dorsal/arxiv
View SchemaPerturbation Theory and Numerical Modeling of Quantum Logic Operations with a Large Number of Qubits
| Authors | G. P. Berman, G. D. Doolen, D. I. Kamenev, G. V. Lopez, V. I. Tsifrinovich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0107038 |
| URL | https://arxiv.org/abs/quant-ph/0107038 |
Abstract
The perturbation theory is developed based on small parameters which naturally appear in solid state quantum computation. We report the simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain is considered in which selective excitations of spins are provided by having a uniform gradient of the external magnetic field. Quantum logic operations are utilized by applying resonant electromagnetic pulses. The spins interact with their nearest neighbors. We simulate the creation of the long-distance entanglement between remote qubits in the spin chain. Our method enables us to minimize unwanted non-resonant effects in a controlled way. The method we use cannot simulate complicated quantum logic (a quantum computer is required to do this), but it can be useful to test the experimental performance of simple quantum logic operations. We show that: (a) the probability distribution of unwanted states has a ``band'' structure, (b) the directions of spins in typical unwanted states are highly correlated, and (c) many of the unwanted states are high-energy states of a quantum computer (a spin chain). Our approach can be applied to simple quantum logic gates and fragments of quantum algorithms involving a large number of qubits.
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"abstract": "The perturbation theory is developed based on small parameters which\nnaturally appear in solid state quantum computation. We report the simulations\nof the dynamics of quantum logic operations with a large number of qubits (up\nto 1000). A nuclear spin chain is considered in which selective excitations of\nspins are provided by having a uniform gradient of the external magnetic field.\nQuantum logic operations are utilized by applying resonant electromagnetic\npulses. The spins interact with their nearest neighbors. We simulate the\ncreation of the long-distance entanglement between remote qubits in the spin\nchain. Our method enables us to minimize unwanted non-resonant effects in a\ncontrolled way. The method we use cannot simulate complicated quantum logic (a\nquantum computer is required to do this), but it can be useful to test the\nexperimental performance of simple quantum logic operations. We show that: (a)\nthe probability distribution of unwanted states has a ``band\u0027\u0027 structure, (b)\nthe directions of spins in typical unwanted states are highly correlated, and\n(c) many of the unwanted states are high-energy states of a quantum computer (a\nspin chain). Our approach can be applied to simple quantum logic gates and\nfragments of quantum algorithms involving a large number of qubits.",
"arxiv_id": "quant-ph/0107038",
"authors": [
"G. P. Berman",
"G. D. Doolen",
"D. I. Kamenev",
"G. V. Lopez",
"V. I. Tsifrinovich"
],
"categories": [
"quant-ph"
],
"title": "Perturbation Theory and Numerical Modeling of Quantum Logic Operations with a Large Number of Qubits",
"url": "https://arxiv.org/abs/quant-ph/0107038"
},
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