Intern. J. Fuzzy Mathematical Archive Vol. 10, No. 2, 2016, 139-145 ISSN: 2320 –3242 (P), 2320 –3250 (online) Published on 12 May 2016 www.researchmathsci.org 139    Neutrosophic Quantum Computer Florentin Smarandache University of New Mexico Mathematics & Science Department 705 Gurley Ave., Gallup, NM 87301, USA Email: smarand@unm.edu Received 4 May 2016; accepted 11 May 2016 Abstract. This paper is a theoretical approach for a potential neutrosophic quantum computer to be built in the future, which is an extension of the classical theoretical quantum computer, into which the indeterminacy is inserted. Keywords: neutrobit, indeterminacy, neutrosophic quantum, neutrosophic polarization, neutrosophic particle, entangled neutrosophic particles, neutrosophic superposition, neutrosophic dynamic system, neutrosophic Turing machine, neutrosophic quantum functions AMS Mathematics Subject Classification (2010): 46N50 1. Introduction Neutrosophic quantum communication is facilitated by the neutrosophic polarization, that favors the use the neutrosophic superposition and neutrosophic entanglement. The neutrosophic superposition can be linear or non-linear. While into the classical presumptive quantum computers there are employed only the coherent superpositions of two states (0 and 1), in the neutrosophic quantum computers one supposes the possibilities of using coherent superpositions amongst three states (0, 1, and I = indeterminacy) and one explores the possibility of using the decoherent superpositions as well. 2. Neutrosophic polarization The neutrosophic polarization of a photon is referred to as orientation of the oscillation of the photon: oscillation in one direction is interpreted as 0, oscillation in opposite direction is interpreted as 1, while the ambiguous or unknown or vague or fluctuating back and forth direction as I (indeterminate). Thus, the neutrosophic polarization of a photon is 0, 1, or I. Since indeterminacy (I) does exist independently from 0 and 1 , we cannot use fuzzy nor intuitionistic fuzzy logic / set, but neutrosophic logic / set. These three neutrosophic values are used for neutrosophically encoding the data. 3. Refined neutrosophic polarization In a more detailed development, one may consider the refined neutrosophic polarization, where we refine for example I as I 1 (ambiguous direction), I 2 (unknown direction), I 3 (fluctuating direction), etc.