Quantum computing requires use of various physical techniques together with quantum theory. One of the promising systems is spin systems as applied and seen in pulsed nuclear magnetic resonance (NMR) and pulsed electron paramagnetic resonance (EPR) spectroscopies and hence spin-based quantum information technology. Construction of higher spin systems and related rotation operators is important for the theoretical infrastructure that can be used in quantum information theory. It is expected that as the value of spin increases, it will give way to longer time in the computation with bigger data. Spin operators up to spin-4 have been published in previous studies. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spin-4 were worked out via exponential operator for each element of related spin operator matrices and simple linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. It can be predicted that quantum rotation operators for higher spins, like spin-4, will theoretically and practically contribute to spin-based quantum information technology.
Quantum computing requires use of various physical techniques together with quantum theory. One of the promising systems is spin systems as applied and seen in pulsed nuclear magnetic resonance (NMR) and pulsed electron paramagnetic resonance (EPR) spectroscopies and hence spin-based quantum information technology. Construction of higher spin systems and related rotation operators is important for the theoretical infrastructure that can be used in quantum information theory. It is expected that as the value of spin increases, it will give way to longer time in the computation with bigger data. Spin operators up to spin-4 have been published in previous studies. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spin-4 were worked out via exponential operator for each element of related spin operator matrices and simple linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. It can be predicted that quantum rotation operators for higher spins, like spin-4, will theoretically and practically contribute to spin-based quantum information technology.
Quantum mechanical rotation operators are the subject of quantum mechanics, mathematics and pulsed magnetic resonance spectroscopies, namely NMR, EPR and ENDOR. They are also necessary for spin based quantum information systems. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schrödinger equation, or by evaluating Wigner-d formula or by evaluating recently established expressions in polynomial forms discussed in the text. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spins 1 to 2 are worked out by evaluating series expansion of exponential operator for each element of operators and utilizing linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. The operators of spins greater than 2 are under study and will be published in a separate paper.
With the creation of logic gates and algorithms for quantum computers and entering our lives, it is predicted that great developments will take place in this area and important efforts are made. Spin rotation processors are quantum mechanical rotation processors and have no classic counterparts. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schr?dinger equation, by evaluation of Wigner-d formula or by recently established expressions in polynomial forms discussed in the text. In a previous paper, rotation operators for spins 1/2 to 2 were published. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spin 5/2, 3 and 7/2 are worked via exponential operator for each element of related spin operators and utilizing simple linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators.
There are many methods for designing quantum computers, which are generated by rapid progress of computer technology. In this work, it is aimed to find matrices and processors by using an algorithm for spin 1 and 3/2, which can be observed with EPR spectroscopy and used for Quantum information processing. Spin matrices or processors that can be formed using the basic properties of processors. Some of the spin processors, some of which are known, are the most well-known Pauli spin matrices, which can be found in various sources, but are computed with an algorithm for convenience in practice. Matrix representations for s= 1 and 3/2 are found in the theoretical calculations. In addition to the s = 1/2 spin operators given in the literature, matrix representations of spin processors and spin systems are found for s = 1 and s = 3/2 using an algorithm. Thus it can be used in theoretical studies and applications in quantum information theory. For other spin systems spin operators can be created.
With the development of quantum information science, the active manipulation of quantum systems is becoming an important research frontier. To build realistic quantum information processors, one of the challenges is to implement arbitrary desired operations with high precision on quantum systems. A large number of quantum control methods and relevant numerical techniques have been put forward in recent years, such as quantum optimal control and quantum feedback control. Nuclear magnetic resonance (NMR) spin systems offer an excellent testbed to develop benchmark tools and techniques for controlling quantum systems. In this review paper, we briefly introduce some of the basic control ideas developed for NMR systems in recent years. We first explain, for the liquid spin systems, the physics of various couplings and the causes of relaxation effects. These mechanisms govern the system dynamics, and thus are crucial for constructing rigorous and efficient control models. We also identify three types of available control means: 1) raido-frequency fields as coherent controls; 2) phase cycling, gradient fields and relaxation effects as non-unitary controls; 3) radiation damping effect as feedback control mechanism. Then, we elucidate some important control tasks, which may arise from the conventional NMR spectroscopy (e.g., pulse design and polarization transfer) or from quantum information science (e.g., algorithmic cooling and pseudo-pure state preparation). In the last part, we review some of the most important control methods that are applicable to NMR control tasks. For systems with a relatively small number of spins, it is possible to use analytic optimal control theory to realize the target unitary operations. However, for larger systems, numerical methods are necessary. The gradient ascent pulse engineering algorithm and pulse compiler techniques are the most successful techniques for implementing complicated quantum networks currently. There are some interesting topics of utilizing radiation damping and relaxation effects to achieve more powerful controls. Finally, we give an outline of the possible future work.
Regarding the end of the 1900s, a small community of researchers in physics, computer science, mathematics and chemistry began to explore the fertile ground at the intersection of quantum mechanics with information theory, which led to a new and powerful paradigm of quantum computing.Quantum information processing promises to extend today's computing resources.Quantum computers, theoretically, could solve problems much more quickly than any classic computer.Intensive experimental efforts have been made to implement quantum computing since Shor and Grover developed their algorithms.In 1997, Nuclear Magnetic Resonance (NMR) emerged as one of the most promising experimental techniques for the implementation of quantum computing protocols.The isolation of nuclear spins and consequent long relaxation times, combined with the perfect dynamics implemented by radiofrequency pulses, led to important studies in the area.Therefore, nuclear spins are picked out as good candidates for quantum bits.In this scenario, quantum chemistry covers a vast field of quantum information science and can lead to advances in scientific research.
Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1 , are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover’s algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1 and quadrupolar spin 3 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.