03 or so. This idea also leads to a substantially higher provable bounds and there are several papers, including I believe the one you cited, that demonstrate it. This is an exciting direction.
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