Abstract
In this paper, we propose a quantum–classical hybrid filtering scheme used for denoising of a classical noisy image field. This includes an iterative procedure of transforming pairs of classical image and noise fields into quantum states using standard classical–quantum conversion and then posing the problem of constructing an optimal unitary operator based on the Hudson–Parthasarathy quantum stochastic calculus. The noisy quantum image state is filtered using an optimum unitary operator followed by quantum–classical conversion of the denoised quantum image state. Finally, filtering of the resultant classical image is performed using the standard median filtering approach. In addition to the proposed algorithm, our work includes a theoretical display of the Schrodinger evolution in the presence of classical randomness. The results demonstrate the marked superiority of our proposed algorithm over the existing classical denoising scheme.
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Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, USA, pp. 124–134 (1994). https://doi.org/10.1109/SFCS.1994.365700
Benioff, P.A.: Quantum mechanical Hamiltonian models of Turing machines. J. Stat. Phys. 29(3), 515–546 (1982)
Feynman, R.: Simulating physics with computers. Int. J. Theor. Phys. 21(6/7), 467–488 (1982)
Feynman, R.: Quantum mechanical computers. Opt. News 11, 11–20 (1985)
Deutsch, D.: Quantum theory, the Church–Turing principle, and the universal quantum Turing machine. Proc. R. Soc. Lond. A400, 97–117 (1985)
Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Long, G.L.: Grover algorithm with zero theoretical failure rate. Phys. Rev. A 64, 022307 (2001). https://doi.org/10.1103/PhysRevA.64.022307
Long, G.L., Zhang, W.L., Li, Y.S., Niu, L.: Arbitrary phase rotation of the marked state cannot be used for Grover’s quantum search algorithm. Commun. Theor. Phys. 32, 335–338 (1999)
Long, G.L., Li, Y.S., Zhang, W.L., Tu, C.C.: Dominant gate imperfection in Grover’s quantum search algorithm. Phys. Rev. A 61(4), 042305 (2000). https://doi.org/10.1103/PhysRevA.61.042305
Kato, T.: Perturbation Theory for Linear Operators. Springer, Berlin (1995). Reprint of the 1980 edition
Ai, Q., Li, Y.S., Long, G.L.: Influences of gate operation errors in the quantum counting algorithm. J. Sci. Technol. 21(6), 927–932 (2007)
Choi, M.: Completely positive linear maps on complex matrices. Linear Algebra Appl. 10(3), 285–290 (1975)
Kraus, K.: General state changes in quantum theory. Ann. Phys. 64(2), 311–355 (1971)
Stinespring, W.F.: Positive functions on \(\text{ C }^{*}\)-algebras. Proc. Am. Math. Soc. 6, 211–216 (1955)
Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976)
Brasil, C.A., Fanchini, F.F., Napolitano, R.J.: A simple derivation of the Lindblad equation. arXiv:1110.2122v2 [quant-ph] (2012)
Mastriani, Mario: Quantum Boolean image denoising. Quantum Inf. Process. 14(5), 1647–1673 (2015)
Wheeler, N.: Problems at the quantum/classical interface (2001). http://ebookily.org/pdf/problems-at-the-quantum-classical interface-174658500.html
Baylis, W.E., Cabrera, R., Keselica, D.: Quantum/classical interface: fermion spin. (2007) arXiv:0710.3144v2
Landsman, N.P.: Between classical and quantum (2005). arXiv:quant-ph/0506082v2
Wood, C.J., Biamonte, J.D., Cory, D.G.: Tensor networks and graphical calculus for open quantum systems. Quantum Inf. Comput. 15(9–10), 0759–0811 (2015)
Usher, N., Browne, D.E.: Noise in one-dimensional measurement-based quantum computing. arXiv:1704.07298v1 [quant-ph] (2017)
Wei, T.-C.: Quantum spin models for measurement-based quantum computation. Adv. Phys. X 3(1), 1461026 (2018)
Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum systems. Quantum Inf. Process. 9(1), 1–11 (2010)
Venegas-Andraca, S.E., Ball, J.L.: Storing images in entangled quantum systems. arXiv:quant-ph/0402085 (2003)
Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. Proc. SPIE Conf. Quantum Inf. Comput. 5105, 137–147 (2003). https://doi.org/10.1117/12.485960
Latorre, J.I.: Image compression and entanglement. arXiv:quant-ph/0510031v1 (2005)
Caruso, F., Giovannetti, V., Lupo, C., Mancini, S.: Quantum channels and memory effects. Rev. Mod. Phys. 86(4), 1203–1259 (2014)
Parthasarathy, K.R.: An Introduction to Quantum Stochastic Calculus. Birkhauser, Basel (1992)
Berg-Sørensen, K., Flyvbjerg, H.: The colour of thermal noise in classical Brownian motion: a feasibility study of direct experimental observation. N. J. Phys. 7, 38 (2005)
Kunita, H.: Itô’s stochastic calculus: its surprising power for applications. Stoch. Process. Appl. 120, 622–652 (2010)
Kupferman, R., Pavliotis, G.A., Stuart, A.M.: Itô versus Stratonovich white-noise limits for systems with inertia and colored multiplicative noise. Phys. Rev. E 70, 036120 (2004)
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Singh, R., Parthasarathy, H. & Singh, J. Quantum image restoration based on Hudson–Parthasarathy Schrodinger equation. Quantum Inf Process 18, 351 (2019). https://doi.org/10.1007/s11128-019-2466-4
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DOI: https://doi.org/10.1007/s11128-019-2466-4