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Quantum Preprocessing for Deep Convolutional Neural Networks in Atherosclerosis Detection
Published in Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan Cruz-Aceves, Hybrid Quantum Metaheuristics, 2022
Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan Cruz-Aceves
where ϑ and φ correspond to two angles in spherical coordinates. In such a way, a quantum state is visualized as a unit vector in the 3-D space (on the Bloch sphere). The two basic states |0〉 and |1〉 are then represented by ϑ=0 and ϑ=ϕ, pointing in z and −z directions, respectively, as illustrated in Figure 7.3.
Formalism
Published in Shabnam Siddiqui, Quantum Mechanics, 2018
A Bloch sphere is a visualization tool for the spin state of a particle. Using Bloch sphere any superposition state of the spin of the electron can be written as, |ψ⟩=cosθ2|↑⟩+sinθ2eiφ|↓⟩.
Future Semiconductor Devices
Published in Lambrechts Wynand, Sinha Saurabh, Abdallah Jassem, Prinsloo Jaco, Extending Moore’s Law through Advanced Semiconductor Design and Processing Techniques, 2018
Wyn Lambrechts, Saurabh Sinha, Jassem Abdallah, Jaco Prinsloo
The qubit’s state can be visually represented by the Bloch sphere in Figure 5.12. In the Bloch sphere, two angles are considered in the state of the qubit: the polar angle with 0≤θ≤π and the azimuthal angle with 0≤φ≤2π. Thus, (5.17) can be rewritten as follows (Bergou and Hillery 2013):
Diamond quantum sensors: from physics to applications on condensed matter research
Published in Functional Diamond, 2022
Kin On Ho, Yang Shen, Yiu Yung Pang, Wai Kuen Leung, Nan Zhao, Sen Yang
The magnetic field sensed by the NV centre can be, in principle, extracted from the resonances of the ODMR spectrum associated with the Zeeman splitting term. Nonetheless, this method can only resolve a relatively high magnetic field that contributes to an observable splitting in resonance peaks. Measuring weak magnetic fields with pulsed sequences are, therefore, developed. Since the magnetic field influences the precession of the spin in the Bloch sphere, the magnetic field can be obtained by analysing the signal from certain pulsed sequences [16, 39–41].
Spin and charge localisation due to the interplay of Ac gate voltage and spin–orbit interaction
Published in Philosophical Magazine, 2021
The energy spectrum of time-independent Hamiltonian given in Equation (7) with V =0 obtained by exact diagonalisation is shown in Figure 3. The left-hand panel shows crossing of singlet and triplet levels and (shown by the oval) for the case . We clearly see that for a symmetric potential , the ground state for the system will consist of singly occupied orbitals, i.e. either the singlet or the triplet state depending on the energy of singlet (triplet) . However, alternating the detuning, by methods such as gated pulse voltage, to positive or negative values favours state or . Moreover, for positive ε a hybridised singlet state is formed by due to the presence of inter-dot tunnelling while contribution from is energetically inaccessible [49]. Here, the and can be regarded as a two-level qubit forming a Bloch sphere. In the presence of spin mixing term additional finite energy gap between and converts the crossing into an anti-crossing for particular value of ε (right oval in Figure 3). Note that for , state with singly occupied orbitals is degenerate with double occupancy of one of the dots while the singly occupied triplet state occurs in Pauli spin blockaded regime (tunnelling is forbidden). This blockade is lifted by SOI. Our focus is the qubit subspace defined in the vicinity of avoided crossing.
Quantum-computing with AI & blockchain: modelling, fault tolerance and capacity scheduling
Published in Mathematical and Computer Modelling of Dynamical Systems, 2019
For each bit string, , gives the probability of the system being found in the state after a measurement. However, because a complex number encodes not just a magnitude but also a direction in the complex plane, the phase difference between any two coefficients (states) denotes a meaningful parameter. This is a fundamental difference between quantum computing and probabilistic classical computing. Under this computational basis, a state of -qubit register can be represented by its coefficients . For examples, if , and if , while , where, the prime denotes the transpose of a vector. Note that, if , a single qubit can be used to denote a particle spinning up and down at the same time. The possible quantum states for a single qubit is visualized by the so-called Bloch sphere as in the left-upper graph of Figure 6, where . Note that, the Bloch sphere is the surface of a ball and hence is a two-dimensional manifold since it can be represented by a collection of two-dimensional maps. In the sequel, we just simply call it a 2-sphere by mathematical convention. A pure qubit state can be represented by any point on such a 2-sphere with corresponding angles and . More precisely, is the angle between -axis and , and is the angle between -axis and the projection of onto -plane.