arXiv subjects

Mohammad Hossein Zarei

Publications and source records attributed to Mohammad Hossein Zarei.

At least 19 recordsLinked to original sources

arXiv2026

Resources of the advantage in quantum illumination: Discord and entanglement

We investigate how the quantum advantage in quantum illumination is determined by an interplay between entanglement and discord of the probe state. In particular, we consider a setup in which the probe is a maximally mixed marginal (MMM) state and the environmental state is completely mixed where the quantum advantage equals the amount of discord consumed for illumination. Through a conditional extremal analysis, we determine the range of accessible advantages for given values of entanglement and discord. At fixed discord, high entanglement restricts the accessible advantage to high values, making high entanglement sufficient for high advantage. Conversely, at fixed entanglement, low discord limits the advantage to low values, indicating that high discord is necessary for high advantage. These conclusions remain unchanged when alternative correlation measures, including relative entropy and Bures entanglement and geometric discord, are used. The consistency of our results across multiple conceptually distinct measures indicates that the observed resource-advantage relation is not an artifact of a specific quantifier, but a robust feature of the protocol within the family of MMM states. We finally find that in the high-noise regime (near-maximally-mixed state), quantum advantage is, to leading order, a linear function of the initial discord highlighting discord as the key resource for resilience to noise in the protocol.

quant-ph↗

arXiv2026

Shot-based variational simulation of the toric code phase transition: Energy, global entanglement, and noise resilience

We investigate the capability of variational quantum circuits in detecting a topological phase transition within the toric code model subjected to a uniform magnetic field. The detection is carried out via shot-based computations of both the ground state energy and the global entanglement. We begin by employing well-established renormalization techniques to construct a quantum circuit that accurately represents the pure toric code under periodic boundary condition. This circuit is subsequently parameterized to enable a shot-based variational simulation of the ground state in the presence of the magnetic field. Our results demonstrate that even for the minimal lattice sizes and a finite number of measurement shots, the ground state energy exhibits a distinct singularity at the transition point which can be reliably approximated through finite-size scaling analysis. Furthermore, we introduce a secondary variational circuit designed to compute the global entanglement of the generated ground state. We observe that both global entanglement and its conditional counterpart display the expected qualitative behavior at the transition point, consistent with the topological nature of the phase transition. To evaluate the practical viability of our variational approach on real quantum hardware, we systematically examine the detrimental effects of gate noise on the analysis. We find that the topological phase exhibits a notable robustness against noise, manifesting as a linear decrease in the transition point with increasing noise strength.

quant-ph↗

arXiv2026

Spin stiffness and resilience phase transition in a noisy toric-rotor code

We use a quantum formalism for the partition function of the classical $XY$ model to identify a resilience phase transition in the zero-syndrome postselected sector of a noisy toric-rotor code. To this end, we consider a logical state of toric-rotor code under phase-shift noise described by a von Mises probability distribution. We then show that the fidelity of the noisy state with respect to the initial logical state is proportional to the partition function of the $XY$ model, such that a Kosterlitz-Thouless phase transition at a critical temperature $T_c$ corresponds to a resilience phase transition at a critical width $σ_c$. To characterize this transition, we map the spin stiffness of the $XY$ model to a topological order parameter $0\leq λ\leq 1$, which quantifies the intrinsic resilience of the code to decoherence within the zero-syndrome subspace. We show that the initial logical state exhibits partial resilience to noise for widths less than $σ_c \approx 0.89$, where $λ$ satisfies $0< λ<1$ and drops discontinuously to zero at $σ_c$. We further discuss the implications of our results for postselected quantum error correction in the toric-rotor code in higher dimensions. Our work shows that the quantum formalism for partition functions provides a mathematically rigorous framework for studying noisy continuous-variable quantum codes.

quant-ph↗

arXiv2025

Universal representation of the long-range entanglement in the family of Toric Code states

