High-Spin Paramagnetic Ions as Qubits and Qutrits for Quantum Computations
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QUANTUM ELECTRONICS HIGH-SPIN PARAMAGNETIC IONS AS QUBITS AND QUTRITS FOR QUANTUM COMPUTATIONS M. R. Arifullin and V. L. Berdinskiy
UDC 538.915; 538.955
Paramagnetic ions having two electrons and spin S = 1 in zero magnetic field are proposed for new physical performance of elementary quantum computing operations by pulsed manipulations with electron spins. For this purpose, a new type of microwave pulses with variable phases and different polarizations are shown can be used. Such pulses are able to induce different transitions between ion spin states. Some of those transitions are described by operators similar to quantum computing operators. To describe the effects of such pulses on hig-spin ions, a new way to represent exponential operators as polynomials of the Pauli matrices is proposed. Keywords: paramagnetic ions, quantum calculations, qubit.
INTRODUCTION Recently the quantum computing science and quantum computations have reached considerable, mainly theoretical, successes. Quantum algorithms are being developed, various variants of architecture of quantum computers and various physical realizations of qubits [1], qutrits, and other elements of higher order are proposed. There are many different suggestions for physical realization of a quantum computer [2–8], and all of them are defined by physics of their qubits and by the nature of interaction between the qubits. For example, they involve polymeric systems [9], qubit representation by means of a magnetic flux through a superconducting contour [10], or use of electrons on the liquid helium surface as qubits. However, for practical implementation of many proposed physical systems of quantum information processing, very expensive, complex, and as a rule, unreliable physical and technical methods are required, for example, ultralow temperatures, superstrong magnetic fields, superdeep vacuum, and complex laser and optical methods of cooling. Therefore, solid-state quantum computers are considered to be the most promising. This is the area of active research, and it is expected that it would be easier to scale a solid-state system to a considerable number of qubits. One of the variants is the use of the electron charge and the spin at quantum points [11], but the use of the charge as a qubit implies very small coherence times (10-10–10-13 s) because of strong interaction with the environment and fluctuations of the potential created by external charges. In the present work, we proposed to use paramagnetic ions with the total electron spin S = 1 and zero nuclear spin in the simple cubic or tetragonal crystal lattice as parts of the quantum computer. In the absence of external magnetic field (in zero magnetic field), the dipole-dipole and spin-orbit interactions eliminate degeneration of levels with total spin SZ = 0 and SZ = ±1 [12, 13]. Such splitting of levels in zero magnetic field permits to abandon the use of strong magnetic fields for implementation of spin qubits or qutrits. Depending on the ion types and on the crystal lattice, splitting in zero fiel
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