A quantum-inspired version of the nearest mean classifier
- 303 Downloads
We introduce a framework suitable for describing standard classification problems using the mathematical language of quantum states. In particular, we provide a one-to-one correspondence between real objects and pure density operators. This correspondence enables us: (1) to represent the nearest mean classifier (NMC) in terms of quantum objects, (2) to introduce a quantum-inspired version of the NMC called quantum classifier (QC). By comparing the QC with the NMC on different datasets, we show how the first classifier is able to provide additional information that can be beneficial on a classical computer with respect to the second classifier.
KeywordsBloch sphere Quantum classifier Non-standard application of quantum formalism
This work has been partly supported by the project “Computational quantum structures at the service of pattern recognition: modeling uncertainty” (CRP-59872) funded by Regione Autonoma della Sardegna, L.R. 7/2007 (2012) and the FIRB project “Structures and Dynamics of Knowledge and Cognition” (F21J12000140001).
Funding This study was funded by Regione Autonoma della Sardegna, L.R. 7/2007, CRP-59872 (2012).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Aerts D, D’Hooghe B (2009) Classical logical versus quantum conceptual thought: examples in economics, decision theory and concept theory. Quantum interaction (Lecture Notes in Computer Science), vol 5494. Springer, Berlin, pp 128–142Google Scholar
- Aerts D, Gabora L, Sozzo S (2013) Concepts and their dynamics: a quantum-theoretic modeling of human thought. Top Cogn Sci 5(4):737–772Google Scholar
- Aharonov D, Kitaev A, Nisan N (1998) Quantum circuits with mixed states. In: Proceedings of the 30th annual ACM symposium on theory of computing, pp 20–30. ACMGoogle Scholar
- Barnett SM (2009) Quantum information, 16, Oxford Master Series in Physics. Oxford University Press, Oxford. Oxford Master Series in Atomic, Optical, and Laser PhysicsGoogle Scholar
- Caraiman S, Manta V (2012) Image processing using quantum computing. In: IEEE 16th international conference on system theory, control and computing (ICSTCC), 2012, pp 1–6Google Scholar
- Chefles A (2000) Quantum state discrimination. Contemp Phys 41(6):401–424. arXiv:quant-ph/0010114
- Jaeger G (2007) Quantum information. Springer, New York (An overview, With a foreword by Tommaso Toffoli)Google Scholar
- Kimura G, Kossakowski A (2005) The Bloch-vector space for N-level systems: the spherical-coordinate point of view. Open Syst Inf Dyn 12(03):207–229. arXiv:quant-ph/0408014
- Lloyd S, Mohseni M, Rebentrost P (2013) Quantum algorithms for supervised and unsupervised machine learning. arXiv:1307.0411
- Miszczak JA (2012) High-level structures for quantum computing, 6 synthesis (Lectures on Quantum Computing). Morgan and Claypool Publishers, San RafaelGoogle Scholar
- Nagel E (1963) Assumptions in economic theory. Am Econ Rev 53(2):211–219Google Scholar
- Ostaszewski M, Sadowski P, Gawron P (2015) Quantum image classification using principal component analysis. Theor Appl Inf 27:3. arXiv:1504.00580
- Schuld M, Sinayskiy I, Petruccione F (2014a) An introduction to quantum machine learning. Contemp Phys 56(2). arXiv:1409.3097
- Schuld M, Sinayskiy I, Petruccione F(2014b) Quantum computing for pattern classification. In: PRICAI 2014: trends in artificial intelligence, pp 208–220. SpringerGoogle Scholar
- Sozzo S (2015) Effectiveness of the quantum-mechanical formalism in cognitive modeling. Soft Comput. doi: 10.1007/s00500-015-1834-y
- Wiebe N, Kapoor A, Svore KM (2015) Quantum nearest-neighbor algorithms for machine learning. Quantum Inf Comput 15(34):0318–0358Google Scholar