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Journal of Applied Physics

Quantum logic gates based on ballistic transport in graphene

Daniela Dragoman, Mircea Dragoman

Published Mar 2, 2016• 16 citations
Publisher

Abstract

The paper presents various configurations for the implementation of graphene-based Hadamard, C-phase, controlled-NOT, and Toffoli gates working at room temperature. These logic gates, essential for any quantum computing algorithm, involve ballistic graphene devices for qubit generation and processing and can be fabricated using existing nanolithographical techniques. All quantum gate configurations are based on the very large mean-free-paths of carriers in graphene at room temperature.

DOI
10.1063/1.4943000

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The paper presents various configurations for the implementation of graphene-based Hadamard, C-phase, controlled-NOT, and Toffoli gates working at room temperature. These logic gates, essential for any quantum computing algorithm, involve ballistic graphene devices for qubit generation and processing and can be fabricated using existing nanolithographical techniques. All quantum gate configurations are based on the very large mean-free-paths of carriers in graphene at room temperature.
Proposed configurations for the implementation of graphene-based CNOT and Toffoli gates working at room temperature are presented. These two logic gates, essential for any quantum computing algorithm, involve ballistic Y junctions for qubit implementation, quantum interference for qubit interaction and oblique gates for optimizing the output, and can be fabricated using existing nanolitographical techniques. The proposed configurations of CNOT and Toffoli quantum logic gates are based on the very large mean-free-paths of carriers in graphene at room temperature.
Quantum computing is expected to increase significantly the computational speed since it operates on completely different principles in comparison to classical computers. Quantum computing can be implemented in small, nano-sized systems, such as trapped atom or ions, spin states, superconductors or conductors in the ballistic transport regime. In particular, graphene is a suitable material for implementing quantum logic gates due to its large room-temperature mean free path. Several graphene-based configurations of quantum gates such as Hadamard, C-phase, C-NOT, and universal Toffoli gates, as well as of a modified Deutsch-Jozsa quantum algorithm are presented in this paper. In all cases, the quantum logic circuits operate at room temperature and the readout procedure implies current measurements only.
We have fabricated at wafer-scale graphene-based configurations suitable for implementing at room temperature one-qubit quantum gates and a modified Deutsch-Jozsa algorithm. Our measurements confirmed the (quasi-)ballistic nature of charge carrier propagation through both types of devices, which have dimensions smaller than the room-temperature mean-free-path in graphene. As such, both graphene-based configurations were found to be suitable for quantum computation. These results are encouraging for demonstrating a miniaturized, room-temperature quantum computer based on graphene.
Quantum computing, based on different principles than classical computing, has raised high expectations regarding the increase of computational speed in nano-sized quantum systems. Therefore, the search for implementations of quantum logic gates in photons, spin states, atom/ion traps or superconducting materials, for example, is a very active research area. Graphene has demonstrated already the possibility of implementing reversible logic gates, therefore becoming a compelling candidate for quantum computing applications. The paper presents several proposals of quantum logic gates implementation in graphene, which could work at room temperature and require only current measurements as readout procedures; examples of such quantum gates are Hadamard, C-NOT, C-phase and Toffoli gates. Besides these gates, it is shown that quantum algorithms, such as the modified Deutsch-Jozsa algorithm, can be implemented also in graphene.
We present an implementation of a one-qubit and two-qubit modified Deutsch-Jozsa quantum algorithm based on graphene ballistic devices working at room temperature. The modified Deutsch-Jozsa algorithm decides whether a function, equivalent to the effect of an energy potential distribution on the wave function of ballistic charge carriers, is constant or not, without measuring the output wave function. The function need not be Boolean. Simulations confirm that the algorithm works properly, opening the way toward quantum computing at room temperature based on the same clean-room technologies as those used for fabrication of very-large-scale integrated circuits.
A quantum gate is the quantum analog of the classical logic gate of digital computers. It is a basic structural unit of a quantum circuit which operates on a small number of qubits to deliver a predefined output. A quantum circuit is a graphical representation of the sequence of the quantum gates used and the measurements performed in a quantum computation. Various quantum logic gates, namely, the Hadamard, T phase, NOT, Pauli-X, controlled NOT (CNOT), controlled-Z, SWAP and controlled phase gates as well as higher-level Toffoli and Fredkin gates are described. Conventions of reading quantum circuit diagrams are explained. Operation of a quantum full adder consisting of registers and gates is discussed, elaborating the role of the NOT gate, the sum calculation with CNOTgates and the carry C-out calculation with Toffoli gates. A primary tool used for performing arithmetic operations on a quantum computer is the quantum Fourier transform (QFT). The QFT adder and multiplier circuits are presented.