Since the long range entanglement is a universal characteristic of topological quantum states belonging to the same class, a suitable mathematical representation of the long range entanglement has to be also universal. In this Letter, we introduce such a representation for the family of Toric Code states by using Kitaev's Ladders as building blocks. We consider Toric Code states corresponding to various planar graphs and apply non-local dientanglers to qubits corresponding to non-contractible cycles that satisfy a topological constraint. We demonstrate that, independent of the geometry of the underlying graph, disentanglers convert Toric Code states into a tensor product of Kitaev's Ladder states. Since Kitaev's Ladders with arbitrary geometric configurations include the short-range entanglements, we conclude that the above universal and non-local pattern of entanglement between ladders is responsible of the long-range entanglement inherent in Toric Code states. Our result emphasizes in the capability of such non-local representations to describe topological order in ground-state wave functions of topological quantum systems.

quant-ph↗

arXiv2025

Partial Anyon Condensation in the Color Code: A Hamiltonian Approach

Lattice Hamiltonians, which can be tuned between different topological phases, are known as important tools for understanding physical mechanism behind topological phase transitions. In this paper, we introduce a perturbed Color Code Hamiltonian with a rich phase structure which can be well matched to the mechanism of anyon condensation in the Color Code. We consider Color Code model defined on a three-colorable hexagonal lattice and add Ising interactions between spins corresponding to edges of the lattice. We show that Ising interactions play the role of physical factor for condensing anyons in the Color Code. In particular, corresponding to three different colors of edges in the hexagonal lattice, we consider three different coupling parameters. Then, we are able to condense anyons with different colors by tuning power of Ising interactions in the corresponding edges. In particular, we explicitly show that condensation of one type of anyons in the Color Code leads to a phase transition to the Toric Code state. On the other hand, by condensing two types of anyons, we observe a phase transition to a modified version of the Toric Code where partial set of anyons in the Toric Code are condensed and we call it a partially topological phase. Our main method for derivation of the above results is based on a suitable basis transformation on the main Hamiltonian in the sense that our model is mapped onto three decoupled transverse-field Ising models, corresponding to the three colors. We use the above mapping to analyze behavior of string order parameters as non-local indicators of topological order. We introduce three string order parameters that can well characterize different phases of the model. Specifically we give a simple description of the partially condensed phase by using string order parameters.

quant-ph↗

arXiv2023

Layer-by-layer disentangling two-dimensional topological quantum codes

While local unitary transformations are used for identifying quantum states which are in the same topological class, non-local unitary transformations are also important for studying the transition between different topological classes. In particular, it is an important task to find suitable non-local transformations that systematically sweep different topological classes. Here, regarding the role of dimension in the topological classes, we introduce partially local unitary transformations namely Greenberger-Horne-Zeilinger (GHZ) disentanglers which reduce the dimension of the initial topological model by a layer-by-layer disentangling mechanism. We apply such disentanglers to two-dimensional (2D) topological quantum codes and show that they are converted to many copies of Kitaev's ladders. It implies that the GHZ disentangler causes a transition from an intrinsic topological phase to a symmetry-protected topological phase. Then, we show that while Kitaev's ladders are building blocks of both color code and toric code, there are different patterns of entangling ladders in 2D color code and toric code. It shows that different topological features of these topological codes are reflected in different patterns of entangling ladders. In this regard, we propose that the layer-by-layer disentangling mechanism can be used as a systematic method for classification of topological orders based on finding different patterns of the long-range entanglement in topological lattice models.

quant-ph↗

arXiv2023

Conditional global entanglement in a Kosterlitz-Thouless quantum phase transition

Entanglement is known as an important indicator for characterizing different types of quantum phase transitions (QPTs), however it faces some challenges in the Kosterlitz-Thouless (KT) phase transitions due to an essential singularity which cannot be identified in finite derivatives of the ground state energy. In this paper, we consider global entanglement (GE) in a KT phase transition and show that while it does not indicate any clear signature of the phase transition, the conditional version of GE is a good indicator with strong signatures of the KT transition. In particular, we study a deformed version of the $Z_d$ Kitaev model which has an intermediate KT phase which separates a $Z_d$ topological phase from a magnetized phase at two different KT transition points. Using a mapping to the classical $d$-state clock model, we consider GE and the generalized GE and show that they do not provide a reliable indicator of transition points. However, their difference called conditional global entanglement (Q) shows a peak at the first KT transition point. Additionally, we show that it can characterize various phases of the model as it behaves substantially different in each phase. We therefore conclude that Q is a useful measure that can characterize various phases of KT QPTs as well as their related critical points.

