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Variational Quantum Eigensolver
In quantum computing, the variational quantum eigensolver (VQE) is a quantum algorithm for quantum chemistry, quantum simulations and optimization problems. It is a hybrid algorithm that uses both classical computers and quantum computers to find the ground state of a given physical system. Given a guess or ansatz, the quantum processor calculates the expectation value of the system with respect to an observable, often the Hamiltonian, and a classical optimizer is used to improve the guess. The algorithm is based on variational method of quantum mechanics. It was originally proposed in 2013, with corresponding authors Alberto Peruzzo, Alán Aspuru-Guzik and Jeremy O'Brien. The algorithm has also found applications in quantum machine learning and has been further substantiated by general hybrid algorithms between quantum and classical computers. It is an example of a noisy intermediate-scale quantum (NISQ) algorithm. Description Pauli encoding The objective of the VQE is to f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though current quantum computers may be too small to outperform usual (classical) computers for practical applications, larger realizations are believed to be capable of solving certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. There are several models of quantum computation with the most widely used being quantum circuits. Other models include the quantum Turing machine, quantum annealing, and adiabatic quantum computation. Most models are based on the quantum bit, or "qubit", which is somewhat analogous to the bit in classical computation. A qubit can be in a 1 or 0 quantum s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Creation And Annihilation Operators
Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted \hat) lowers the number of particles in a given state by one. A creation operator (usually denoted \hat^\dagger) increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator. In many subfields of physics and chemistry, the use of these operators instead of wavefunctions is known as second quantization. They were introduced by Paul Dirac. Creation and annihilation operators can act on states of various types of particles. For example, in quantum chemistry and many-body theory the creation and annihilation operators often act on electron states. They can also refer specifically to the ladder operators for the quantum harmonic oscillator. In the latter case, the raising operator is in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sycamore Processor
Sycamore is a quantum processor created by Google's Artificial Intelligence division. It has 53 qubits. In 2019, Sycamore completed a task in 200 seconds that Google claimed, in a ''Nature (journal), Nature'' paper, would take a state-of-the-art supercomputer 10,000 years to finish. Thus, Google claimed to have achieved quantum supremacy. To estimate the time that would be taken by a classical supercomputer, Google ran portions of the quantum circuit simulation on the Summit (supercomputer), Summit, the most powerful classical computer in the world. Later, IBM made a counter-argument, claiming that the task would only take 2.5 days on a classical system like Summit. If Google's claims are upheld, then it would represent an exponential leap in computing power. In August 2020, quantum engineers working for Google reported the largest chemical simulation on a quantum computer – a Hartree–Fock method, Hartree–Fock approximation with Sycamore paired with a classical computer tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google
Google LLC () is an American multinational technology company focusing on search engine technology, online advertising, cloud computing, computer software, quantum computing, e-commerce, artificial intelligence, and consumer electronics. It has been referred to as "the most powerful company in the world" and one of the world's most valuable brands due to its market dominance, data collection, and technological advantages in the area of artificial intelligence. Its parent company Alphabet is considered one of the Big Five American information technology companies, alongside Amazon, Apple, Meta, and Microsoft. Google was founded on September 4, 1998, by Larry Page and Sergey Brin while they were PhD students at Stanford University in California. Together they own about 14% of its publicly listed shares and control 56% of its stockholder voting power through super-voting stock. The company went public via an initial public offering (IPO) in 2004. In 2015, Google was reor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beryllium Hydride
Beryllium hydride (systematically named poly eryllane(2)'' and beryllium dihydride) is an inorganic compound with the chemical formula ()''n'' (also written ()''n'' or ). This alkaline earth hydride is a colourless solid that is insoluble in solvents that do not decompose it. Unlike the ionically bonded hydrides of the heavier Group 2 elements, beryllium hydride is covalently bonded (three-center two-electron bond). Synthesis Unlike the other group 2 metals, beryllium does not react with hydrogen.Egon Wiberg, Arnold Frederick Holleman (2001) ''Inorganic Chemistry'', Elsevier , p. 1048 Instead, BeH2 is prepared from preformed beryllium(II) compounds. It was first synthesised in 1951 by treating dimethylberyllium, Be(CH3)2, with lithium aluminium hydride, LiAlH4. Purer BeH2 forms from the pyrolysis of di-tert-butylberyllium, Be(C(CH3)3)2 at 210 °C. A route to highly pure samples involves the reaction of triphenylphosphine, PPh3, with beryllium borohydride, Be(BH4)2: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helium Hydride Ion
