dorsal/arxiv
View SchemaA Study on the Noise Threshold of Fault-tolerant Quantum Error Correction
| Authors | Y. C. Cheng, R. J. Silbey |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412168 |
| URL | https://arxiv.org/abs/quant-ph/0412168 |
| DOI | 10.1103/PhysRevA.72.012320 |
| Journal | Phys. Rev. A 72, 012320 (2005) |
Abstract
Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian where the system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. This noise model enables us to investigate the effect of noise in quantum circuits under realistic device conditions and avoid strong assumptions such as maximal parallelism and weak storage errors. Noise thresholds of the QEC codes are calculated. In addition, the effects of imprecision in projective measurements, collective bath, fault-tolerant repetition protocols, and level of parallelism in circuit constructions on the threshold values are also studied with emphasis on determining the optimal design for the fault-tolerant QEC circuit. These results provide insights into the fault-tolerant QEC process as well as useful information for designing the optimal fault-tolerant QEC circuit for particular physical implementation of quantum computer.
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"abstract": "Quantum circuits implementing fault-tolerant quantum error correction (QEC)\nfor the three qubit bit-flip code and five-qubit code are studied. To describe\nthe effect of noise, we apply a model based on a generalized effective\nHamiltonian where the system-environment interactions are taken into account by\nincluding stochastic fluctuating terms in the system Hamiltonian. This noise\nmodel enables us to investigate the effect of noise in quantum circuits under\nrealistic device conditions and avoid strong assumptions such as maximal\nparallelism and weak storage errors. Noise thresholds of the QEC codes are\ncalculated. In addition, the effects of imprecision in projective measurements,\ncollective bath, fault-tolerant repetition protocols, and level of parallelism\nin circuit constructions on the threshold values are also studied with emphasis\non determining the optimal design for the fault-tolerant QEC circuit. These\nresults provide insights into the fault-tolerant QEC process as well as useful\ninformation for designing the optimal fault-tolerant QEC circuit for particular\nphysical implementation of quantum computer.",
"arxiv_id": "quant-ph/0412168",
"authors": [
"Y. C. Cheng",
"R. J. Silbey"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.012320",
"journal_ref": "Phys. Rev. A 72, 012320 (2005)",
"title": "A Study on the Noise Threshold of Fault-tolerant Quantum Error Correction",
"url": "https://arxiv.org/abs/quant-ph/0412168"
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