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IEEE International Symposium on Circuits and Systems proceedings

A CNOT-gate implementation for information transfer by the phonon bus

K. Pahlke, L. Kroneberg, Wolfgang M. Mathis

Published Jan 1, 2000• 1 citation
Publisher

Abstract

A scheme of quantum state manipulation is presented to implement a new kind of CNOT-gate in a two stored ion arrangement. This type of quantum gate enables the designer of quantum algorithms to "send information into the phonon bus" controlled by the information stored in one of the ions. Some simulation results are given to show the dynamics of the system during the step by step implementation.

DOI
10.1109/iscas.2000.857203

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A scheme of quantum state manipulation is presented to implement a new kind of CNOT-gate in a two stored ion arrangement. This type of quantum gate enables the designer of quantum algorithms to "send information into the phonon bus" controlled by the information stored in one of the ions. Some simulation results are given to show the dynamics of the system during the step by step implementation.
We show how to construct a multiqubit control gate on a quantum register of an arbitrary size N. This gate performs a single-qubit operation on a specific qubit conditioned by the state of other $N\ensuremath{-}1$ qubits. We provide an algorithm how to build up an array of networks consisting of single-qubit rotations and multiqubit control-NOT (CNOT) gates for the synthesis of an arbitrary entangled quantum state of N qubits. We illustrate the algorithm on a system of cold trapped ions. This example illuminates the efficiency of the direct implementation of the multiqubit CNOT gate compared to its decomposition into a network of two-qubit CNOT gates.
Trapped ions are a near ideal system to study quantum information processing due to the high degree of control over the ion's external confinement and internal degrees of freedom. We demonstrate the key steps necessary for trapped ion quantum computing and focus on phonon-mediated entangling gates. We highlight several key algorithms implemented over the last decade with these gates and give a detailed description of Grover's quantum database search implemented with two trapped ion qubits.
A sequence of five laser pulses is presented, implementing a controlled-NOT gate in a linear arrangement of trapped ions. This gate works if the quantum number of the collective vibration (phonon bus) is zero or one. We interpret this property as tolerance against errors caused by imperfect ground-state preparation. The periodicity of two Rabi frequencies is used in order to obtain this property. The gate implementation is designed in a way which does not correspond to the well-known phase-gate construction.
In this paper, based on the recent experiment by Roos et al. [Science 304, 1478 (2004)], a theoretical scheme is proposed to create the multipartite entanglement of many trapped ions and implement a two-qubit quantum phase gate between two ions in ion trap. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. We also show that the scheme can be used to directly transfer information between two ions. The scheme has the advantage that it does not use the vibrational mode as the data bus and only requires a single resonant interaction. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed. In view of the decoherence mechanism, the simplification for the entangled state preparation and experimental implementation of quantum logic operation may become crucial.
Single qubit rotation gate and the controlled-NOT (CNOT) gate constitute a complete set of gates for universal quantum computation. In general the CNOT gate are only for two nearby qubits. For two qubits which are remote from each other, we need a series of swap gates to transfer these two qubits to the nearest neighboring sites, and then after the CNOT gate we should transfer them to their original sites again. However, a series of swap gates are resource for quantum information processing. One economy way which does not consume so much resource is to implement CNOT gate remotely. The remote CNOT gate is to implement the CNOT gate for two remotely separated qubits with the help of one additional maximally entangled state. The original remote CNOT gate is for two qubits, here we will present the d-dimensional remote CNOT gate. The role of quantum teleportation is identified in the process of the remote CNOT gate.
We propose a simple scheme for implementing quantum logic gates with a string of two-level trapped cold ions outside the Lamb-Dicke limit. Two internal states of each ion are used as one computational qubit (CQ) and the collective vibration of ions acts as the information bus, i.e., the bus qubit (BQ). Using the quantum dynamics for the laser-ion interaction as described by a generalized Jaynes-Cummings model, we show that quantum entanglement between any one CQ and the BQ can be coherently manipulated by applying classical laser beams. As a result, universal quantum gates, i.e., the one-qubit rotation and two-qubit controlled gates, can be implemented exactly. The required experimental parameters for the implementation, including the Lamb-Dicke (LD) parameter and the durations of the applied laser pulses, are derived. Neither the LD approximation for the laser-ion interaction nor the auxiliary atomic level is needed in the present scheme.