quant-ph↗

arXiv2022

Foliated order parameter in a fracton phase transition

Finding suitable indicators for characterizing quantum phase transitions plays an important role in understanding different phases of matter. It is especially important for fracton phases where a combination of topology and fractionalization leads to exotic features not seen in other known quantum phases. In this paper, we consider the above problem by studying phase transition in the X-cube model in the presence of a non-linear perturbation. Using an analysis of the ground state fidelity and identifying a discontinuity in the global entanglement, we show there is a first order quantum phase transition from a type I fracton phase with a highly entangled nature to a magnetized phase. Accordingly, we conclude that the global entanglement, as a measure of the total quantum correlations in the ground state, can well capture certain features of fracton phase transitions. Then, we introduce a non-local order parameter in the form of a foliated operator which can characterize the above phase transition. We particularly show that such an order parameter has a geometric nature which captures specific differences of fracton phases with topological phases. Our study is specifically based on a well-known dual mapping to the classical plaquette Ising model where it shows the importance of such dualities in studying different quantum phases of matter.

quant-ph↗

arXiv2022

Global entanglement in a topological quantum phase transition

A useful approach to characterize and identify quantum phase transitions lies in the concept of multipartite entanglement. In this paper, we consider well-known measures of multipartite (global) entanglement, i.e., average linear entropy of one-qubit and two-qubit reduced density matrices, in order to study topological quantum phase transition (TQPT) in the Kitaev Toric code Hamiltonian with a nonlinear perturbation. We provide an $exact$ mapping from aforementioned measures in the above model to internal energy and energy-energy correlations in the classical Ising model. Accordingly, we find that the global entanglement shows a continuous and sharp transition from a maximum value in the topological phase to zero in the magnetized phase in a sense that its first-order derivative diverges at the transition point. In this regard, we conclude that not only can the global entanglement serve as a reasonable tool to probe quantum criticality at TQPTs, but it also can reveal the highly entangled nature of topological phases. Furthermore, we also introduce a conditional version of global entanglement which becomes maximum at the critical point. Therefore, regarding a general expectation that multipartite entanglement reaches maximum value at the critical point of quantum many-body systems, our result proposes that the conditional global entanglement can be a good measure of multipartite entanglement in TQPTs.

quant-ph↗

arXiv2020

Kosterlitz-Thouless phase and $Z_d$ topological quantum phase

It has been known that encoding Boltzmann weights of a classical spin model in amplitudes of a many-body wave function can provide quantum models whose phase structure is characterized by using classical phase transitions. In particular, such correspondence can lead to find new quantum phases corresponding to well-known classical phases. Here, we investigate this problem for Kosterlitz-Thouless (KT) phase in the d-state clock model where we find a corresponding quantum model constructed by applying a local invertible transformation on a d-level version of Kitaev's Toric code. In particular, we show the ground state fidelity in such quantum model is mapped to the heat capacity of the clock model. Accordingly, we identify an extended topological phase transition in our model in a sense that, for $d \geq 5$, a KT-like quantum phase emerges between a $Z_d$ topological phase and a trivial phase. Then, using a mapping to the correlation function in the clock model, we introduce a non-local (string) observable for the quantum model which exponentially decays in terms of distance between two endpoints of the corresponding string in the $Z_d$ topological phase while it shows a power law behavior in the KT-like phase. Finally, using well-known transition temperatures for d-state clock model we give evidences to show that while stability of both $Z_d$ topological phase and the KT-like phase increases by increasing d, the KT-like phase is even more stable than the $Z_d$ topological phase for large d.

quant-ph↗

arXiv2020

Classical criticality establishes quantum topological order

We establish an important duality correspondence between topological order in quantum many body systems and criticality in ferromagnetic classical spin systems. We show how such a correspondence leads to a classical and simple procedure for characterization of topological order in an important set of quantum entangled states, namely the Calderbank-Shor-Steane (CSS) states. To this end, we introduce a particular quantum Hamiltonian which allows us to consider the existence of a topological phase transition from quantum CSS states to a magnetized state. We study the ground state fidelity in order to find non-analyticity in the wave function as a signature of a topological phase transition. Since hypergraphs can be used to map any arbitrary CSS state to a classical spin model, we show that fidelity of the quantum model defined on a hypergraph $H$ is mapped to the heat capacity of the classical spin model defined on dual hypergraph $\tilde{H}$. Consequently, we show that a ferromagnetic-paramagnetic phase transition in a classical model is mapped to a topological phase transition in the corresponding quantum model. We also show that magnetization does not behave as a local order parameter at the transition point while the classical order parameter is mapped to a non-local measure on the quantum side, further indicating the non local nature of the transition. Our procedure not only opens the door for identification of topological phases via the existence of a local and classical quantity, i.e. critical point, but also offers the potential to classify various topological phases through the concept of universality in phase transitions.

