SearcharxivSearch

arXiv · 2112.00006

Towards algorithm-free physical equilibrium model of computing

Abstract

Our computers today, from sophisticated servers to small smartphones, operate based on the same computing model, which requires running a sequence of discrete instructions, specified as an algorithm. This sequential computing paradigm has not yet led to a fast algorithm for an NP-complete problem despite numerous attempts over the past half a century. Unfortunately, even after the introduction of quantum mechanics to the world of computing, we still followed a similar sequential paradigm, which has not yet helped us obtain such an algorithm either. Here a completely different model of computing is proposed to replace the sequential paradigm of algorithms with inherent parallelism of physical processes. Using the proposed model, instead of writing algorithms to solve NP-complete problems, we construct physical systems whose equilibrium states correspond to the desired solutions and let them evolve to search for the solutions. The main requirements of the model are identified and quantum circuits are proposed for its potential implementation.

Explore related subjects

Keep this discovery

BibTeXRIS

Seyed Mousavi. 2021-11-30. Towards algorithm-free physical equilibrium model of computing. https://doi.org/10.26421/qic21.15-16-3

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

The Computational Complexity of Holant Problems on 4-regular Graphs from the Stable Subgroup Sequence of $SL(2,\mathbb{C})$

The Holant framework provides a general setting for studying counting problems and includes graph homomorphisms (\#GH) and counting constraint satisfaction problems (\#CSP) as special cases. Over the past twenty years, a series of computational complexity dichotomies have been established for Holant problems, but the classification for complex-valued signatures is still open. The main obstacle is the case in which all signatures have even arity. In this paper, we establish a dichotomy for Holant problems with a complex-valued 4-ary signature, which is a key base case for the full classification of Holant problems. We present a new strategy by introducing Schur's theorem, the classification of finite subgroups of $\mathrm{SL}(2,\mathbb{C})$ and stable subgroup sequences into the proof. These new techniques are of independent interest.

cs.CC

Topology inside NC$^1$

We show that ACC$^0$ is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC$^0$. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing number and thickness. We show that constant-width circuits of polynomial size and thickness two already suffice to capture all of NC$^1$.

cs.CC