Combinatorial and rotational quantum abstract detecting systems

Quantum abstract detecting systems (QADS) were introduced as a common framework for the study and design of detecting algorithms in a quantum computing setting. In this paper, we introduce new families of such QADS, known as combinatorial and rotational, which, respectively, generalize detecting sys...

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Bibliographic Details
Published in:Quantum information processing 2022-02, Vol.21 (2), Article 66
Main Authors: Hernández Cáceres, J. M., Combarro, E. F., Rúa, I. F.
Format: Article
Language:English
Subjects:
Algorithms
Combinatorial analysis
Data Structures and Information Theory
Eigenvalues
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Qubits (quantum computing)
Spintronics
Tensors
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Summary:Quantum abstract detecting systems (QADS) were introduced as a common framework for the study and design of detecting algorithms in a quantum computing setting. In this paper, we introduce new families of such QADS, known as combinatorial and rotational, which, respectively, generalize detecting systems based on single qubit controlled gates and on Grover’s algorithm. We study the algorithmic closure of each family and prove that some of these QADS are equivalent (in the sense of having the same detection rate) to others constructed from tensor product of controlled operators and their square roots. We also apply the combinatorial QADS construction to a problem of eigenvalue decision, and to a problem of phase estimation.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-021-03356-x