Performance and error modeling of Deutsch's algorithm in IBM Q

E. Buksman, A. L. Fonseca de Oliveira, C. Allende

Abstract


The performance of quantum computers today can be studied by analyzing the
eect of errors in the result of simple quantum algorithms. The modeling and char-
acterization of these errors is relevant to correct them, for example, with quantum
correcting codes. In this article we characterize the error of the ve qubits quantum
computer ibmqx4 (IBM Q), using a Deutsch algorithm and modeling the error by
Generalized Amplitude Damping (GAD) and a unitary misalignment operation.


Keywords


Quantum Information, Quantum Deutsch's algorithm, Quantum error models,

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References


Richard P. Feynman. Simulating physics with computers. Int J. Theor. Phys., 21:467{488,

David Deutsch and Roger Penrose. Quantum theory, the church;turing principle and the universal quantum computer. Proceedings of the Royal Society of London. A. Mathematical

and Physical Sciences., 400(1818):97{117, 1985.

Ran Raz and Avishay Tal. Oracle separation of bqp and ph. Technical report, Weizmann

Institute of Science Electronic Colloquium on Computational Complexity., 2018.

V Dunjko and HJ Briegel. Machine learning & articial intelligence in the quantum domain: a review of recent progress. Rep Prog Phys., 81(7), 2018.

ibmq,https://www.research.ibm.com/ibm-q

Lov K. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing, 1996.

Peter W. Shor. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A, 52:R2493{R2496, Oct 1995.

Simon J Devitt, William Munro, and Kae Nemoto. Quantum error correction for beginners.Reports on progress in physics. Physical Society (Great Britain)., 76:076001, 06 2013.

Matthew Otten and Stephen K. Gray. Recovering noise-free quantum observables. Phys. Rev. A., 99:012338, Jan 2019.

Daniel Gottesman. Quantum error correction and fault-tolerance. Encyclopedia of Mathematical Physics., 08 2005.

David Deutsch and Richard Jozsa. Rapid solution of problems by quantum computation. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.,439(1907):553{558, 1992.

Davide Ferrari and Michele Amoretti. Efcient and efective quantum compiling for entanglement-based machine learning on ibm q devices. International Journal of Quantum Information, 16(08):1840006, 2018.

Diego Riste, Marcus P. da Silva, Colm A. Ryan, Andrew W. Cross, Antonio D. Crcoles,12 John A. Smolin, Jay M. Gambetta, Jerry M. Chow, and Blake R. Johnson. Demonstration of

quantum advantage in machine learning. npj Quantum Information, 3, 2017.

Robin Harper and Steven T. Flammia. Fault-tolerant logical gates in the ibm quantum experience. Phys. Rev. Lett., 122:080504, Feb 2019.

André L. Fonseca de Oliveira, Efrain Buksman, Ilan Cohn, and Jesús García López de Lacalle. Characterizing error propagation in quantum circuits: the isotropic index. Quantum

Information Processing, 16(2):48, 2017.

Michel A. Nielsen and Isaac L. Chuang. Quantum computation and quantum information. Cambridge University Press., 2000.

Harold V. Henderson and S. R. Searle. The vec-permutation matrix, the vec operator and kronecker products: a review. Linear and Multilinear Algebra, 9(4):271{288, 1981.

Robert Alicki, Michal Horodecki, Pawel Horodecki, and Ryszard Horodecki. Dynamical description of quantum computing: Generic nonlocality of quantum noise. Phys. Rev. A.,

:062101, May 2002.

Daniel Greenbaum and Zachary Dutton. Modeling coherent errors in quantum error correction. Quantum Science and Technology, 3(1), 2017.

K. Kraus. Lecture notes in physics. In States, Efects and Operations. Fundamental Notions of Quantum Theory., volume 190. Springer-Verlag, 1983.

Ilan Cohn, André L. Fonseca De Oliveira, Efrain Buksman, and Jesús García López De Lacalle. Grovers search with local and total depolarizing channel errors: Complexity analysis. International Journal of Quantum Information, 14(02):1650009, 2016.




DOI: https://doi.org/10.31349/RevMexFis.66.239

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