The helium hydride ion or hydridohelium(1+) ion or helonium is a cation (positively charged ion) with chemical formula HeH+. It consists of a helium atom bonded to a hydrogen atom, with one electron removed. It can also be viewed as protonated helium. It is the lightest heteronuclear ion, and is believed to be the first compound formed in the Universe after the Big Bang. The ion was first produced in a laboratory in 1925. It is stable in isolation, but extremely reactive, and cannot be prepared in bulk, because it would react with any other molecule with which it came into contact. Noted as the strongest known acid—stronger than even fluoroantimonic acid—its occurrence in the interstellar medium had been conjectured since the 1970s, and it was finally detected in April 2019 using the airborne SOFIA telescope. Physical properties The helium hydrogen ion is isoelectronic with molecular hydrogen (). Unlike the dihydrogen ion , the helium hydride ion has a permanent dipole ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient Descent
In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Haskell Curry in 1944, with the method becoming increasingly well-studied and used in the following decades. Description Gradient descent is based on the observation that if the multi-variable function F(\mathbf) is def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Method (quantum Mechanics)
In quantum mechanics, the variational method is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states. This allows calculating approximate wavefunctions such as molecular orbitals. The basis for this method is the variational principle. The method consists of choosing a "trial wavefunction" depending on one or more parameters, and finding the values of these parameters for which the expectation value of the energy is the lowest possible. The wavefunction obtained by fixing the parameters to such values is then an approximation to the ground state wavefunction, and the expectation value of the energy in that state is an upper bound to the ground state energy. The Hartree–Fock method, Density matrix renormalization group, and Ritz method apply the variational method. Description Suppose we are given a Hilbert space and a Hermitian operator over it called the Hamiltonian H . Ignoring complications about continuous spectra, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Gates
In quantum computing and quantum information theory, the Clifford gates are the elements of the Clifford group, a set of mathematical transformations which normalize the ''n''-qubit Pauli group, i.e., map tensor products of Pauli matrices to tensor products of Pauli matrices through conjugation. The notion was introduced by Daniel Gottesman and is named after the mathematician William Kingdon Clifford. Quantum circuits that consist of only Clifford gates can be efficiently simulated with a classical computer due to the Gottesman–Knill theorem. Clifford group Definition The Pauli matrices, : \sigma_0=I=\begin 1 & 0 \\ 0 & 1 \end, \quad \sigma_1=X=\begin 0 & 1 \\ 1 & 0 \end, \quad \sigma_2=Y=\begin 0 & -i \\ i & 0 \end, \text \sigma_3=Z=\begin 1 & 0 \\ 0 & -1 \end provide a basis for the density operators of a single qubit, as well as for the unitaries that can be applied to them. For the n-qubit case, one can construct a group, known as the Pauli group, according to : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bloch Sphere
In quantum quantum mechanics, mechanics and Quantum computing, computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level system, two-level quantum mechanical system (qubit), named after the physicist Felix Bloch. Quantum mechanics is mathematically formulated in Hilbert space or projective Hilbert space. The pure states of a quantum system correspond to the one-dimensional subspaces of the corresponding Hilbert space (and the "points" of the projective Hilbert space). For a two-dimensional Hilbert space, the space of all such states is the complex projective line \mathbb^1. This is the Bloch sphere, which can be mapped to the Riemann sphere. The Bloch sphere is a unit N-sphere, 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors. The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors , 0\rangle and , 1\rangle, respectively, which in turn migh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hartree–Fock Method
In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state. The Hartree–Fock method often assumes that the exact ''N''-body wave function of the system can be approximated by a single Slater determinant (in the case where the particles are fermions) or by a single permanent (in the case of bosons) of ''N'' spin-orbitals. By invoking the variational method, one can derive a set of ''N''-coupled equations for the ''N'' spin orbitals. A solution of these equations yields the Hartree–Fock wave function and energy of the system. Especially in the older literature, the Hartree–Fock method is also called the self-consistent field method (SCF). In deriving what is now called the Hartree equation as an approximate solution of the Schrödinger equation, Hartree required the final field as computed from the charge distribution to be "s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Circuit
In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly other actions. The minimum set of actions that a circuit needs to be able to perform on the qubits to enable quantum computation is known as DiVincenzo's criteria. Circuits are written such that the horizontal axis is time, starting at the left hand side and ending at the right. Horizontal lines are qubits, doubled lines represent classical bits. The items that are connected by these lines are operations performed on the qubits, such as measurements or gates. These lines define the sequence of events, and are usually not physical cables. The graphical depiction of quantum circuit elements is described using a variant of the Penrose graphical notation. Richard Feynman used an early version of the quantum circuit notation in 1986. Reversible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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