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Quantum Information Processes
Published in Thiruselvan Subramanian, Archana Dhyani, Adarsh Kumar, Sukhpal Singh Gill, Artificial Intelligence, Machine Learning and Blockchain in Quantum Satellite, Drone and Network, 2023
B.S. Tewari, P. Mandal, Prashant Rawat
The quantum information processes are held in quantum circuits, which can be built from quantum gates. The quantum circuits are obtained by arranging the quantum gates in a particular fashion so that it is possible to execute a particular type of quantum algorithm, wherein running the quantum gates is actually a unitary transformation that acts on a single qubit or pair of qubits. A measurement determines a traditional result such as 0 or 1 at the end of the process. The typical operations of quantum logic gates, which are discussed in the previous section and used in quantum circuits, are based on the following postulates of quantum informatics [37]: First Postulate: The first postulate defines the state space with a state vector (unit length and complex coefficients) in a Hilbert space.Second Postulate: In the second postulate, the evolution of a closed system is defined by means of unitary transforms.Third Postulate: The third postulate is responsible to relate the measurements of quantum system and classical world.Fourth Postulate: Composite systems are specified in the last postulate.
Elements of Quantum Electronics
Published in Michael Olorunfunmi Kolawole, Electronics, 2020
The most general type of errors in the state of a qubit can be described as follows. Suppose a single qubit |ψ〉 in the state α|0〉+β|1〉 undergoes some random unitary transformation, or decoheres, by becoming entangled with the environment it transits through. We define the state of the environment before the interaction with the qubit as |E〉. Basically, the qubit will undergo some unitary transformation in the combined system of qubit and environment. The most general unitary transformation on system and environment can be described as [21] U=|ψ〉⊗|E〉
Lasers in Quantum Information Science
Published in Pradip Narayan Ghosh, Laser Physics and Spectroscopy, 2018
Such a choice of quantum superposition of states gives enough flexibility to a quantum computer. A quantum computer can be in a coherent superposition of all 2N N-bit numbers. A quantum operation is a unitary transformation that simultaneously operates on all the 2N states, and not on a single state or qubit as the classical computers do. This offers the possibility of parallel computation.
State discrimination of two pure states with a fixed rate of inconclusive answer
Published in Journal of Modern Optics, 2018
where and , and equal prior probabilities . From Equation (26), we have that , , and . A unitary transformation is defined
Unambiguous discrimination among three linearly independent symmetric states
Published in Journal of Modern Optics, 2019
Wen-Hai Zhang, Wen-Yan Nie, Gang Ren
We first give definition of the symmetric quantum states. A set of quantum states spanning a Hilbert space H is symmetric if there exists a unitary transformation on H such that (33)
Angle estimation in MIMO radar using a new sparse representation approach
Published in International Journal of Electronics, 2019
Baobao Liu, Ercan Engin. Kuruoglu, Junying Zhang, Fulvio Gini, Tao Xue, Wenying Lei
where represents the complex conjugate transpose, and is defined for even and odd order, respectively, which is the unitary transformation matrix, can be expressed as