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Quantum improvement in Spatial Discretization
Published 14 Dec 2023 in quant-ph | (2312.09036v1)
Abstract: Quantum algorithms have begun to surpass classical ones in several computation fields, yet practical application remains challenging due to hardware and software limitations. Here, we introduce a quantum algorithm that quadratically improves spatial discretization within these constraints. Implemented in the quantum software library Pennylane, our algorithm bridges the gap from theoretical models to tangible quantum circuitry. The approach promises enhanced efficiency in quantum spatial analysis, with simulations and hardware experiments validating its potential.
- Robert D Skeel and Martin Berzins, “A method for the spatial discretization of parabolic equations in one space variable,” SIAM journal on scientific and statistical computing 11, 1–32 (1990).
- Jonathan L Lustgarten, Vanathi Gopalakrishnan, Himanshu Grover, and Shyam Visweswaran, “Improving classification performance with discretization on biomedical datasets,” in AMIA annual symposium proceedings, Vol. 2008 (American Medical Informatics Association, 2008) p. 445.
- Divya Grover and Christos Dimitrakakis, “Adaptive belief discretization for pomdp planning,” arXiv preprint arXiv:2104.07276 (2021).
- Parfait Atchade-Adelomou, “Quantum algorithms for solving hard constrained optimisation problems,” (2022).
- Amit Sanyal, Nikolaj Nordkvist, and Monique Chyba, “An almost global tracking control scheme for maneuverable autonomous vehicles and its discretization,” IEEE Transactions on Automatic control 56, 457–462 (2010).
- Joseph Funke, Matthew Brown, Stephen M Erlien, and J Christian Gerdes, “Collision avoidance and stabilization for autonomous vehicles in emergency scenarios,” IEEE Transactions on Control Systems Technology 25, 1204–1216 (2016).
- David Molina, Julián Pérez-Beteta, Alicia Martínez-González, Juan Martino, Carlos Velásquez, Estanislao Arana, and Víctor M Pérez-García, “Influence of gray level and space discretization on brain tumor heterogeneity measures obtained from magnetic resonance images,” Computers in biology and medicine 78, 49–57 (2016).
- Feng Cao, Yong Ge, and Jinfeng Wang, “Spatial data discretization methods for geocomputation,” International journal of applied earth observation and geoinformation 26, 432–440 (2014).
- Lorena Fiorini, Federico Falasca, Alessandro Marucci, and Lucia Saganeiti, “Discretization of the urban and non-urban shape: Unsupervised machine learning techniques for territorial planning,” Applied Sciences 12, 10439 (2022).
- Parfait Atchade-Adelomou, Guillermo Alonso-Linaje, Jordi Albo-Canals, and Daniel Casado-Fauli, “qrobot: A quantum computing approach in mobile robot order picking and batching problem solver optimization,” Algorithms 14 (2021), 10.3390/a14070194.
- Atchade Parfait Adelomou, Elisabet Golobardes Ribe, and Xavier Vilasis Cardona, “Using the parameterized quantum circuit combined with variational-quantum-eigensolver (vqe) to create an intelligent social workers’ schedule problem solver,” (2020a).
- Saul Gonzalez-Bermejo, Guillermo Alonso-Linaje, and Parfait Atchade-Adelomou, “Gps: A new tsp formulation for its generalizations type qubo,” Mathematics 10, 416 (2022).
- Parfait Atchade-Adelomou and Kent Larson, “Fourier series weight in quantum machine learning,” (2023), arXiv:2302.00105 [quant-ph] .
- Atchade Parfait Adelomou, Elisabet Golobardes Ribe, and Xavier Vilasis Cardona, “Using the parameterized quantum circuit combined with variational-quantum-eigensolver (vqe) to create an intelligent social workers’ schedule problem solver,” arXiv e-prints , arXiv–2010 (2020).
- S. Consul-Pacareu, R. Montaño, Kevin Rodriguez-Fernandez, Àlex Corretgé, Esteve Vilella-Moreno, Daniel Casado-Faulí, and Parfait Atchade-Adelomou, “Quantum machine learning hyperparameter search,” (2023), arXiv:2302.10298 [cs.LG] .
- Parfait Atchade-Adelomou and Guillermo Alonso-Linaje, “Quantum-enhanced filter: Qfilter,” Soft Computing , 1–8 (2022).
- Guillermo Alonso-Linaje and Parfait Atchade-Adelomou, “Eva: a quantum exponential value approximation algorithm,” (2021), arXiv:2106.08731 [quant-ph] .
