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arXiv:1110.3190 · Physics in Perspective

Quantum Computing: Theoretical versus Practical Possibility

Gheorghe Sorin Paraoanu

Published Aug 11, 2011• 10 citations
arXivHTMLPDF
DOI
10.1007/s00016-011-0057-6

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An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is possible in principle—there are no known laws of Nature that prevent it—yet scaling up the few qubits demonstrated so far has proven to be exceedingly difficult. While this could be regarded merely as a technological or practical impediment, I argue that this difficulty might be a symptom of new laws of physics waiting to be discovered. I distinguish between ‘‘strong’’ and ‘‘weak’’ emergentist positions. The former assumes that a critical value of a parameter exists (one that is most likely related to the complexity of the states involved) at which the quantum-mechanical description breaks down, in other words, that quantum mechanics will turn out to be an incomplete description of reality. The latter assumes that quantum mechanics will remain as a universally valid theory, but that the classical resources required to build a real quantum computer scale up with the number of qubits, which hints that a limiting principle is at work.

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An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is possible in principle—there are no known laws of Nature that prevent it—yet scaling up the few qubits demonstrated so far has proven to be exceedingly difficult. While this could be regarded merely as a technological or practical impediment, I argue that this difficulty might be a symptom of new laws of physics waiting to be discovered. I distinguish between ‘‘strong’’ and ‘‘weak’’ emergentist positions. The former assumes that a critical value of a parameter exists (one that is most likely related to the complexity of the states involved) at which the quantum-mechanical description breaks down, in other words, that quantum mechanics will turn out to be an incomplete description of reality. The latter assumes that quantum mechanics will remain as a universally valid theory, but that the classical resources required to build a real quantum computer scale up with the number of qubits, which hints that a limiting principle is at work.
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The evolution of quantum computing poses a profound challenge to traditional cryptographic systems based on number-theoretic assumptions such as integer factorization and discrete logarithms. This paper presents a comparative analysis between lattice-based and group-theoretic cryptographic schemes, two promising post-quantum approaches. The study highlights their mathematical foundations, underlying hardness assumptions, and operational principles. Furthermore, practical examples such as NewHope and Ko–Lee key exchange protocols are examined to illustrate the working mechanisms of both paradigms. The findings indicate that lattice-based cryptography demonstrates superior quantum resistance, efficiency, and standardization potential, whereas group-theoretic cryptography remains primarily theoretical but offers fertile ground for future innovations.