arXiv subjects

M. H. Zarei

Publications and source records attributed to M. H. Zarei.

5 recordsLinked to original sources

arXiv2026

`It from Bit': is there a second law of quantum complexity?

At a deeper level the principle of least action is interpreted as the law of least entropy increase consistent with Prigogine's principle of minimum entropy production, and the implications of quasistatic information quantization rule (Proc. R. Soc. A 480: 20240024), are explored for the conjectured second law of quantum complexity. It is thus shown that the conjectured second law of complexity is derivable from the information quantization rule such that long after heat-death the quantum state complexity evolves as $C(t)=C_{\rm max}\exp(-1/t)$, increasing with time to a saturation value $C_{\rm max}$ that is exponential in the equilibrium entropy $S_{\rm max}$. For the out-of-equilibrium circumstances, however, the quantum complexity can decrease with the time, asymptotically tending to a minimum determined by the distance from equilibrium.

quant-ph↗

arXiv2024

"IT FROM BIT": How does information shape the structures in the universe?

Based on a synthesis of three main ingredients: (i) the Shannon information in nonequilibrium systems, (ii) the semiclassical energy-time quantization rule, and (iii) the quasistatic information-energy correspondence, a new general rule for the quantization of quasistatic information states supported by an environment away from equilibrium is introduced if the history of the environment is known as a function of time in terms of its thermodynamic potential for information $T(t)ΔS(t)$ that is a free energy measuring the distance from equilibrium $ΔS(t)$, and $T(t)$ is the mean temperature of the environment at time $t$. This all new quasistatic information-time quantization rule is applied to the expanding universe using a phenomenological thermodynamic potential for information in the matter dominated era in order to find the eigen-informations of the persistent structures that are supported by the universe (or the local environments therein) at any given epoch, thus providing an information-theoretic foundation for formation of structures and rise of complexity with time that embodies the cosmic evolution as epitomized by the late Wheeler's famous conjecture ``{\it it from bit}". This theoretical procedure must also open new avenues for further research into the quantum theory of information and complexity in nonequilibrium thermodynamics.

cond-mat.stat-mech↗

arXiv2023

Partially topological phase in a quantum loop gas model with tension and pressure

Enhancing robustness of topological orders against perturbations is one of the main goals in topological quantum computing. Since the kinetic of excitations is in conflict with the robustness of topological orders, any mechanism that reduces the mobility of excitations will be in favor of robustness. A strategy in this direction is adding frustration to topological systems. In this paper we consider a frustrated toric code on a kagome lattice, and show that although increasing the strength of perturbation reduces the topological order of the system, it cannot destroy it completely. Our frustrated toric code is indeed a quantum loop gas model with string tension and pressure which their competition leads to a partially topological phase (PTP) in which the excitations are restricted to move in particular sublattices. In this phase the ground state is a product of many copies of fluctuating loop states corresponding to quasi one dimensional ladders. By defining a non-local matrix order parameter and studying the behavior of ground state global entanglement (GE), we distinguish the PTP from the standard topological phase. The partial mobility of excitations in our system is a reminiscent of fracton codes with restricted mobility, and therefore our results propose an alternative way for making such a restriction in three dimension.

cond-mat.str-el↗

arXiv2021

Topological line in frustrated Toric code models

Typical topological systems undergo a topological phase transition in the presence of a strong enough perturbation. In this paper, we propose an adjustable frustrated Toric code with a "topological line" at which no phase transition happens in the system and the topological order is robust against a non-linear perturbation of arbitrary strength. This important result is a consequence of the interplay between frustration and nonlinearity in our system, which also causes to the emergence of other interesting phenomena such as reentrant topological phases and survival of the topological order under local projection operations. Our study opens a new window towards more robust topological quantum codes which are cornerstones of large-scale quantum computing.

cond-mat.str-el↗

arXiv2012

An algorithmic proof for the completeness of two-dimensional Ising model

We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all its spin-spin coupling equal to iπ/4 and all the parameters of the original model are contained in the local magnetic fields of the Ising model. This result has already been derived by using techniques from quantum information theory and by exploiting the universality of cluster states. Here we do not use the quantum formalism and hence make the completeness result accessible to a wide audience. Furthermore our method has the advantage of being algorithmic in nature so that by following a set of simple graphical transformations, one is able to transform any discrete lattice model to an Ising model defined on a (polynomially) larger 2D lattice.

quant-ph↗