The equation of motion for the spin magnetic dipole in nuclear magnetic resonance imaging (MRI) and the qubit state vector in the Bloch sphere in quantum Computing (QC) are derived and shown to be similar. The solutions in both cases are given, and the behavioral similarity is discussed. The paper should help the understanding of the concept of Qubits, their behavior, excitation, and readout from the perspectives of Electrical Engineering. A minimum knowledge of Quantum Mechanics is needed, if any. Another objective of the paper is to highlight the possibility of using the rather matured MRI technologies to implement feasible Qubits.
The equation of motion for the spin magnetic dipole in nuclear magnetic resonance imaging (MRI) and the qubit state vector in the Bloch sphere in quantum Computing (QC) are derived and shown to be similar. The solutions in both cases are given, and the behavioral similarity is discussed. The paper should help the understanding of the concept of Qubits, their behavior, excitation, and readout from the perspectives of Electrical Engineering. A minimum knowledge of Quantum Mechanics is needed, if any. Another objective of the paper is to highlight the possibility of using the rather matured MRI technologies to implement feasible Qubits.
We propose a novel MRI (Magnetic Resonance Imaging) technique based quantum bit (qubit) generation with water proton NMR (1H-NMR), distinct from previously proposed NMR chemical shift or spectroscopic techniques based qubit generation. We briefly review prior NMR-based techniques in the context of quantum computing, focusing on MRI-related methods. The proposed technique utilizes MRI-based gradient methods combined with set of local reverse gradients to generate multiple qubits. This configuration enables the creation of multiple localized constant magnetic fields, each producing a qubit with highly homogeneous field, therefore, a unique single frequency. The RF electronics and signal processing techniques are analogous to those used in conventional MRI scanners, allowing operation at room temperature, with the exception of the main magnet, which remains identical to that of standard MRI systems. Additional advantages of this method include the ability to leverage the extensive pulse techniques and hardware developed for MRI scanners over the past 50 years. Furthermore, the wide array of MRI pulse sequences enables highly sophisticated signal processing for quantum computing applications, such as the spin purification.
Explosive increase of interest in quantum computing has resulted in various proposals for generation of quantum bits or qubits, the basic quantum computing unit. The superconducting qubits of Josephson Junction are the most widely accepted and currently used, while the Ion-trap and a similar molecule-based qubits have been proposed more recently. In these methods, each qubit is generated individually with great effort. Here we proposed a new technique using magnetic resonance imaging (MRI)-based qubit generation, by which multiple qubits can be generated. Simultaneously this provides a complete qubit platform for quantum computing. Central to the proposed method is the simultaneous generation of multiple qubits using the 'gradient' concept together with multiple radiofrequency coils, one for all qubits, and others for individual qubits with each small Q-coil. Another key concept is the time-encoded probability amplitude (TEPA) technique, using individual Q-coils together with the spin-echo series in each qubit incorporating readout gating for time-encoding. This MRI-based qubit-generation and qubit-encoding technique allowed us to develop an entirely new class of quantum computing platform. Our newly proposed MRI-based qubits are well-suited to currently available electronics, superconducting and semiconductor technologies, as well as nuclear magnetic resonance and MRI physics and technology.
Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.
The work develops an approach to researching the dynamics of qubits that makes it possible to monitor the behavior of the system in the process of quantum computing using computer simulation. The study deals with individual and interacting qubits based on spin ½ in a magnetic field. The goal of the work is to obtain evolutionary equations (equations of motion) for observables that adequately describe the state of the system and provide opportunities for computer modeling of processes. The dynamics of qubits are described using the formalism of the density matrix of pure states. The paper shows derivation of the equations of motion for observables being the average values of operators of physical quantities that describe the state of the system. For spin ½ in magnetic fields, the derivation of the dynamic equation for the spin polarization vector, which is a unit vector in real three-dimensional space, is shown. The shape and parameters of radiofrequency pulses that implement single-qubit operations are presented. In the case of two interacting spins ½, an expression is given for the density matrix and the Hamiltonian of the system for scalar indirect interaction of the magnetic moments of nuclei through the electron shells of atoms in the molecule. Evolution equations are derived for the average dipole moments and quadrupole moment of the system. It is shown that in the case of weak interaction the dynamics of the system can be described using a closed system of equations for the average dipole moments, which in this case coincide with the spin polarization vectors of individual spins. The presentation is accompanied by examples of numerical solutions of the resulting equations describing one-qubit and two-qubit operations. A conclusion is made about the adequacy of the created mathematical model and the possibility of its use for computer modeling of quantum computing processes, the influence of the environment on them and the stabilization of states to prevent or reduce errors in quantum computing.
The nuclear spin, which is the fundamental atomic attribute underlying the magnetic resonance imaging, is an exact two-state quantum system. Therefore, it is a suitable candidate for use as a qubit in quantum computing. The aim of this letter is to review the main equations governing the dynamics of the spin magnetic dipole moment in Magnetic Resonance Imaging. It is also shown that exposing the magnetic dipole moment to a continuous-wave results in travelling back and forth between its two energy states. It absorbs energy from its environment when going from the lower to the higher energy state, and emits the same amount of energy back when relaxing from the higher to the lower energy state. In a complete cycle, the dipole moment behaves therefor purely reactive with zero net energy exchange with its environment.
The neurosciences have pioneered the use of quantum technologies for sensing and imaging the brain.Next-generation technologies promise routes towards low-cost, wearable imaging devices with high spatial and temporal resolution.Much of the progress in our understanding of the brain and our ability to assess brain health relies heavily on magnetic resonance imaging (MRI) and quantum technologies that rely on quantum properties of matter or radiation such, e.g., nuclear spin, entanglement or detection of single quanta.These technologies are undergoing a renaissance in funding and research, which has led to some very exciting developments in recent years, for example, reconstructing images, videos [1,2], and the semantics of entire sentences [3] from brain activity and fMRI data alone.The goal of this perspective is to provide a brief overview of some quantum technologies that may have an impact, for example, on the wearability, precision, and cost of these brain reading approaches.Magnetic resonance imaging (MRI) is a noninvasive approach that relies on a quantum effect whereby charged particles can have a spin and thus interact with an external magnetic field that provides information about the conformation of the spins and of the matter that we are probing.One form of MRI known as functional MRI (fMRI)-which measures brain activity by detecting small changes of blood flow in the brain-can now achieve sub-millimetre resolution, albeit typically with a 5 to 10 second time lag that results from the fact that it measures a blood oxygenation level dependent (BOLD) signal.Another noninvasive technology known as magnetoencelphagraphy (MEG) instead measures the magnetic fields generated as a result of the time-varying voltage signals at the cellular level.The quantum technology utilised here lies not in the physics of the signal itself but rather in the detection, which is typically achieved using the extreme sensitivity of superconducting quantum interference devices (SQUIDs).MEG has lower spatial resolution compared to fMRI of order 3 mm but without the BOLD time-lag.It is clear that using fMRI and MEG to image the brain at ever-finer detail is enabling a deeper understanding of how the brain operates.However, fMRI has relatively high costs that severely limit accessibility and the range of experiments is constrained by the fact that lying down in an MRI scanner is not a "natural" environment in which animals or humans operate.MEG based on SQUIDs is moderately more wearable but still expensive, mostly as a result of the experiments needing to be housed in special rooms that shield the instruments from the