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Detection energy levels of a quantum system on a quantum computer by probe spin evolution

Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk

Published Sep 23, 2021• 0 citations
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Abstract

We propose a method for detecting energy levels of a quantum system based on the studies of evolution of probe spin. The method is efficient for estimation of energy levels of many spin systems and opens a possibility to achieve quantum supremacy in solving eigenvalue problem with development of multi-qubit quantum computers. The method is realized for finding energy levels of a spin in magnetic field, spin chain in magnetic field on ibmq-santiago

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We propose a method for detecting energy levels of a quantum system based on the studies of evolution of probe spin. The method is efficient for estimation of energy levels of many spin systems and opens a possibility to achieve quantum supremacy in solving eigenvalue problem with development of multi-qubit quantum computers. The method is realized for finding energy levels of a spin in magnetic field, spin chain in magnetic field on ibmq-santiago
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.
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.
We present a method for solving eigenvalue problems on a quantum computer based on spectroscopy. The method works by coupling a ``probe'' qubit to a set of system simulation qubits and then time evolving both the probe and the system under Hamiltonian dynamics. In this way, we simulate spectroscopy on a quantum computer. We test our method on the IBM quantum hardware for a simple single-spin model and an interacting Kitaev chain model. For the Kitaev chain, we trace out the pseudotopological phase boundary for a two-site model.
Quantum sensors play an important role in many branches of modern science, and they occupy a huge segment of the growing market for quantum devices. Quantum sensors use qubits and their analogs as detecting and analyzing quantum elements. Some sensors can be based on a single qubit, which is often presented as a system making its evolution on the so-called Bloch sphere. Different criteria are used to evaluate the efficiency of the sensing process. One of the most popular is the Quantum Fisher Information Matrix (QFIM) based on Fisher information. The magnitudes of the QFIM elements are strongly related to the precision of the sensing. As an analog of the classical Cramér theorem, one can define the quantum Cramér-Rao bound for the variance V, which is equal to V = 1/NF where F is the corresponding quantum Fisher information element, and N stands for the number of repeated sensory measurements. In this work, we develop our quantum Fisher information-based approach for a single feedback-driven qubit-type element for sensing external magnetic fields. We demonstrate the efficiency of our algorithm and discuss its further possible improvement. The approach developed here can be easily extended to other sensing schemes: collective spin systems and multi-qubit-based sensors. Alternative control algorithms can be applied to drive the probe state vector for maximization of the QFIM components. The particular choice of the control algorithm is defined by the specific experimental set-up.