arXiv subjects

A. R. Kuzmak

Publications and source records attributed to A. R. Kuzmak.

At least 19 recordsLinked to original sources

arXiv2026

Analytical Investigation of Two-Spin Entanglement Generated by Different Types of Bosonic Environments

Due to the rapid development of research in the field of quantum physics and quantum information over the past decades, the need to study physical models that can effectively implement quantum computing has increased. An integral part of such models is the environment, which, on the one hand, leads to decoherence in the system, and on the other hand, generates interaction between spins, which in turn allows for the induction of entanglement, which is an integral part of many quantum algorithms. Therefore, it is essential to investigate the impact of the environment on the behavior of quantum systems, enabling the effective implementation of quantum information devices. Here, we consider the time evolution of two spins generated by the interaction through a bosonic environment. The behavior of negativity as a measure of entanglement between spins is studied for different models of environment. As a result, conditions on the parameters of the environment are obtained to achieve the maximum values of entanglement between spins. In this case, environmental models were obtained that minimize the decoherence of the system while maximizing its entanglement. It became possible to derive an effective unitary operator describing the corresponding evolution, since the influence of decoherence was negligibly small.

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arXiv2025

Detecting the purely imaginary Fisher zeros of an Ising spin system on a quantum computer

We propose a protocol for studying the purely imaginary Fisher zeros of the Ising model on a quantum computer. Our protocol is based on the direct relation between the partition function for purely imaginary temperature and the evolution operator of the Ising model. In this case, the inverse temperature is equal to the time of evolution. This protocol allows one to measure the zeros only those localized on the imaginary axes. We test this protocol on the ibm-lagos quantum computer in the cases of a 3-spin chain and a triangle cluster in a purely imaginary magnetic field, as well as a 7-spin cluster in which the interaction between spins reproduces the architecture of the quantum computer.

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arXiv2025

Entanglement of a spin-1/2 Ising-Heisenberg diamond spin cluster in the thermal bosonic bath

With the rapid development of quantum information over the last decade, there is a growing need to identify physical systems that can effectively implement quantum computing. One such system is the diamond spin cluster, which appears in various chemical compounds, including the natural mineral azurite, where copper ions are arranged in this structure. Here, we study the time evolution of a diamond spin cluster with Ising-Heisenberg interaction under the influence of a thermal bosonic bath, which simulates the environment. Using negativity as a measure, we analyze the entanglement behavior between the central spins of the system. We demonstrate how the environment influences the presence of entanglement in the system. Specifically, we show that for certain values of the environment parameters, entanglement increases significantly. Furthermore, we identify the conditions under which entanglement reaches its maximum possible values.

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arXiv2023

Probing mean values and correlations of high-spin systems on a quantum computer

We consider simulation of the high spins on a quantum computer. The protocols which allow one to measure the mean value of spin and correlations between spins are proposed. As a result, we determine the time dependence of the mean values of spin-1 in the magnetic field prepared on the ibmq-santiago quantum computer. In addition, we study the evolution of two interacting spins on the ibmq-lima quantum computer. The time-dependencies of the mean value of spin-1 and correlations between these spins are detected. Finally, we generalize these protocols for the spins of arbitrary values.

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arXiv2023

Preparation of two-qubit entangled states on a spin-1/2 Ising-Heisenberg diamond spin cluster by controlling the measurement

The preparation of entangled quantum states is an inherent and indispensable step for the implementation of many quantum information algorithms. Depending on the physical system, there are different ways to control and measure them, which allow one to achieve the predefined quantum states. The diamond spin cluster is the system that can be applied for this purpose. Moreover, such a system appears in chemical compounds such as the natural mineral azurite, where the $Cu^{2+}$ are arranged in a spin-1/2 diamond chain. Herein, we propose the method of preparation of pure entangled states on the Ising-Heisenberg spin-1/2 diamond cluster. We suppose that the cluster consists of two central spins which are described by an anisotropic Heisenberg model and interact with the side spins via Ising interaction. Controlling the measurement direction of the side (central) spins allows us to achieve predefined pure quantum states of the central (side) spins. We show that this directly affects the entanglement and fidelity of the prepared states. For example, we obtain conditions and fidelities for preparations of the Bell states.

