Abstract
One of the challenges facing current noisy-intermediate-scale-quantum devices is achieving efficient quantum circuit measurement or readout. The process of extracting classical data from the quantum domain, termed in this work as quantum-to-classical (Q2C) data decoding, generally incurs significant overhead, since the quantum circuit needs to be sampled repeatedly to obtain useful data readout. In this paper, we propose and evaluate time-efficient and depth-optimized Q2C methods based on the multidimensional, multilevel-decomposable, quantum wavelet transform (QWT) whose packet and pyramidal forms are leveraged and optimized. We also propose a zero-depth technique that uses selective placement of measurement gates to perform the QWT operation. To demonstrate their efficiency, the proposed techniques are quantitatively evaluated in terms of their temporal complexity (circuit depth and execution time), spatial complexity (total gate count), and accuracy (fidelity/similarity) in comparison to existing Q2C techniques. Experimental evaluations of the proposed Q2C methods are performed on a 27-qubit state-of-the-art quantum computing device from IBM Quantum using real high-resolution multispectral images. The proposed QHT-based Q2C method achieved up to \(15\times\) higher space efficiency than the QFT-based Q2C method, while the proposed zero-depth method achieved up to 14% and 78% improvements in execution time compared to conventional Q2C and QFT-based Q2C, respectively.
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Rønnow TF, Wang Z, Job J, Boixo S, Isakov SV, Wecker D, Martinis JM, Lidar DA, Troyer M (2014) Defining and detecting quantum speedup. Science 345(6195):420–424
Shor PW (1999) Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev 41(2):303–332
Grover LK (1997) Quantum mechanics helps in searching for a needle in a haystack. Phys Rev Lett 79(2):325
Guan W, Perdue G, Pesah A, Schuld M, Terashi K, Vallecorsa S, Vlimant J-R (2021) Quantum machine learning in high energy physics. Mach Learn Sci Technol 2(1):011003
Preskill J (2018) Quantum computing in the nisq era and beyond. Quantum 2:79
Weigold M, Barzen J, Leymann F, Salm M (2020) Data encoding patterns for quantum computing. In HILLSIDE Proc of Conf on Pattern Lang of Prog. 22
Lanzagorta M, Uhlmann J (2008) Is quantum parallelism real? In quantum information and computation VI, volume 6976, page 69760W. International Society for Optics and Photonics
Mahmud N, Jeng MJ, Nobel M, Chaudhary M, Islam SM, Levy D, El-Araby E (2022) Time-efficient quantum-to-classical data decoding. In: The International Conference on Emergent Quantum Technologies (ICEQT 2022), Las Vegas, Nevada, USA, July 2022. To appear in Transactions on Computational Science and Computational Intelligence, Springer Nature—Research Book Series
Fijany A, Williams CP (1998) Quantum wavelet transforms: Fast algorithms and complete circuits. In NASA International Conference on Quantum Computing and Quantum Communications, pages 10–33. Springer
Li HS, Fan P, Peng H, Song S, Long GL (2021) Multilevel 2-D quantum wavelet transforms. IEEE Trans Cybern 52(8):8467–80
Mahmud N, MacGillivray A, Chaudhary M, El-Araby E (2022) Decoherence-optimized circuits for multi-dimensional and multi-level decomposable quantum wavelet transform. IEEE Internet Comput 26(01):15–25
Mahmud N, Haase-Divine B, MacGillivray A, El-Araby E (2020) Quantum dimension reduction for pattern recognition in high-resolution spatio-spectral data. IEEE Trans Comput 71(1):1–12
IBM Quantum (2021) Qiskit: An open-source framework for quantum computing
Williams CP, Clearwater SH (1998) Explorations in quantum computing. Springer
IBM Quantum (2023) QuantumCircuit.depth() [computer software]. https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.depth.html, Accessed 23 May 2023
Zhang C, Chen Y, Jin Y, Ahn W, Zhang Y, Zhang EZ (2020) A depth-aware swap insertion scheme for the qubit mapping problem. arXiv preprint arXiv:2002.07289
El-Araby E, El-Ghazawi T, Le Moigne J, Gaj K (2004) Wavelet spectral dimension reduction of hyperspectral imagery on a reconfigurable computer. In Proceedings. 2004 IEEE International Conference on Field-Programmable Technology (IEEE Cat. No. 04EX921), pp 399–402. IEEE
Wickerhauser MV (1994) Adapted wavelet analysis: from theory to software. Routledge
Kaewpijit S, Le Moigne J, El-Ghazawi T (2003) Automatic reduction of hyperspectral imagery using wavelet spectral analysis. IEEE Trans Geosci Remote Sens 41(4):863–871
Pearson K (1895) Note on regression and inheritance in the case of two parents. Proc R Soc Lond 58:240–242
IBM Quantum (2023) QFT [computer software]. https://qiskit.org/documentation/stubs/qiskit.circuit.library.QFT.html. Accessed 23 May 2023
IBM Quantum (2023) https://quantum-computing.ibm.com/. Accessed 23 May 2023
IBM Quantum (2023) Initialize [computer software]. https://qiskit.org/documentation/stubs/qiskit.extensions.Initialize.html. Accessed 23 May 2023
IBM Quantum (2023) StatePreparation [computer software]. https://qiskit.org/documentation/stubs/qiskit.circuit.library.StatePreparation.html. Accessed 23 May 2023
Shende VV, Bullock SS, Markov IL (2006) Synthesis of quantum-logic circuits. IEEE Trans Comput Aided Des Integr Circuits Syst 25(6):1000–1010
IBM Quantum (2023) QuantumCircuit.count_ops() [computer software]. https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.count_ops.html. Accessed 23 May 2023
Han D, Guo C, Wang X (2022) Density matrix reconstruction using non-negative matrix product states. Phys Rev A 106(4):042435
Cramer M, Plenio MB, Flammia ST, Somma R, Gross D, Bartlett SD, Landon-Cardinal O, Poulin D, Liu YK (2010) Efficient quantum state tomography. Nature Commun 1(1):149
Pivoluska M, Plesch M (2022) Implementation of quantum compression on ibm quantum computers. Sci Rep 12(1):5841
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This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.
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All authors reviewed the manuscript. All authors, particularly DL, VJ, JB, and AM, participated in preparing the figures and tables. The lead author, MJ, lead the effort of conducting the experimental work with SIUI, MC, MAIN, and DK. The lead author, MJ, and AR, participated in developing the analytical models, writing the coding scripts, and analyzing and discussing the experimental data. EEA and NM generated the idea for this work, and developed the initial system design and code. EEA guided the direction of the paper and ensured that the quality of its contribution was sufficient for publication.
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Jeng, M., Islam, S.I.U., Levy, D. et al. Improving quantum-to-classical data decoding using optimized quantum wavelet transform. J Supercomput 79, 20532–20561 (2023). https://doi.org/10.1007/s11227-023-05433-7
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DOI: https://doi.org/10.1007/s11227-023-05433-7