- Atchade Parfait Adelomou, Elisabet Golobardes Ribé, and Xavier Vilasis Cardona, “Formulation of the social workers’ problem in quadratic unconstrained binary optimization form and solve it on a quantum computer,” Journal of Computer and Communications 8, 44–68 (2020b).
- Parfait Atchade Adelomou, Daniel Casado Fauli, Elisabet Golobardes Ribé, and Xavier Vilasís-Cardona, “Quantum case-based reasoning (qcbr),” Artificial Intelligence Review 56, 2639–2665 (2023).
- Parfait Atchade-Adelomou, Elisabet Golobardes-Ribe, and Xavier Vilasis-Cardona, “Using the parameterized quantum circuit combined with variational-quantum-eigensolver (vqe) to create an intelligent social workers’ schedule problem solver,” (2020), arXiv:2010.05863 [quant-ph] .
- Juan Miguel Arrazola and Xanadu, “From nisq to isq,” https://pennylane.ai/blog/2023/06/from-nisq-to-isq/ (2023), (accessed November 1, 2023).
- Jean Braun and Malcolm Sambridge, “Modelling landscape evolution on geological time scales: a new method based on irregular spatial discretization,” Basin Research 9, 27–52 (1997).
- Florian Kummer, “Extended discontinuous galerkin methods for two-phase flows: the spatial discretization,” International Journal for Numerical Methods in Engineering 109, 259–289 (2017).
- Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, Shahnawaz Ahmed, Vishnu Ajith, M. Sohaib Alam, Guillermo Alonso-Linaje, B. AkashNarayanan, Ali Asadi, Juan Miguel Arrazola, Utkarsh Azad, Sam Banning, Carsten Blank, Thomas R Bromley, Benjamin A. Cordier, Jack Ceroni, Alain Delgado, Olivia Di Matteo, Amintor Dusko, Tanya Garg, Diego Guala, Anthony Hayes, Ryan Hill, Aroosa Ijaz, Theodor Isacsson, David Ittah, Soran Jahangiri, Prateek Jain, Edward Jiang, Ankit Khandelwal, Korbinian Kottmann, Robert A. Lang, Christina Lee, Thomas Loke, Angus Lowe, Keri McKiernan, Johannes Jakob Meyer, J. A. Montañez-Barrera, Romain Moyard, Zeyue Niu, Lee James O’Riordan, Steven Oud, Ashish Panigrahi, Chae-Yeun Park, Daniel Polatajko, Nicolás Quesada, Chase Roberts, Nahum Sá, Isidor Schoch, Borun Shi, Shuli Shu, Sukin Sim, Arshpreet Singh, Ingrid Strandberg, Jay Soni, Antal Száva, Slimane Thabet, Rodrigo A. Vargas-Hernández, Trevor Vincent, Nicola Vitucci, Maurice Weber, David Wierichs, Roeland Wiersema, Moritz Willmann, Vincent Wong, Shaoming Zhang, and Nathan Killoran, “Pennylane: Automatic differentiation of hybrid quantum-classical computations,” (2022), arXiv:1811.04968 [quant-ph] .
- Scott Aaronson and Andris Ambainis, “Quantum search of spatial regions,” (2005), arXiv:quant-ph/0303041 [quant-ph] .
- Lov K Grover, “A fast quantum mechanical algorithm for database search,” in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (1996) pp. 212–219.
- Shantanav Chakraborty, Leonardo Novo, Serena Di Giorgio, and Yasser Omar, “Optimal quantum spatial search on random temporal networks,” Physical Review Letters 119 (2017), 10.1103/physrevlett.119.220503.
- Erdos RENYI, “On random graph,” Publicationes Mathematicate 6, 290–297 (1959).
- Parfait Atchade-Adelomou and Saul Gonzalez, “Efficient quantum modular arithmetics for the isq era,” (2023), arXiv:2311.08555 [quant-ph] .
- N Metropolis, “Beginning of the monte carlo method. 1987,” Stanislaw Ulam 1984 (1909).
- Ulrich HE Hansmann and Yuko Okamoto, “New monte carlo algorithms for protein folding,” Current opinion in structural biology 9, 177–183 (1999).
- Engin Şahin, “Quantum arithmetic operations based on quantum fourier transform on signed integers,” International Journal of Quantum Information 18, 2050035 (2020).
- Charles R Baugh and Bruce A Wooley, “A two’s complement parallel array multiplication algorithm,” IEEE Transactions on computers 100, 1045–1047 (1973).
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