quant-ph↗

arXiv2019

Noisy Toric code and random bond Ising model: The error threshold in a dual picture

It is known that noisy topological quantum codes are related to random bond Ising models where the order-disorder phase transition in the classical model is mapped to the error threshold of the corresponding topological code. On the other hand, there is a dual mapping between classical spin models and quantum Calderbank-Shor-Stean (CSS) states where the partition function of a classical model defined on a hypergraph $H$ is written as an inner product of a product state and a CSS state on dual hypergraph $\tilde{H}$. It is then interesting to see what is the interpretation of the classical phase transition in the random bond Ising model within the framework of the above duality and whether such an interpretation has any connection to the error threshold of the corresponding topological CSS code. In this paper, we consider the above duality relation specifically for a two-dimensional random bond Ising model. We show that the order parameter of this classical system is mapped to a coherence order parameter in a noisy Toric code model. In particular, a quantum phase transition from a coherent phase to a non-coherent phase occurs when the initial coherent state is affected by two sequences of bit-flip quantum channels where a quenched disorder is induced by measurement of the errors after the first channel. On the other hand, the above transition is directly related to error threshold of the Toric code model. Accordingly, and since the noisy process can be applied to other topological CSS states, we conclude that the dual correspondence can also provide a useful tool for the study of error thresholds in different topological CSS codes.

quant-ph↗

arXiv2019

Ising order parameter and topological phase transitions: Toric code in a uniform magnetic field

Quantum Ising model in a transverse field is of the simplest quantum many body systems used for studying universal properties of quantum phase transitions. Interestingly, it is well-known that such phase transitions can be mapped to topological phase transitions in Toric code models. Therefore, one can expect that well known properties of the transverse Ising model are used for characterizing topological phase transition in Toric code model. In this paper, we consider the magnetization of Ising model and show while it is a local order parameter, it is mapped to a non local order parameter in the topological side. Consequently, we introduce a string order parameter for topological phase transitions in Toric code models defined on different lattices with different dimensions in presence of a uniform magnetic field. Since such string order parameter is dual of the Ising order parameter with well known properties, it leads to a topological (non local) characterization of phase transition in the Toric code model in the uniform field. Our results show that although topological phase transitions do not follow a symmetry breaking mechanism, it might be still possible to use concepts of symmetry breaking phase transitions for topological ones by finding suitable mappings.

quant-ph↗

arXiv2019

Phase transition in a noisy Kitaev toric code model

It is well-known that the partition function of a classical spin model can be mapped to a quantum entangled state where some properties on one side can be used to find new properties on the other side. However, the consequences of the existence of a classical (critical) phase transition on the corresponding quantum state has been mostly ignored. This is particularly interesting since the classical partition function exhibits non-analytic behavior at the critical point and such behavior could have important consequences on the quantum side. In this paper, we consider this problem for an important example of Kitaev toric code model which has been shown to correspond to the two-dimensional (2D) Ising model though a duality transformation. Through such duality transformation, it is shown that the temperature on the classical side is mapped to bit-flip noise on the quantum side. It is then shown that a transition from a coherent superposition of a given quantum state to a non-coherent mixture corresponds exactly to paramagnetic-ferromagnetic phase transition in the Ising model. To identify such a transition further, we define an order parameter to characterize the decoherency of such a mixture and show that it behaves similar to the order parameter (magnetization) of 2D Ising model, a behavior that is interpreted as a robust coherency in the toric code model. Furthermore, we consider other properties of the noisy toric code model exactly at the critical point. We show that there is a relative stability to noise for the toric code state at the critical noise which is revealed by a relative reduction in susceptibility to noise. We close the paper with a discussion on connection between the robust coherency as well as the critical stability with topological order of the toric code model.

