The clusters are obtained based on mutual information reflecting maximal entanglement between qubits, whereas inter-cluster correlation is taken into account via a new “dressed” Hamiltonian. Our ClusterVQE algorithm splits the initial qubit space into clusters which are further distributed on individual (shallower) quantum circuits. Here we present an approach to reduce quantum circuit complexity in VQE for electronic structure calculations. The practical realization is limited by the complexity of quantum circuits. June 1992.The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenstates of a given Hamiltonian on noisy intermediate-scale quantum devices (NISQ). Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-7-0 Thermodynamics in Nuclear Power Plant Systems. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer 4th edition, 1994, ISBN: 978-0412985317 Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 8-1. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983). That is, the period is independent of amplitude. For small swings the period of swing is approximately the same for different size swings. Where L is the length of the pendulum and g is the local acceleration of gravity. If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is: On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points. The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. The pendulum is subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible. It is dependent upon the spring constant k as well as the distance stretched.Įlectric potential energy is a potential energy that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. For example, if a positive charge Q is fixed at some point in space, any other positive charge which is brought close to it will experience a repulsive force and will therefore have potential energy.Īssume a pendulum (ball of mass m suspended on a string of length L that we have pulled up so that the ball is a height H < L above its lowest point on the arc of its stretched string motion. The most common use of gravitational potential energy is for an object near the surface of the Earth where the gravitational acceleration can be assumed to be constant at about 9.8 m/s 2.Įlastic potential energy is potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. Gravitational potential (V the gravitational energy per unit mass) at a location is equal to the work (energy transferred) per unit mass that would be needed to move the object from a fixed reference location to the location of the object. In classical mechanics, the gravitational potential energy (U) is energy an object possesses because of its position in a gravitational field.
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