Quantum Computing models and Quantum Algorithms
Researchers have designed various quantum computing models and algorithms to take advantage of quantum properties such as entanglement and superposition and thereby solve problems more efficiently.
Common quantum computing models include the following:
? A quantum circuit model uses quantum gates that act as basic circuits operating on a qubit set. In contrast to classic computing models, however, in the quantum model, the gates are reversible and do not include AND gates.
? A measurement-based model, also known as one-way quantum computing, starts with an initial entangled state (a cluster) and applies to it a sequence of single-qubit measurements that correspond to the desired quantum circuit.
? An adiabatic model slowly transforms an initial Hamiltonian system into a final Hamiltonian whose ground states contain the solution.
? The quantum annealing model is a specialized adiabatic model used for solving optimization problems.
?Following are a few examples of quantum algorithms
Grover’s algorithm is used to search unsorted databases of N items; whereas classical algorithms require O(N) for such a search, Grover’s algorithm provides a quadratic speedup. Application areas include database searches as well as efforts to increase the speed of existing search algorithms. A classical search algorithm needs about O(N) operations in order to find a specified item in a disordered list containing N elements. The quantum search algorithm, created by Grover is quadratically faster than its classical analogous, since only O N operations are needed
Shor’s algorithm offers a quantum solution for prime factorization that offers an exponential speedup over existing factorization options, thus posing a threat to classic RSA encryption. Among the first quantum algorithms that demonstrated advantage over classical ones we find Shor's algorithm. In general terms, Shor's algorithm allows us to find prime decomposition of very big numbers in O((logN)^3) time and O(logN) space
The quantum Fourier transform is used to efficiently compute the discrete Fourier transform of a data sequence. Application areas include signal processing and cryptography. The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator, and algorithms for the hidden subgroup problem.
The variational quantum eigensolver (VQE) is used for solving optimization problems and is currently being developed for applications in areas such as drug discovery and materials?science. 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 the variational method of quantum mechanics.
Quantum simulation algorithms simulate complex quantum systems that are beyond the capabilities of classical computers; application areas include materials science, condensed-matter physics, and?chemistry. Efficient (that is, polynomial-time) quantum algorithms have been developed for simulating both Bosonic and Fermionic systems and in particular, the simulation of chemical reactions beyond the capabilities of current classical supercomputers requires only a few hundred qubits.
The quantum approximate optimization algorithm (QAOA) is a general-purpose quantum algorithm for solving combinatorial optimization problems. Application areas include finance, mapping applications, and telecommunication