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arXiv:2205.10800 · Europhysics Letters (EPL)

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

Andrij Romanovych Kuzmak, V. M. Tkachuk

Published Nov 1, 2023• 2 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1209/0295-5075/ad0952

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Abstract 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.
Finding energy levels of a quantum system is an important problem that can be solved using quantum computers. We showed that transition energies of a quantum system are related with the evolution of mean value of a physical quantity. In particular case when the operator of a physical quantity anticommutes with the Hamiltonian of a system we found that studies of the evolution of the mean value of this physical quantity give a possibility to determine the energy levels of the system and their degeneracy. On the basis of the results the energy levels of spin systems were detected on IBMs quantum computers ibmq manila and ibmq melbourne. It is worth noting that spin systems are one of the most suitable systems for modeling them on a quantum computer. We considered a spin in magnetic field, spin chain with Ising interaction, spin square-lattice with isotropic and spatially anisotropic Ising interactions. The results obtained on the quantum devices correspond to the analytical one. It is important to note that finding the maximal or the minimal energy of the Ising model on square lattice with spatially anisotropic interaction is not a trivial problem. Therefore, the proposed algorithm for obtaining the energy levels opens a possibility to achieve the quantum supremacy in solving this problem on many qubit quantum computers.
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.
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.
IBM quantum computers are used to simulate the dynamics of small systems of interacting quantum spins. For time-independent systems with fewer than three spins, we compute the exact time evolution at arbitrary times and measure spin expectation values and energy. It is demonstrated that even in such small systems, one can observe the connection between conservation laws and symmetries in the model. Larger systems require approximating the time-evolution operator, and we investigate the case of N=3 spins explicitly. While it is shown to be unfeasible to use such devices to probe such larger systems without more advanced algorithms or reliable error correction, we demonstrate that the quantum circuit simulator is an easy-to-use method for studying spin dynamics in systems with N∼O(10) spins. The computations presented provide an interesting experimental component to the standard treatment of quantum spin in an undergraduate quantum mechanics course.
In this paper the speed of evolution of a two-spin system with XY interaction is studied.The analysis is carried out both analytically and using quantum computing.The dependence of the speed on the coupling constants and the parameters of the initial state is investigated.The evolution speed is calculated through quantum calculations on AerSimulator, based on the study of quantum correlators and the time dependence of the mean value of the evolution operator.The results of the quantum calculations are in close agreement with the theoretical predictions.