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arXiv2023

Entanglement of the Ising-Heisenberg diamond spin-1/2 cluster in evolution

In the last two decades, magnetic, thermodynamic properties and bipartite thermal entanglement in diamond spin clusters and chains have been studied. Such spin structures are presented in various compounds. The ions of $Cu^{2+}$ in the natural mineral azurite are arranged in a diamond spin chain. There are no studies of the entanglement behaviour during the quantum evolution of such systems. Herein, we consider the evolution of entanglement in the diamond spin-1/2 cluster. This cluster consists of two central spins described by the anisotropic Heisenberg model, which interact with two side spins via Ising interaction. The influence of the interaction coupling with side spins on the entanglement of central spins is investigated. It is shown that choosing the value of this coupling allows us to control the behaviour of entanglement between central spins. As a result, we find conditions for achieving the maximal values of entanglement. In addition, the entanglement behaviour between the side spins, central and side spins, and between a certain spin and the rest of the system is studied. In these cases, the conditions for achieving maximal entanglement are also obtained.

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arXiv2021

Measuring distance between quantum states on a quantum computer

We propose protocols for determining the distances in Hilbert space between pure and mixed quantum states prepared on a quantum computer. In the case of pure quantum states, the protocol is based on measuring the square of modulus of scalar product between certain states. Determination of the distance between mixed quantum states is reduced to measuring the squares of modules of scalar products between all pure states included in the mixed states. In addition, we develop a protocol that allows one to determine the speed of evolution of the spin system simulated by a quantum computer. These protocols we apply to measure distances and speeds of evolution of different quantum systems implemented on the ibmq-santiago quantum computer.

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arXiv2021

Derivation of the robustness from the concurrence

Adding the maximally mixed state with some weight to the entanglement system leads to disentanglement of the latter. For each predefined entangled state there exists a minimal value of this weight for which the system loses its entanglement properties. These values were proposed to be used as a quantitative measure of entanglement called robustness [G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999)]. Using the concurrence, we propose the derivation of this measure for the system of two-qubit. Namely, for a two-qubit pure state, an exact expression of robustness is obtained. Finally, in the same way, the robustness of special cases of mixed two-qubit states is calculated.

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arXiv2021

Measuring entanglement of a rank-2 mixed state prepared on a quantum computer

We study the entanglement between a certain qubit and the remaining system in rank- 2 mixed states prepared on the quantum computer. The protocol, which we propose for this purpose, is based on the relation of geometric measure of entanglement with correlations between qubits. As a special case, we consider a two-qubit rank-2 mixed state and find the relation of concurrence with the geometric measure of entanglement. On the ibmq-melbourne quantum computer we measure the geometric measure of entanglement in the cases of 2- and 4-qubit mixed quantum states which consist of Schrödinger cat states. We study the dependence of the value of entanglement on the parameter which defines the weight of pure states. Finally, we determine the concurrence of 2-qubit mixed state.

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arXiv2021

Preparation and study of the entanglement of the Schrödinger cat state on the ibmq-melbourne quantum computer

We study the entanglement between a certain qubit and the remaining system in the Schrödinger cat state prepared on the ibmq-melbourne quantum computer. The protocol, which we use for this purpose, is based on the determination of the mean value of spin corresponding to a certain qubit. We explore the dependence of the entanglement on a parameter of the Schrödinger cat state which consists of different numbers of qubits. In addition, we explore the entanglement of each qubit with the remaining system in the maximum entangled Schrödinger cat state.

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arXiv2020

Detecting entanglement by the mean value of spin on a quantum computer

We implement a protocol to determine the degree of entanglement between a qubit and the rest of the system on a quantum computer. The protocol is based on results obtained in paper [Frydryszak et al. (2017)]. This protocol is tested on a 5-qubit superconducting quantum processor called ibmq-ourense provided by the IBM company. We determine the values of entanglement of the Schrödinger cat and the Werner states prepared on this device and compare them with the theoretical ones. In addition, a protocol for determining the entanglement of rank-2 mixed states is proposed. We apply this protocol to the mixed state which consists of two Bell states prepared on the ibmq-ourense quantum device.

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arXiv2020

Implementation of a two-qubit state by an auxiliary qubit on the three-spin system

The method for preparation of a two-qubit state on two spins-1/2 that mutually interact through an auxiliary spin is proposed. The essence of the method is that, initially, the three spins evolve under the action of an external magnetic field during a predefined period of time. Then, the auxiliary spin is measured by a monochromatic electromagnetic radiation that allows obtaining a certain state of the remaining spins. We study the entanglement of this state and obtain the condition for achieving the maximally entangled state. The implementation of the method on the physical system of nuclear spins of xenon difluoride is described. As a results, the conditions which allow preparing the maximally entangled state on this system are obtained.

