Abstract
In this study we consider a qubit (quantum bit) as the spin degree of freedom of a spin-1/2 particle. Since the 2D plane and the 2-sphere minus the north pole are topologically equivalent, one can represent motion on the 2D plane on the 2-sphere. We use inverse stereographic projection to map the 2D plane to the 2-sphere minus the north pole. Because the 2-sphere can be thought of as the Bloch sphere where any point represents a qubit, the time evolution of a particle on the 2D plane corresponds to the time evolution of the corresponding qubit on the Bloch sphere. We use the property of magnetic field to rotate spins to provide exact time dependent magnetic field to simulate, using a single qubit, the path followed by a particle on the 2D plane.
Thanks
We would like to thank Soley Ersoy and Mehmet Ali Güngör who provided useful comments about the draft of this paper. We would also like to thank anonymous referees for useful suggestions that improved the paper.
References
- Barnett SM., Quantum Information. Oxford University Press (2014)
- Goldstein H., Poole C., Safko J., Classical Mechanics, Addison-Wesley, Third International edition, (2002)
- Griffiths DJ., Introduction to Quantum Mechanics, Pearson Prentice Hall, Second International edition, (2005)
- Huggett S. Jordan D., A Topological Aperitif. Springer Science & Business Media, (2009)
- Sakurai JJ. and Napolitano J., Modern Quantum Mechanics. Addison-Wesley, Second International edition (2011)
Abstract
Bu çalışmada bir spin-1/2 parçacığın spin serbesti derecesi olarak bir kübiti (kuantum bit) ele alıyoruz. İki boyutlu düzlem ve kuzey kutbu çıkartılmış 2-küre topolojik olarak eşdeğer olduklarından, iki boyutlu düzlemdeki hareket 2-küre üzerinde temsil edilebilir. Ters stereografik fonksiyonu kullanarak iki boyutlu düzlemi 2-küre üzerine aktarıyoruz. Öte yandan 2-küre, üzerindeki her noktanın bir kübiti temsil ettiği Bloch küresi olarak düşünülebildiğinden, bir parçacığın iki boyutlu düzlem üzerindeki zaman içindeki evrimi, buna karşılık gelen kübitin Bloch küresi üzerinde zaman içindeki evrimine karşılık gelir. Manyetik alanın spini döndürebilme özelliğini kullanarak iki boyutlu bir düzlemdeki parçacığın hareketinin tek bir kübit kullanılarak simüle edilmesini sağlayacak zamana bağımlı manyetik alanın tam formunu veriyoruz.
References
- Barnett SM., Quantum Information. Oxford University Press (2014)
- Goldstein H., Poole C., Safko J., Classical Mechanics, Addison-Wesley, Third International edition, (2002)
- Griffiths DJ., Introduction to Quantum Mechanics, Pearson Prentice Hall, Second International edition, (2005)
- Huggett S. Jordan D., A Topological Aperitif. Springer Science & Business Media, (2009)
- Sakurai JJ. and Napolitano J., Modern Quantum Mechanics. Addison-Wesley, Second International edition (2011)
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Physics |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 28, 2021 |
| Submission Date | March 8, 2021 |
| Published in Issue | Year 2021 Volume: 3 Issue: 1 |
Cite
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