Benchmarking and Analysis of Quantum Error Correction Codes
DOI:
https://doi.org/10.47611/jsrhs.v12i3.5127Keywords:
Quantum Computing, Qubits, Error CorrectionAbstract
Quantum Computing is a computing framework that takes advantage of unique quantum mechanical properties (such as superposition and entanglement) to perform calculations and implement algorithms that could offer exponential speed-ups over classical computing. However, in physical implementations of such quantum computers, qubits – the fundamental components of these systems – can accumulate errors that must be accounted for. In order to mitigate these errors, various quantum error correction (QEC) codes have been developed, including the repetition code and surface codes. In this experiment I implement and evaluate three types of QEC codes on the Qiskit simulator to compare their efficacy and applicability in correcting for different kinds of errors. I hypothesize that surface codes, with their more effective design and range of correction methods, should perform the best with much lower error thresholds and resultant logical error rates. The results support the hypothesis and suggest that surface codes are a viable method of implementing scalable error correction in quantum computers.
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Bravyi, S., Englbrecht, M., König, R., & Peard, N. (2018). Correcting coherent errors with surface codes. Npj Quantum Information, 4(1). https://doi.org/10.1038/s41534-018-0106-y
Chatterjee, A. (2023, April 18). Quantum Error Correction For Dummies. arXiv.org. https://arxiv.org/abs/2304.08678
Fowler, A. G., Mariantoni, M., Martinis, J. M., & Cleland, A. (2012). Surface codes: Towards practical large-scale quantum computation. Physical Review A, 86(3). https://doi.org/10.1103/physreva.86.032324
Grover, L. K. (1996, May 29). A fast quantum mechanical algorithm for database search. arXiv.org. https://arxiv.org/abs/quant-ph/9605043
Gutierrez, M., & Brown, K. H. (2015). Comparison of a quantum error-correction threshold for exact and approximate errors. Physical Review A, 91(2). https://doi.org/10.1103/physreva.91.022335
O’Gorman, J., Nickerson, N. H., Ross, P., Morton, J. M., & Benjamin, S. C. (2016). A silicon-based surface code quantum computer. Npj Quantum Information, 2(1). https://doi.org/10.1038/npjqi.2015.19
Shor, P. W. (1995). Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM Journal on Computing, 26(5), 1484–1509. https://doi.org/10.1137/s0097539795293172
Xue, X., Russ, M., Samkharadze, N., Undseth, B., Sammak, A., Scappucci, G., & Vandersypen, L. M. K. (2022). Quantum logic with spin qubits crossing the surface code threshold. Nature, 601(7893), 343–347. https://doi.org/10.1038/s41586-021-04273-w
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