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Sanchayan Dutta
Sanchayan Dutta
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Sanchayan Dutta
Sanchayan Dutta
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What exactly is meant by "noise" in the following context?

The strengthened version of the Church-Turing thesis states that:

Any algorithmic process can be simulated efficiently using a Turing machine.

Now, on page 5 (chapter 1), the book Quantum Computation and Quantum Information: 10th Anniversary Edition By Michael A. Nielsen, Isaac L. Chuang goes on to say that:

One class of challenge to the the strong Church Turing thesis comes from the field of analog computation. In the years since Turing, many different teams of researchers have noticed that certain types of analog computers can efficiently solve problems believed to have no efficient solution on a Turing machine. At the first glance these analog computers appear to violate the strong form of the Church-Turing thesis. Unfortunately for analog computation it turns out that when realistic assumptions about the presence of noise in analog computers are made, their power disappears in all known instances; they cannot efficiently solve problems which are not solvable on a Turing machine. This lesson – that the effects of realistic noise must be taken into account in evaluating the efficiency of a computational model – was one of the great early challenges of quantum computation and quantum information, a challenge successfully met by the development of a theory of quantum error-correcting codes and fault-tolerant quantum computation. Thus, unlike analog computation, quantum computation can in principle tolerate a finite amount of noise and still retain its computational advantages.

What exactly is meant by noise in this context? Do they mean thermal noise? It's strange that the authors did not define or clarify what they mean by noise in the previous pages of the textbook.

I was wondering if they were referring to noise in a more generalized setting. Like, even if we get rid of the conventional noise - like industrial noise, vibrational noise, thermal noise (or reduce them to negligible levels), noise could still refer to the uncertainties in amplitude, phase, etc, which arise due to the underlying quantum mechanical nature of the system.