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高能物理与核物理计算国际会议公报：英文版

The Temperature Effects on the Ion Trap Quantum Computer

Hong-min, JiatiLIN

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

We consider one source of decoherence for a quantum computer composed of many trapped ions due to the thermal effects of the system in the presence of laser-ion interaction.The upper limit of the temperature at which the logical gate operations could be carried out reliably is given,and our result is agreement with the experiment.

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•May 1, 1997•0 citations
This thesis is concerned with various aspects of ion traps and their use as a quantum simulation and computation device. In its first part we investigate various sources of noise and decoherence in ion traps. As quantum information is very fragile, a detailed knowledge of noise and decoherence sources in a quantum computation device is essential. In the special case of an ion trap quantum computer we investigate the effects of intensity and phase noise in the laser, which is used to perform the gate operations. We then look at other sources of noise which are present without a laser being switched on. These are fluctuations in the trapping frequency caused by noise in the electric potentials applied to the trap and fluctuating electrical fields which will cause heating of the centre-of-mass vibrational state of the ions in the trap. For the case of fluctuating electrical fields we estimate the effect on a quantum gate operation. We then propose a scheme for performing quantum gates without having the ions cooled down to their motional ground state. The second part deals with various aspects of the use of ion traps as a device for quantum computation. We start with the use of ionic qubits as a measurement device for the centre-of-mass vibrational mode and investigate in detail the effect these measurements will have on the vibrational mode. If one wants to use quantum computation devices as systems to simulate quantum mechanics, it is of interest to know how to simulate say a k-level system with N qubits. We investigate the easiest case of this wider problem and look at how to simulate a three-level system (a so called trit) with two qubits in an ion trap quantum computer. We show how to get and measure a SU (3) geometric phase with this toy model. Finally we investigate how to simulate collective angular momentum models with a string of qubits in an ion trap. We assume that the ionic qubits are coupled to a thermal reservoir and derive a master equation for this case. We investigate the semiclassical limit of this master equation and, in the case for two qubits in the trap, determine the entanglement of the steady state. We also outline a way to find the steady state for the master equation using coherence vectors.
After years of effort by quantum scientists, decoherence due to thermal effects still remains a huge hindrance to the upscaling of quantum computers. This thesis presents the temperature scaling of decoherence in a trapped-ion qubit. Microscopic quantum noise simulations are carried out. The resulting numerical scaling laws of coherence times, T1 and T2, are presented. The results enable experimentalists to determine, as a function of temperature, an upper bound for the time over which a quantum computer can be operated without a disastrous loss of quantum coherence, and the duration over which a memory qubit retains its information. Given the tradeoff between the enormous resource overhead demanded by quantum error correction protocols and the adverse effects of decoherence, the results provide guidance for the implementation and optimization of practical error suppression methods in the current era of quantum computers.
Using simple physical arguments we investigate the capabilities of a quantum computer based on cold trapped ions of the type recently proposed by Cirac and Zoller. From the limitations imposed on such a device by decoherence due to spontaneous decay, laser phase coherence times, ion heating and other possible sources of error, we derive bounds on the number of laser interactions and on the number of ions that may be used. As a quantitative measure of the possible performance of these devices, the largest number which may be factored using Shor`s quantum factoring algorithm is determined for a variety of species of ion.