Eigen-Spectrum Estimation and Source Detection in a Massive Sensor Array Based on Quantum Assisted Hamiltonian Simulation Framework

Laskar, Mostafizur Rahaman; Mondal, Subhadeep; Dutta, Asudeb

doi:10.1109/tcomm.2022.3167057

Cited by 4 publications

(1 citation statement)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…10, we have shown a comparison plot for the probability error in detecting objects using the classical and quantum algorithms. For the source detection in array processing, we have followed the QA-SDA algorithm as shown in [59] using the estimated Toeplitz matrix Ty . We have varied the SNR and kept all other parameters the same as Table 2.…”

Section: Comparison Of Estimated Spectrum In Array Processingmentioning

confidence: 99%

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

Laskar

Mondal

Dutta

2023

IEEE Trans. Quantum Eng.

Self Cite

View full text Add to dashboard Cite

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 matrices that demand very high computational complexity for large arrays. We demonstrate a low-complexity quantum simulation framework exploiting the structured Hamiltonian of Toeplitz and circulant variants. In this framework, we consider two approaches for the estimation of the eigenvalue spectrum of a given Toeplitz-structured matrix: first, an analytical framework with Jordan form-based sparse-decomposition of a dense-Toeplitz matrix, and second, an approximation method for the conversion of a Toeplitz matrix into a circulant matrix embedding quantum subroutines. We have also compared the efficacy of the proposed algorithms with standard Hamiltonian simulation and quantum phase estimation techniques for different quantum time resolutions and gate complexities. We show quantum gate-complexity analysis for our proposed algorithms. Considering the large dimensions of the Toeplitz matrix, we have employed random matrix theory in deriving the error bounds for the estimated eigenvalues. The numerical results are obtained partly in a classical computer and in an IBM quantum simulator.

show abstract

Section: Comparison Of Estimated Spectrum In Array Processingmentioning

confidence: 99%

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

Laskar

Mondal

Dutta

2023

IEEE Trans. Quantum Eng.

Self Cite

View full text Add to dashboard Cite

show abstract

A complexity efficient penta-diagonal quantum smoothing filter for bio-medical signal denoising: a study on ECG

Laskar,

Pratiher,

Dutta

et al. 2024

Sci Rep

View full text Add to dashboard Cite

Extracting information-bearing signal from a noisy environment has been a practical challenge in both classical and quantum computing formalism, especially in critical signal processing applications. To filter out the effect of noise, we propose a quantum smoothing filter built upon quantum formalism-based circuits applied for electrocardiogram signal denoising. The proposed quantum filter is a conceptually novel framework with an advantage in computational complexity as compared to the existing classical filters, such as discrete wavelet transform and empirical mode decomposition, whereas it achieves similar performance metrics for the accuracy of the filter. Further, we exploit the penta-diagonal Toeplitz structure of the smoothing filter, which gives approximately $$48\%$$ 48 % gate cost reduction for 10 qubit circuit compared to the standard Hamiltonian simulation without structure. The run-time complexity using the quantum matrix inversion technique for the structured matrix is given by $$\tilde{{\mathscr {O}}}\left( \frac{\kappa ^2 \text {poly}(\log {N})}{\varepsilon _P}\right)$$ O ~ κ 2 poly ( log N ) ε P for condition number $$\kappa$$ κ of the $$N\times N$$ N × N filter matrix within precision $$\varepsilon _P$$ ε P . Embedding fixed sparsity of the banded matrix, the quantum filter shows potentially better run-time complexity than classical filtering techniques. For the quantifiable research results of our work, we have shown several performance metrics, such as mean-square error and peak signal-to-noise ratio analysis, with a bound of error due to observation noise, simulation error and quantum measurement uncertainty.

show abstract

A Complexity-Efficient Quantum Architecture and Simulation for Eigen Spectrum Estimation of Vandermonde System in a Large Antenna Array

Laskar

Dutta

2023

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

Eigen-Spectrum Estimation and Source Detection in a Massive Sensor Array Based on Quantum Assisted Hamiltonian Simulation Framework

Cited by 4 publications

References 47 publications

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

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

A complexity efficient penta-diagonal quantum smoothing filter for bio-medical signal denoising: a study on ECG

A Complexity-Efficient Quantum Architecture and Simulation for Eigen Spectrum Estimation of Vandermonde System in a Large Antenna Array

Contact Info

Product

Resources

About