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Approximating the Tutte polynomial
Published in Joanna A. Ellis-Monaghan, Iain Moffatt, Handbook of the Tutte Polynomial and Related Topics, 2022
It follows that an ability to additively approximate T(G;e−2πi/5,e−2πi/5), with a suitable normalization, is sufficient to simulate any quantum computation. Bordewich et al. [177] gave a number of elementary additive approximations for Tutte evaluations, and asked whether the evaluation of T(G;e−2πi/5,e−2πi/5) had a suitable additive approximation, which would amount to a simulation of a BQP-complete problem. For a precise statement see [177]. BQP (bounded error quantum polynomial time) is the complexity class of decision problems solvable by a quantum computer in polynomial time with bounded error. It is analogous to the classical complexity class BPP; for further information see [100].
Fault tolerance and ultimate physical limits of nanocomputation
Published in David Crawley, Konstantin Nikolić, Michael Forshaw, 3D Nanoelectronic Computer Architecture and Implementation, 2020
A S Sadek, K Nikolić, M Forshaw
If a computation can be solved in polynomial time, then it is classified as belonging to the complexity class P. This complexity class is thought to be a subset of a larger class of decisional problems NP, where the solution requires additional information in the form of a certificate (factoring is an example of such a problem). P and NP are classes of deterministic algorithms, which means they perform the same set of operations every time they are executed on the same input. Once noise becomes a factor (i.e. ϵ > 0), such algorithms are no longer deterministic but random. Such random algorithms, implemented by design or as a result of noise, are part of the greater complexity class BPP (bounded-probabilistic polynomial time). The noise-tolerant architectures that we will explore for nanocomputation will necessarily belong to this complexity class. A corresponding class exists encompassing fault tolerant quantum computation called BQP.
Leveraging the power of quantum computing for breaking RSA encryption
Published in Cyber-Physical Systems, 2021
Moolchand Sharma, Vikas Choudhary, R. S. Bhatia, Sahil Malik, Anshuman Raina, Harshit Khandelwal
The class of issues that may be efficiently resolved by QCs is named BQP, which stands for “bounded error, quantum, and polynomial time.” Since QCs only run probabilistic algorithms, thus BPP (which stands for bounded error, probabilistic, polynomial time) for classical computers in the counterpart of BQP for quantum computers. It is outlined because of the set of issues soluble with a polynomial-time formula, whose likelihood of error is finite far from one-half, as shown below in Figure 8.