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Chinese journal of atomic and molecular physics

A scheme for realizing the quantum discrete Fourier transform in the ion trap

Jiang Yu

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

Under the framework of the Cirac Zoller model, a scheme for realizing the quantum discrete Fourier transform in the ion trap by some unitary operations is discussed. Since any operation in the quantum computing can be decomposed into a series of two basic operations, our scheme focusing on the problem of one qubit and two qubit is actually valid for treating many qubit problem.

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Under the framework of the Cirac Zoller model, a scheme for realizing the quantum discrete Fourier transform in the ion trap by some unitary operations is discussed. Since any operation in the quantum computing can be decomposed into a series of two basic operations, our scheme focusing on the problem of one qubit and two qubit is actually valid for treating many qubit problem.
The Cirac-Zoller mechanism is generally used for the implementation of CNOT gates in ion trap quantum computers. We present here a highly detailed quantum physical description of this approach. To keep the presentation simple, the qubits are modeled as rigid rotors and the radiation field of each of the lasers is treated as a classical field. In combination with the corresponding first part (Ion Trap Quantum Computer Part 1: 1-Qubit Gates), this results in the complete quantum theory of a universal set of quantum gates. This presentation is intended for readers with basic knowledge of quantum physics and assumes familiarity with Part 1.
The purpose of this article is to review two complementary schemes for quantum computation with trapped ions. We initially discuss the first proposal of quantum computations with cold trapped ions (J. I. Cirac and P. Zoller; Phys. Rev. Lett. 74, 4091, 1995) which requires, prior to any computation, laser cooling to the motional ground state. This proposal is closely related to the physics of generating and manipulating N-particles entangled states in both ion traps and high-Q cavities (cavity quantum electrodynamics). The second scheme is that of quantum computations with hot trapped ions (J.F. Poyatos, J.I. Cirac and P. Zoller; Phys. Rev. Lett. 81, 1322, 1998) which works at finite temperature and resembles physical ideas found in atom interferometry.
We discuss possibilities of quantum manipulations of trapped ions from the perspective of quantum information processing. We show how from a restricted set of feasible microscopic interactions a physical implementation of an arbitrary unitary operator can be realized. An example is given for the discrete Fourier transform. The synthesis of operators enables to realize universal quantum gates to process unknown input qubits which can be encoded into vibrational levels of trapped ions. We discuss also problem of an arbitrary measurement which can be performed using quantum gates.