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Advances in Mathematical Physics

Cluster State Computation with Quantum‐Dot Charge Qubits

Matthew Lubelski Katz, Jingbo B. Wang

Published Jan 1, 2010• 2 citations
Publisher

Abstract

Quantum computers are expected to far surpass the capabilities of today′s most powerful supercomputers, particularly in areas such as the theoretical simulation of quantum systems, cryptography, and information processing. The cluster state is a special, highly entangled quantum state that forms the universal resource on which measurement‐based quantum computation can be performed. This paper provides a brief review of the theoretical foundations of cluster state quantum computation and how it evolved from the traditional model of digital computers. It then proposes a scheme for the generation of such entanglement in a solid‐state medium through the suppression of resonant tunneling of a ballistic electron by a single‐electron charge qubit. To investigate the viability of the scheme for the creation of cluster states, numerical calculations are performed in which the entanglement interaction is modeled in detail.

DOI
10.1155/2010/482598

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•Apr 27, 2015•0 citations
Quantum computers are expected to far surpass the capabilities of today′s most powerful supercomputers, particularly in areas such as the theoretical simulation of quantum systems, cryptography, and information processing. The cluster state is a special, highly entangled quantum state that forms the universal resource on which measurement‐based quantum computation can be performed. This paper provides a brief review of the theoretical foundations of cluster state quantum computation and how it evolved from the traditional model of digital computers. It then proposes a scheme for the generation of such entanglement in a solid‐state medium through the suppression of resonant tunneling of a ballistic electron by a single‐electron charge qubit. To investigate the viability of the scheme for the creation of cluster states, numerical calculations are performed in which the entanglement interaction is modeled in detail.
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.
We propose a method to efficiently generate cluster states in charge qubits, both semiconducting and superconducting, as well as flux qubits. We show that highly entangled cluster states can be realized by a "one-touch" entanglement operation by tuning gate bias voltages for charge qubits. We also investigate the robustness of these cluster states for nonuniform qubits, which are unavoidable in solid-state systems. We find that quantum computation based on cluster states is a promising approach for solid-state qubits.
Cluster states, a special type of highly entangled states, are a universal resource for measurement-based quantum computation. Here, we propose an efficient one-step generation scheme for cluster states in semiconductor quantum dot molecules, where qubits are encoded on singlet and triplet states of two coupled quantum dots. By applying a collective electrical field or simultaneously adjusting interdot bias voltages of all double-dot molecules, we get a switchable Ising-like interaction between any two adjacent quantum molecule qubits. The initialization, the single-qubit measurement, and the experimental parameters are discussed. It is shown that preparation of large cluster states and one-way quantum computation are implementable in semiconductor quantum dots with the present techniques.
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of these systems to a large number of qubits, essential for practical applications such as the Shor algorithm, represents a formidable challenge. Most of the current experiments are designed to implement sequences of highly controlled interactions between selected particles (qubits), thereby following models of a quantum computer as a (sequential) network of quantum logic gates. Here we propose a different model of a scalable quantum computer. In our model, the entire resource for the quantum computation is provided initially in form of a specific entangled state (a so-called cluster state) of a large number of qubits. Information is then written onto the cluster, processed, and read out form the cluster by one-particle measurements only. The entangled state of the cluster thus serves as a universal substrate for any quantum computation. Cluster states can be created efficiently in any system with a quantum Ising-type interaction (at very low temperatures) between two-state particles in a lattice configuration.
Ever since its discovery, quantum mechanics has remained an intensely active field, and its real-world applications continue to unfold rapidly. In 1982, Richard Feynman proposed a new type of computer operating directly under quantum mechanics laws: – the quantum computer \cite{Feynman1982}. Compared with the classical computer, whose information is encoded in “bits”, the quantum computer, whose information is encoded in “quantum bits”, or “qubits”, will be able to perform calculations exponentially faster for such problems as factoring large integers into primes and simulating complicated quantum systems. Due to their extremely powerful calculation speeds and abilities, quantum computers have been the long-pursued dreams for both experimentalists and theorists in many research groups, government agencies, industrial companies, etc., and the fast-paced developments in their architecture and speed continue to make them more and more attractive. There are two principal models of quantum computing: the circuit model and the measurement-based model. The circuit model is similar to a traditional computer where there are inputs, gates and outputs. The measurement-based model is different, as it is crucially based on the cluster state, a type of highly entangled quantum state. In this new model, quantum computing begins with an initial cluster state and then carries out calculations by physical measurements of the cluster state itself along with feedforward. Thus, the cluster state serves as the material and resource for the entire set of calculations, and it is an extremely important part of measurement-based quantum computing. This thesis will discuss an experimental and theoretical work that holds the world record for the largest entangled cluster state ever created whose 60 qumodes (optical versions of qubits) are all available simultaneously. Moreover, the entangled state we created is not random, and it is a cluster state which meets the specific requirements for implementing quantum computing. In the race to build a practical quantum computer, the ability to create such a large cluster state is paramount. Also, our creative optical method to generate massive entanglement advances many other methods due to its high efficiency, super-compactness and large scalability. The entanglement proceeds from interfering multiple EPR entangled pairs, which are generated from the down-converting process of a nonlinear crystal in an optical parametric oscillator, into a very long dual-rail wire cluster state. Moreover, many copies of the same state can easily be obtained by merely adjusting the frequencies of the pump lasers. These cluster states serve as building blocks of the universal quantum computer, and also are, in their own right, important resources for studying and exploring quantum mechanics in large systems.