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International Journal of Quantum Information

Temperature Effect on Mølmer and Sørensen Model: A Two-Time Green's Function Method

Wei Li, Hongmin Zhao, Jia-tih Lin

Published Jun 1, 2003• 0 citations
Publisher

Abstract

Using two-time Green's function we analyze the effect of temperature on the Mølmer and Sørensen (M–S) model of cold trapped ion quantum computer. A formula for the deviation of an internal state from its ground state is derived in the first-order approximation. The fluctuation of internal state caused by thermal motion is also discussed. The deviation of internal state when different trap parameters changes with the temperature are given too. The upper temperature limit for regular quantum computation is obtained and our result is in agreement with experiment.

DOI
10.1142/s0219749903000152

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Using two-time Green's function we analyze the effect of temperature on the Mølmer and Sørensen (M–S) model of cold trapped ion quantum computer. A formula for the deviation of an internal state from its ground state is derived in the first-order approximation. The fluctuation of internal state caused by thermal motion is also discussed. The deviation of internal state when different trap parameters changes with the temperature are given too. The upper temperature limit for regular quantum computation is obtained and our result is in agreement with experiment.
We analyzed the influence of the thermal motion from the environment on the internal states of trapped ions and the center-of-mass mode phonon using a Green's-function method. The deviation of the internal states and the variational rules of the phonon number with different trap parameters changing with the temperature are given. The upper limit of the temperature at which the gate operation can be performed safely is convenient to be found out according to different error correction capability.
Abstract We discuss how to simplify the Mølmer–Sørensen (MS) gate which is used for the trapped ion quantum computer. The original MS gate is implemented by illuminating two ions with bichromatic coherent light fields separately at the same time. In this paper, we propose a method for transforming a separable state of two ions into one of the Bell states by illuminating the two ions with monochromatic coherent light fields individually and this point is the advantage of our scheme over the original MS gate. The length of the execution time of our proposed gate is comparable to that of the original MS gate, however, numerical calculations show that our proposed gate is weakly sensitive to thermal fluctuations of the phonons. By giving another example of a simple two-ion gate that can generate entanglement but is strongly vulnerable to thermal fluctuations, we show that our simplified MS gate is more marked than usual.
Constructing a large-scale ion trap quantum processor will require entangling gate operations that are robust in the presence of noise and experimental imperfection. We experimentally demonstrate how a new type of Mølmer-Sørensen gate protects against infidelity caused by heating of the motional mode used during the gate. Furthermore, we show how the same technique simultaneously provides significant protection against slow fluctuations and mis-sets in the secular frequency. Since this parameter sensitivity is worsened in cases where the ions are not ground-state cooled, our method provides a path towards relaxing ion cooling requirements in practical realizations of quantum computing and simulation.