arXiv subjects

A. C. Manoharan

Publications and source records attributed to A. C. Manoharan.

3 recordsLinked to original sources

arXiv2003

Beyond Quantum Computation and Towards Quantum Field Computation

Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum theory of the gravitational field, and are far from a practical implementation of a quantum field computer, some pieces of the puzzle (without gravity) are now available. We consider a general model for computation with quantum field theory, and obtain some results for relativistic quantum computation. Moreover, it is possible to see new connections between principal models of computation, namely, computation over the continuum and computation over the integers (Turing computation). Thus we identify a basic problem in QFT, namely Wightman's computation problem for domains of holomorphy, which we call WHOLO. Inspired by the same analytic functions which are central to the famous CPT theorem of QFT, it is possible to obtain a computational complexity structure for QFT and shed new light on certain complexity classes for this problem WHOLO.

quant-ph↗

arXiv2001

The unity between quantum field computation, real computation, and quantum computation

It is indicated that principal models of computation are indeed significantly related. The quantum field computation model contains the quantum computation model of Feynman. (The term "quantum field computer" was used by Freedman.) Quantum field computation (as enhanced by Wightman's model of quantum field theory) involves computation over the continuum which is remarkably related to the real computation model of Smale. The latter model was established as a generalization of Turing computation. All this is not surprising since it is well known that the physics of quantum field theory (which includes Einstein's special relativity) contains quantum mechanics which in turn contains classical mechanics. The unity of these computing models, which seem to have grown largely independently, could shed new light into questions of computational complexity, into the central P (Polynomial time) versus NP (Non-deterministic Polynomial time) problem of computer science, and also into the description of Nature by fundamental physics theories.

quant-ph↗

arXiv2000

Quantum Field Symbolic Analog Computation: Relativity Model

It is natural to consider a quantum system in the continuum limit of space-time configuration. Incorporating also, Einstein's special relativity, leads to the quantum theory of fields. Non-relativistic quantum mechanics and classical mechanics are special cases. By studying vacuum expectation values (Wightman functions W(n; z) where z denotes the set of n complex variables) of products of quantum field operators in a separable Hilbert space, one is led to computation of holomorphy domains for these functions over the space of several complex variables, C^n. Quantum fields were reconstructed from these functions by Wightman. Computer automation has been accomplished as deterministic exact analog computation (computation over "cells" in the continuum of C^n) for obtaining primitive extended tube domains of holomorphy. This is done in a one dimensional space plus one dimensional time model. By considering boundary related semi-algebraic sets, some analytic extensions of these domains are obtained by non-deterministic methods. The novel methods of computation raise interesting issues of computability and complexity. Moreover, the computation is independent of any particular form of Lagrangian or dynamics, and is uniform in n, qualifying for a universal quantum machine over C^infinity.

quant-ph↗