P $$\hbar $$ ase-Space Approach to Time Evolution of Quantum States in Confined Systems. The Spectral Split-Operator Method

Using the phase space approach, we consider the quantum dynamics of a wave packet in an isolated confined system with three different potential energy profiles. We solve the Moyal equation of motion for the Wigner function with the highly efficient spectral split-operator method. The main aim of this study is to compare the accuracy of the employed algorithm through analysis of the total energy expectation value, in terms of deviation from its exact value. This comparison is performed for the second and fourth order factorizations of the time evolution operator.

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Basic quantum circuits for classification and approximation tasks

Wiśniewska¹,

Sawerwain²,

Obuchowicz³

2020

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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.

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P $$\hbar $$ ase-Space Approach to Time Evolution of Quantum States in Confined Systems. The Spectral Split-Operator Method

Cited by 3 publications

References 36 publications

Exponential unitary integrators for nonseparable quantum Hamiltonians

Exponential unitary integrators for nonseparable quantum Hamiltonians

The Phase–Space Approach to time Evolution of Quantum States in Confined Systems: the Spectral Split–Operator Method

Basic quantum circuits for classification and approximation tasks

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