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arXiv:quant-ph/0512067 · Physical Review A

Cluster-state preparation and multipartite entanglement analyzer with fermions

Xinglai Zhang, Mang Feng, K. Gao

Published Jan 11, 2006• 45 citations
arXivHTMLPDF

Abstract

Quantum cluster states and entangled-state analyzers are essential to measurement-based quantum computing. We propose to generate a quantum cluster state and to make a multipartite entanglement analyzer by using noninteracting free electrons or conduction electrons in quantum dots, based on polarizing beam splitters, charge detectors, and single-spin rotations. Our schemes are deterministic without the need of qubit-qubit interaction.

DOI
10.1103/physreva.73.014301

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Quantum cluster states and entangled-state analyzers are essential to measurement-based quantum computing. We propose to generate a quantum cluster state and to make a multipartite entanglement analyzer by using noninteracting free electrons or conduction electrons in quantum dots, based on polarizing beam splitters, charge detectors, and single-spin rotations. Our schemes are deterministic without the need of qubit-qubit interaction.
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We propose an efficient entanglement concentration protocol (ECP) based on electron-spin cluster states assisted with single electrons. In the ECP, we adopt the electron polarization beam splitter (PBS) and the charge detector to construct the quantum nondemolition measurement. According to the result of the measurement of the charge detection, we can ultimately obtain the maximally entangled cluster states. Moreover, the discarded items can be reused in the next round to reach a high success probability. This ECP may be useful in current solid quantum computation.
The goal of this thesis is to investigate theoretically the generation and behaviour of multipartite entanglement for solid-state nanosystems, in particular electron spin quantum bits (so-called 'qubits') in quantum dots. A quantum dot is a tiny potential well where a single electron can be trapped. A quantum bit can be implemented in this system by applying a magnetic field, and thereby lifting the degeneracy of the spin states of the electron. These spins can then be used as single qubits, and engineering many of these quantum dots next to each other gives as a register of qubits. In this scheme, the so-called Loss-DiVincenzo quantum computer, the single spins can be rotated e.g. by applying a time dependent magnetic field, and two spins can interact through controlling the potential barrier between them. A qubit cannot only be in a superposition of the two computational states 0 and 1 at the same time, but an even stranger characteristic arises for multiple qubits: this phenomenon is called entanglement and refers to a strong correlation between two or more qubits, which can not be achieved within the framework of classical physics, and exponentially enlarges the possible states for a N-qubit system as compared to a classical N-bit system. In this thesis we devise algorithms how to generate multipartite entangled states in electron spin qubits in quantum dots. We compare which classes of entangled states can be generated efficiently in this system. Once the states are created, they decay due to a process called decoherence. We compare how entangled states can be generated and detected in a realistic experiment, and which classes of states are the most suitable. Furthermore, we compare which classes conserve the entanglement, and quantify the robustness of various classes of entangled states. In the last chapter, we devise a scheme of how to execute a simple quantum algorithm, the Deutsch-Jozsa algorithm, in a system containing another type of solid-state qubit, the so-called flux qubit.
The cluster state is a special, highly entangled quantum state that provides a universal resource on which to perform measurement-based quantum computation. In this paper, we propose a scheme for the generation of such entanglement in a solid-state medium by the suppression of resonant tunneling of a ballistic electron by a nearby single-electron charge qubit. To investigate the viability of this scheme for the creation of cluster states, we performed numerical simulations and studied the entanglement interaction in detail. We show that high levels of entanglement can be achieved, with an average concurrence of 0.968.