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Journal of Physics Condensed Matter

Avoiding entanglement loss when two-qubit quantum gates are controlled by electronic excitation

Roberta Rodriquez, Andrew J. Fisher, P. Thornton Greenland, Arthur Marshall Stoneham

Published Apr 9, 2004• 21 citations
Publisher

Abstract

A solid-state two-qubit quantum gate was recently proposed that might be made in a silicon fabrication plant in the near future. In this class of device, entanglement between two quantum bits is controlled by a change from a largely unentangled ground electronic state to an excited state in which useful entanglement can be produced. Such gates have potential advantages, both because they exploit known solid-state behaviour and they separate the storage and manipulation of quantum information. It is important that the excitation step does not create decoherence. We analyse a type of gate proposed before, in which the excitation involves a control electron that interacts with the qubit spins in the excited state. The dynamics of an idealized (but fairly general) gate of this type show that it can be operated to produce a standard two-qubit entangling state.

DOI
10.1088/0953-8984/16/16/001

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A solid-state two-qubit quantum gate was recently proposed that might be made in a silicon fabrication plant in the near future. In this class of device, entanglement between two quantum bits is controlled by a change from a largely unentangled ground electronic state to an excited state in which useful entanglement can be produced. Such gates have potential advantages, both because they exploit known solid-state behaviour and they separate the storage and manipulation of quantum information. It is important that the excitation step does not create decoherence. We analyse a type of gate proposed before, in which the excitation involves a control electron that interacts with the qubit spins in the excited state. The dynamics of an idealized (but fairly general) gate of this type show that it can be operated to produce a standard two-qubit entangling state.
We model the evolving time-dependent electronic structure of a solid-state quantum gate as it performs basic quantum operations. Our time-dependent configuration-interaction method follows the evolution of two donor electron spin qubits interacting with a third, optically excited, control spin in an applied magnetic field, a possible realization of the basic component of a proposed quantum information processor. We identify unitary operations which approximately disentangle the control spin, and use them to construct high-accuracy two-electron operations that are locally equivalent to CNOT, SWAP and operations. From our evaluation of the accuracy of a set of candidate gates we estimate the residual entanglement of the control electron and overall gate operation times. These results attest to the feasibility of the silicon-based quantum gates proposed by Stoneham, Fisher and Greenland.
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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 current status of solid-state implementations of quantum computing is briefly described. There are numerous candidate proposals, but only comparatively recently have some of them begun to progress to the point of demonstrating coherent motion of the individual quantum bits (qubits), and the controlled coupling of more than one qubit remains a significant challenge. We also present a generalization of the fluctuation-dissipation theorem that provides a relationship between the coherent evolution entangling two spatially separated qubits, and the associated irreducible decoherence. This relationship may be used to bound the maximum attainable figures of merit in proposed two-qubit gates.
The interaction of solid-state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid-state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review, we discuss how decoherence affects two of the most successful realizations of solid-state qubits, namely, spin qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behaviour at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin–orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux and bias voltages, and via losses in the dissipative circuit elements.