Abstract
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits (Valiant’s theorem) appear as two special cases. Viewing these simulatable classes as subsets of the space of all quantum computations, we may consider minimal extensions that suffice to regain full quantum computational power, which provides an approach to exploring the efficacy of quantum over classical computation.
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References
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Jozsa, R., Miyake, A.: Appearing as Proc. R. Soc (Lond.) A 464, 3089–3106 (2008); arXiv:quant-ph/0804.4050
Clark, S., Jozsa, R., Linden, N.: Quant. Inf. Comp. 8, 106–126 (2008)
Valiant, L.: SIAM J. Computing 31(4), 1229 (2002)
Knill, E.: (2001); arXiv:quant-ph/0108033
Terhal, B., DiVincenzo, D.: Phys. Rev. A 65, 032325 (2002)
Papadimitriou, C.: Computational Complexity. Addison-Wesley, Reading (1994)
Jordan, P., Wigner, E.: Zeitschrift für Physik. 47, 631 (1928)
Gottesman, D.: Stabilizer Codes and Quantum Error Correction, PhD thesis, California Institute of Technology, Pasadena, CA (1997)
Shi, Y.: Quant. Inf. Comp. 3, 84-92 (2003)
Clark, S.: J. Phys. A: Math. Gen. 39, 2701–2721 (2006)
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Jozsa, R. (2008). Invited Talk: Embedding Classical into Quantum Computation. In: Calmet, J., Geiselmann, W., Müller-Quade, J. (eds) Mathematical Methods in Computer Science. Lecture Notes in Computer Science, vol 5393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89994-5_5
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DOI: https://doi.org/10.1007/978-3-540-89994-5_5
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