quant-ph↗

arXiv2018

Dual correspondence between classical spin models and quantum CSS states

The correspondence between classical spin models and quantum states has attracted much attention in recent years. However, it remains an open problem as to which specific spin model a given (well-known) quantum state maps to. In this Letter, we provide such an explicit correspondence for an important class of quantum states where a duality relation is proved between classical spin models and quantum Calderbank-Shor-Steane (CSS) states. In particular, we employ graph-theoretic methods to prove that the partition function of a classical spin model on a hypergraph $H$ is equal to the inner product of a product state with a quantum CSS state on a dual hypergraph $\tilde{H}$. We next use this dual correspondence to prove that the critical behavior of the classical system corresponds to a relative stability of the corresponding CSS state to bit-flip (and phase-flip) noise, thus called critical stability. We finally conjecture that such critical stability is related to the topological order in quantum CSS states, thus providing a possible practical characterization of such states.

quant-ph↗

arXiv2017

Systematic study of the completeness of two-dimensional classical $ϕ^4$ theory

The completeness of some classical statistical mechanical (SM) models is a recent result that has been developed by quantum formalism for the partition functions. In this paper, we consider a 2D classical $ϕ^4$ filed theory whose completeness has been proved in [V. Karimipour and et al, Phys. Rev. A 85, 032316]. We give a general systematic proof for the completeness of such a model where, by a few simple steps, we show how the partition function of an arbitrary classical field theory can be derived from a 2D classical $ϕ^4$ model. To this end, we start from various classical field theories containing models on arbitrary lattices and also $U(1)$ lattice gauge theories. Then we convert them to a new classical field model on a non-planar bipartite graph with imaginary kinetic terms. After that, we show that any polynomial function of the field in the corresponding Hamiltonian can approximately be converted to a $ϕ^4$ term by adding enough numbers of vertices to the bipartite graph. In the next step, we give a few graphical transformations to convert the final non-planar graph to a 2D rectangular lattice. We also show that the number of vertices which should be added grows polynomially with the number of vertices in the original model.

hep-lat↗

arXiv2017

A strong-weak coupling duality between two perturbed quantum many-body systems: CSS codes and Ising-like systems

Graphs and recently hypergraphs have been known as an important tool for considering different properties of quantum many-body systems. In this paper, we study a mapping between an important class of quantum systems namely quantum Calderbank-Shor-Steane (CSS) codes and Ising-like systems by using hypergraphs. We show that the Hamiltonian corresponding to a CSS code on a hypergraph $H$ which is perturbed by a uniform magnetic field is mapped to Hamiltonian of a Ising-like system on dual hypergraph $\tilde{H}$ in a transverse field. Interestingly, we show that a strong regime of couplings in one of the systems is mapped to a weak regime of couplings in another one. We also give some applications for such a mapping where we study robustness of different topological CSS codes against a uniform magnetic field including Kitaev's toric codes defined on graphs and color codes in different dimensions. We show that a perturbed Kitaev's toric code on an arbitrary graph is mapped to an Ising model in a transverse field on the same graph and a perturbed color code on a D-colex is mapped to a Ising-like model on a D-simplicial lattice in a transverse field. In particular, we use these results to explicitly compare the robustness of TC on different graphs in different dimensions. Interestingly, our results show that the robustness of such topological codes defined on graphs decreases with increasing dimension. Furthermore, we also use the duality mapping for some self-dual models where we exactly derive the point of phase transition.

quant-ph↗

arXiv2017

General scheme for preparation of different topological states on the cluster states

Although it is well known that all quantum states can be produced by single qubit measurements on the cluster states, it is not a simple task to explicitly find which measurement patterns on the cluster states can generate different quantum states. In this paper we introduce a general scheme to find measurement patterns corresponding to different topological CSS states containing Kitaev's toric code states and color code states on different lattices and in different dimensions. Furthermore, we find a measurement pattern for generating non abelian anyons where measurement induced defects on a toric code state play the role of Ising anyons. We also support our scheme by a graphical notation where, by following a few simple graphical transformations, one will be able to convert a CSS topological state to a cluster state. Our scheme can be also used for experimental realization of anyons on cluster states.

quant-ph↗