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arXiv:0808.1618 · New Journal of Physics

Quantum computation with graphene nanoribbon

Guo‐Ping Guo, Zhirong Lin, Tao Tu, Gang Cao, Xiaopeng Li, Guang‐Can Guo

Published Dec 3, 2009• 62 citations
arXivHTMLPDF

Abstract

We propose a scheme to implement quantum computation in graphene nanoribbon (GNR). It is shown that an electron or hole can be naturally localized in each zigzag region for a GNR with a sequence of Z-shaped structures, without using confined gates. A one-dimensional graphene quantum dot chain is formed in such a GNR, where an electron or hole spin can be used as a qubit. The coupling interaction between neighboring qubits is found to be of the always-on Heisenberg type. By exploiting the bang–bang control strategy and the decoherence-free subspaces encoding method, universal quantum gates are argued to be realizable with the present techniques.

DOI
10.1088/1367-2630/11/12/123005

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We propose a scheme to implement quantum computation in graphene nanoribbon (GNR). It is shown that an electron or hole can be naturally localized in each zigzag region for a GNR with a sequence of Z-shaped structures, without using confined gates. A one-dimensional graphene quantum dot chain is formed in such a GNR, where an electron or hole spin can be used as a qubit. The coupling interaction between neighboring qubits is found to be of the always-on Heisenberg type. By exploiting the bang–bang control strategy and the decoherence-free subspaces encoding method, universal quantum gates are argued to be realizable with the present techniques.
We study an array of graphene nano sheets that form a two-dimensional S = 1/2 Kagome spin lattice used for quantum computation. The edge states of the graphene nano sheets are used to form quantum dots to confine electrons and perform the computation. We propose two schemes of bang-bang control to combat decoherence and realize gate operations on this array of quantum dots. It is shown that both schemes contain a great amount of information for quantum computation. The corresponding gate operations are also proposed.
Abstract We study quantum teleportation between the narrow armchair graphene nanoribbons (GNRs) with zigzag ends. Several influences including Coulomb repulsion among electrons, temperature and ribbon length on the output state and teleportation fidelity are discussed in detail. Moreover, we derive the entanglement of the output state and corresponding fidelity as a function of the input and channel entanglement. For practical applications, we also propose a scheme for implementing the single-qubit gates (X, Z and H gates) and two-qubit controlled-NOT gate in GNRs, based on the Bang-Bang control strategy and synchronous step magnetic field.
The works devoted to an issue of quantum computer design have been analyzed.The main problems related to creation of the quantum computer are discussed.A fundamentally new approach to solving the problem of creating a truly quantum computer based on the "up to bottom" strategy has been proposed and justified.The strategy can be implemented by preliminary visualization of the quantum states of qubits using nanotriggers formed from two-dimensional material, in particular, graphene.This refers to the visualization (materialization) of all, including entangled, states, which mainly determine the theoretically possible large mathematical resource of a quantum computer.A block-diagram of the electronic device based on "a priory" quantum states of q-bits is proposed.It is shown that for implementation of quantum computation procedure, each materialized (visualized) Shor's cell should correspond to an element of the electronic scheme.The device includes a block containing at least 10 10 nanotriggers that perform a role of q-bits of quantum computation, which are created using graphene nanoribbons and controlled by a special element.The latter represents a self-organizing quantum dot having two essentially different states in terms of magnetic properties.This quantum dot is prepared on the basis of a compound, the molecules of which are characterized by the intramolular rearrangement.The nanotriggers are employed to form reversible logic blocks or gates.Each gate contains three triggers to perform logical operations.The offered device is an additional electronic unit that is embedded in a digital computer, which makes it possible to implement the computational process in accordance with the requirements of the provisions of quantum physics.
Abstract Among the various approaches to quantum computing, all-optical architectures are especially promising due to the robustness and mobility of single photons. However, the creation of the two-photon quantum logic gates required for universal quantum computing remains a challenge. Here we propose a universal two-qubit quantum logic gate, where qubits are encoded in surface plasmons in graphene nanostructures, that exploits graphene's strong third-order nonlinearity and long plasmon lifetimes to enable single-photon-level interactions. In particular, we utilize strong two-plasmon absorption in graphene nanoribbons, which can greatly exceed single-plasmon absorption to create a “square-root-of-swap” that is protected by the quantum Zeno effect against evolution into undesired failure modes. Our gate does not require any cryogenic or vacuum technology, has a footprint of a few hundred nanometers, and reaches fidelities and success rates well above the fault-tolerance threshold, suggesting that graphene plasmonics offers a route towards scalable quantum technologies.
We investigate a two-electron double quantum dot with both spin and valley degrees of freedom as they occur in graphene, carbon nanotubes or silicon and regard the 16-dimensional space with one electron per dot as a four-qubit logic space. In the spin-only case, it is well known that the exchange coupling between the dots combined with arbitrary single-qubit operations is sufficient for universal quantum computation. The presence of valley degeneracy in the electronic band structure alters the form of the exchange coupling and, in general, leads to spin–valley entanglement. Here, we show that universal quantum computation can still be performed by exchange interaction and single-qubit gates in the presence of an additional (valley) degree of freedom. We present an explicit pulse sequence for a spin-only controlled-NOT consisting of the generalized exchange coupling and single-electron spin and valley rotations. We also propose state preparations and projective measurements with the use of adiabatic transitions between states with (1,1) and (0,2) charge distributions similar to the spin-only case, but with the additional requirement of controlling the spin and valley Zeeman energies by an external magnetic field. Finally, we demonstrate a universal two-qubit gate between a spin and a valley qubit, allowing universal gate operations on the combined spin and valley quantum register.
The works that have been devoted to the topic of quantum computer design have been examined. The main issues surrounding the development of a quantum computer are explored. The “up to bottom” concept has been presented and supported as a fundamentally novel way to solve the problem of building a really quantum computer. The technique can be accomplished by using nanotriggers made of two-dimensional materials, such as graphene, to visualise the quantum states of qubits in advance. This refers to the visualisation (materialisation) of all states, including entangled states, which primarily determine the quantum computer's theoretically large mathematical resource. The proposal is for an electronic device block diagram based on “a priory” quantum states of q-bits. It is demonstrated that each realised (visualised) Shor's cell should correspond to an element of the electronic system for the execution of quantum computation procedures. A block containing at least 1010 nanotriggers that act as q-bits in quantum computation and are generated using graphene nanoribbons and controlled by a specific element is included in the device. The latter is a self-organizing quantum dot with two essentially different magnetic states. This quantum dot is made from a compound whose molecules are distinguished by intramolular rearrangement. Nanotriggers are used to create reversible logic gates or blocks. Three triggers are included in each gate to perform logical operations. The offered device is an additional electronic unit implanted in a digital computer that allows the computational process to be implemented in accordance with the requirements of quantum physics.