Quantum Computing: 1-Way Quantum Automata

In 1980, Russian mathematician Yuri Manin published Computable and Uncomputable. On pages 14 and 15 of his introduction, Manin suggests that “Molecular biology furnishes examples of the behavior of natural (not engineered by humans) systems which we have to describe in terms initially devised for discrete automata.” Manin then describes the remarkable energy efficiency of naturally occurring biomolecular processes such as DNA replication. He proposes modeling such behaviors in terms of unitary rotations in a finite-dimensional Hilbert space. The decomposition of such systems then corresponds to the tensor product decomposition of the state space, that is, to quantum entanglement. Manin’s initial focus on biological molecules as examples of highly energy-efficient quantum automata is unique among quantum computing’s founding figures since both he and other early leaders quickly moved to the then-new and exciting concept of von Neumann automata. The von Neumann formalism reinterpreted molecular quantum computing in terms of qubits, which made it possible to imagine the power of quantum computing as not much more than a superposition of virtual binary computers. This paper provides the original excerpt of Manin’s molecular computing argument. A useful analytical feature of Manin’s pre-von-Neumann model of quantum computation is its openness to new formalisms that avoid accidentally making classical physics dominant over the quantum world by expressing quantum states only in terms of concepts such as automata that assume extreme classical precision and complexity.

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Discrete variable gate-model quantum computing

10.32388/262483 ◽

2019 ◽

Author(s):

Mark Fingerhuth ◽

Tomáš Babej ◽

Peter Wittek

Keyword(s):

Quantum Computing ◽

Discrete Variable

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Surface code quantum computing

Physics Subject Headings (PhySH) ◽

10.29172/7afc8a46-4a16-4509-8db6-2bfa23521cc4 ◽

2018 ◽

Keyword(s):

Quantum Computing ◽

Surface Code

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The Essence of Quantum Computing

10.34048/2018.1.f1 ◽

2018 ◽

Author(s):

Rajendra K. Bera

Keyword(s):

Hilbert Space ◽

Quantum Computing ◽

Quantum Physics ◽

Quantum Algorithms ◽

Quantum Computers ◽

Turing Machines ◽

Classical Physics ◽

Core Set ◽

The World ◽

Subordinate Role

It now appears that quantum computers are poised to enter the world of computing and establish its dominance, especially, in the cloud. Turing machines (classical computers) tied to the laws of classical physics will not vanish from our lives but begin to play a subordinate role to quantum computers tied to the enigmatic laws of quantum physics that deal with such non-intuitive phenomena as superposition, entanglement, collapse of the wave function, and teleportation, all occurring in Hilbert space. The aim of this 3-part paper is to introduce the readers to a core set of quantum algorithms based on the postulates of quantum mechanics, and reveal the amazing power of quantum computing.

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