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Basic quantum circuits for classification and approximation tasks

Wiśniewska Joanna, Sawerwain Marek, Obuchowicz Andrzej

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 4

733--744

We discuss a quantum circuit construction designed for classification. The circuit is built of regularly placed elementary quantum gates, which implies the simplicity of the presented solution. The realization of the classification task is possible after the procedure of supervised learning which constitutes parameter optimization of Pauli gates. The process of learning can be performed by a physical quantum machine but also by simulation of quantum computation on a classical computer. The parameters of Pauli gates are selected by calculating changes in the gradient for different sets of these parameters. The proposed solution was successfully tested in binary classification and estimation of basic non-linear function values, e.g., the sine, the cosine, and the tangent. In both the cases, the circuit construction uses one or more identical unitary operations, and contains only two qubits and three quantum gates. This simplicity is a great advantage because it enables the practical implementation on quantum machines easily accessible in the nearest future.

Manipulation of electron spin in a quantum dot using a magnetic field and voltage gates

Giuliano D., Lucignano P., Tagliacozzo A.

Materials Science Poland

2004

Vol. 22, No. 4

481--495

In this paper, we show that it is possible to manipulate the many-body wave function of an isolated dot with a few electrons by locally applying magnetic and electric fields. We polarize the dot at a level crossing, where the sensitivity is at its maximum. Time-dependent fields produce a superposition of the states involved in the avoided crossing. In the case of N = 2 and N =3 electrons, the results of exact diagonalisation give information about the nature of these states and allow us to construct an effective Hamiltonian describing the coupling. The formalism for evaluating the Berry phase arises naturally. We argue that a quantum dot, capacitively coupled to a quantum point contact, can influence its conductance. The quantum superposition of the states produced by cycling the fields on the dot can be measured this way.