dorsal/arxiv
View SchemaQuantum computation with Kerr-nonlinear photonic crystals
| Authors | Hiroo Azuma |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604086 |
| URL | https://arxiv.org/abs/quant-ph/0604086 |
| DOI | 10.1088/0022-3727/41/2/025102 |
| Journal | J. Phys. D: Appl. Phys. 41 (2008) 025102 |
Abstract
In this paper, we consider a method for implementing a quantum logic gate with photons whose wave function propagates in a one-dimensional Kerr-nonlinear photonic crystal. The photonic crystal causes the incident photons to undergo Bragg reflection by its periodic structure of dielectric materials and forms the photonic band structure, namely, the light dispersion relation. This dispersion relation reduces the group velocity of the wave function of the photons, so that it enhances nonlinear interaction of the photons. (Because variation of the group velocity against the wave vector is very steep, we have to tune up the wavelength of injected photons precisely, however.) If the photonic crystal includes layers of a Kerr medium, we can rotate the phase of the wave function of the incident photons by a large angle efficiently. We show that we can construct the nonlinear sign-shift (NS) gate proposed by Knill, Laflamme, and Milburn (KLM) by this method. Thus, we can construct the conditional sign-flip gate for two qubits, which is crucial for quantum computation. Our NS gate works with probability unity in principle while KLM's original one is a nondeterministic gate conditioned on the detection of an auxiliary photon.
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"abstract": "In this paper, we consider a method for implementing a quantum logic gate\nwith photons whose wave function propagates in a one-dimensional Kerr-nonlinear\nphotonic crystal. The photonic crystal causes the incident photons to undergo\nBragg reflection by its periodic structure of dielectric materials and forms\nthe photonic band structure, namely, the light dispersion relation. This\ndispersion relation reduces the group velocity of the wave function of the\nphotons, so that it enhances nonlinear interaction of the photons. (Because\nvariation of the group velocity against the wave vector is very steep, we have\nto tune up the wavelength of injected photons precisely, however.) If the\nphotonic crystal includes layers of a Kerr medium, we can rotate the phase of\nthe wave function of the incident photons by a large angle efficiently. We show\nthat we can construct the nonlinear sign-shift (NS) gate proposed by Knill,\nLaflamme, and Milburn (KLM) by this method. Thus, we can construct the\nconditional sign-flip gate for two qubits, which is crucial for quantum\ncomputation. Our NS gate works with probability unity in principle while KLM\u0027s\noriginal one is a nondeterministic gate conditioned on the detection of an\nauxiliary photon.",
"arxiv_id": "quant-ph/0604086",
"authors": [
"Hiroo Azuma"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0022-3727/41/2/025102",
"journal_ref": "J. Phys. D: Appl. Phys. 41 (2008) 025102",
"title": "Quantum computation with Kerr-nonlinear photonic crystals",
"url": "https://arxiv.org/abs/quant-ph/0604086"
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