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The Universe and the Quantum Computer

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Abstract

It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement-based quantum computation. Although a rigorous concrete model for the universe has not been completed, a quantum measure and integration theory has been developed which may be useful for future progress. In this work we show that the quantum integral is the unique functional satisfying certain basic physical and mathematical principles. Since the set of paths (or trajectories) for a quantum computer is finite, this theory is easier to treat and more developed. We observe that the sum of the quantum measures of the paths is unity and the total interference vanishes. Thus, constructive interference is always balanced by an equal amount of destructive interference. As an example we consider a simplified two-slit experiment.

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References

  1. Briegel, H., Browne, D., Dür, W., Raussendorf, R., Van der Nest, M.: Measurement-based quantum computation. Nat. Phys. 51, 19–26 (2009)

    Article  Google Scholar 

  2. Dowker, F., Ghazi-Tabatabai, Y.: Dynamical wave function collapse models in quantum measure theory. J. Phys. A 41, 205306 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  3. Dowker, F., Johnston, S., Sorkin, R.: Hilbert spaces from path integrals (2010). arXiv:1002.0589 [quant-ph]

  4. Gross, D., Eisert, J., Shuch, N., Perez-Garcia, D.: Measurement-based quantum computation beyond the one-way model. Phys. Rev. A 76, 052315 (2007)

    Article  ADS  Google Scholar 

  5. Gudder, S.: Quantum measure theory. Math. Slovaca 60, 681–700 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gudder, S.: Quantum measure and integration theory. J. Math. Phys. 50, 123509 (2009). arXiv:0909.2203 [quant-ph]

    Article  MathSciNet  ADS  Google Scholar 

  7. Haliwell, J.J.: Partial decoherence of histories and the Diosi test. arXiv:0904.4388 [quant-ph], and Quant. Info. Proc. (2009, to appear)

  8. Isham, C.: Quantum logic and the histories approach to quantum theory. J. Math. Phys. 35, 2157–2185 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Jozsa, R.: An introduction to measurement based quantum computation (2009). arXiv:quant-ph/0508124

  10. Martin, X., O’Connor, D., Sorkin, R.: The random walk in generalized quantum theory. Phys. Rev. D 71, 024029 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  11. Sorkin, R.: Quantum mechanics as quantum measure theory. Mod. Phys. Lett. A 9, 3119–3127 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Sorkin, R.: Quantum measure theory and its interpretation. In: Feng, D., Hu, B.-L. (eds.) Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, pp. 229–251 (1994)

    Google Scholar 

  13. Sorkin, R.: Quantum mechanics without the wave function. J. Phys. A 40, 3207–3231 (2007)

    MathSciNet  ADS  MATH  Google Scholar 

Download references

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  1. Department of Mathematics, University of Denver, Denver, CO, 80208, USA

    Stan Gudder

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  1. Stan Gudder
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Correspondence to Stan Gudder.

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Gudder, S. The Universe and the Quantum Computer. Int J Theor Phys 50, 3800–3811 (2011). https://doi.org/10.1007/s10773-011-0667-4

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  • DOI: https://doi.org/10.1007/s10773-011-0667-4

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