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arXiv2019

Probing the Lee-Yang zeros of a spin bath by correlation functions and entanglement of two spins

We study the Lee-Yang zeros of the ferromagnetic Ising bath via the interaction with the two probe spins. Similarly as in paper [Bo-Bo Wei, Ren-Bao Liu, Phys. Rev. Lett. 109, 185701 (2012)] the problem of detecting the zeros is reduced to the exploration of time evolution of probe spins. As a result, the relation between the Lee-Yang zeros of the bath and correlation functions of the probe system is obtained. Also we obtain relation between the Lee-Yang zeros and values of the entanglement of probe spins. We apply these results to the 1D Ising spin model with nearest-neighbor interaction which can be prepared on trapped atoms.

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arXiv2019

Geometry and speed of evolution for a spin-s system with long-range zz-type Ising interaction

We study the evolution of a spin-s system described by the long-range zz-type Ising interaction. The Fubini-Study metric of the quantum state manifold defined by this evolution is obtained. We explore the topology of this manifold and show that it corresponds to a sphere. Exploration of the Riemannian curvature allows us to determine the manifold geometry. Also we calculate the speed of evolution of the system and represent the curvature by means of this speed. This is important for an experimental measurement of the curvature. The conditions for achieving the minimal and maximal values of the speed of evolution are obtained. Also we examine the geometry of state manifold and speed of evolution of spin system in the thermodynamic limit. We propose the physical system of methane molecule for application of our considerations. Finally, we study the influence of an external magnetic field on the metric of state manifold and on the speed of evolution. In this case we obtain the conditions for achieving the minimal possible speed of evolution. For some predefined initial states the orientations of magnetic fields to reach the minimal and maximal values of the speed are found.

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arXiv2019

Detecting the Lee-Yang zeros of a high-spin system by the evolution of probe spin

Recently in paper [Peng et al., Phys. Rev. Lett. 114, 010601 (2015)] the experimental observation of the Lee-Yang zeros of an Ising-type spin-1/2 bath, by measuring the coherence of a probe spin, was reported. We generalize this problem to the case of an arbitrary high-spin bath. Namely, we consider the evolution of a probe arbitrary spin which interacts with bath composed by N arbitrary spins. As a result, the connection between the observed values of the probe spin, such as magnetization and susceptibility, and the Lee-Yang zeros is found. We apply these results to some models, namely, a triangle spin cluster, the Ising model with a long-range interaction and the 1D Ising model with nearest-neighbor interaction. Also we propose the implementation of these models on real physical systems.

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arXiv2018

Preparation of an arbitrary two-qubit quantum gate on two spins with an anisotropic Heisenberg interaction

We consider the two-step method [A. R. Kuzmak and V. M. Tkachuk, Phys. Lett. A 378 (2014) 1469] for preparation of an arbitrary quantum gate on two spins with anisotropic Heisenberg interaction. At the first step, the system evolves during some period of time. At the second step, we apply pulsed magnetic field individually to each spin. We obtain the conditions for realization of SWAP, iSWAP, $\sqrt{SWAP}$ and entangled gates. Finally, we consider the implementation of this method on the physical system of ultracold atoms in optical lattice.

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arXiv2018

Entanglement and quantum state geometry of spin system with all-range Ising-type interaction

The evolution of $N$ spin-$1/2$ system with all-range Ising-type interaction is considered. For this system we study the entanglement of one spin with the rest spins. It is shown that the entanglement depends on the amount of spins and the initial state. Also the geometry of manifold which contains entangled states is obtained. Finally we find the dependence of entanglement on the scalar curvature of manifold and examine it for different number of spins in the system.

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arXiv2018

Geometry of quantum state manifolds generated by the Lie algebra operators

The Fubini-Study metric of quantum state manifold generated by the operators which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the manifold generated by the so(3) Lie algebra operators. Using these results we calculate the Fubini-Study metrics of state manifolds generated by the position and momentum operators. Also the metrics of quantum state manifolds generated by some spin systems are obtained. Finally, we generalize this problem for operators of an arbitrary Lie algebra.

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