Eigenvalues and eigenfunctions Archives - IEEE Transactions on Quantum Engineering

A Low-Complexity Quantum Simulation Framework for Toeplitz-Structured Matrix and Its Application in Signal Processing

June 14, 2023Mostafizur Rahaman LaskarEnabling TechnologiesComputational modeling, Covariance matrices, Eigenvalues and eigenfunctions, Estimation, Quantum computing, Quantum state, Sparse matrices

Toeplitz matrix reconstruction algorithms (TMRAs) are one of the central subroutines in array processing for wireless communication applications. The classical TMRAs have shown excellent accuracy in the spectral estimation for both uncorrelated and coherence sources in the recent era. However, TMRAs incorporate the classical eigenvalue decomposition technique for estimating the eigenvalues of the Toeplitz-structured covariance […]

Perfect and Quasi-Perfect Codes for the Bosonic Classical-Quantum Channel

March 30, 2023Andreu Blasco CollQuantum InformationCodes, Eigenvalues and eigenfunctions, Error probability, Indexes, Quantum channels, Quantum state, Testing

In this article, we explore perfect and quasi-perfect codes for the Bosonic channel, where information is generated by a laser and conveyed in the form of coherent states. In particular, we consider the phase-modulation codebook for coherent states in a Bosonic channel. We show that these phase-modulation codes are quasi-perfect as long as the cardinality […]

A Low-Complexity Quantum Principal Component Analysis Algorithm

November 2, 2022Chen HeOpen Access, Quantum ComputingEigenvalues and eigenfunctions, Phase estimation, Principal component analysis, Quantum circuit, Quantum state, Registers, Runtime

In this article, we propose a low-complexity quantum principal component analysis (qPCA) algorithm. Similar to the state-of-the-art qPCA, it achieves dimension reduction by extracting principal components of the data matrix, rather than all components of the data matrix, to quantum registers, so that the samples of measurement required can be reduced considerably. Both our qPCA […]