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International Journal of Quantum Information

QUANTUM DOT COMPUTING GATES

Goong Chen, Zijian Diao, Jong U. Kim, Arup Neogi, Kerim Urtekin, Zhigang Zhang

Published Apr 1, 2006• 7 citations
Publisher

Abstract

Semiconductor quantum dots are a promising candidate for future quantum computer devices. Presently, there are three major proposals for designing quantum computing gates based on quantum dot technology: (i) electrons trapped in microcavity; (ii) spintronics; (iii) biexcitons. We survey these designs and show mathematically how, in principle, they will generate 1-bit rotation gates as well as 2-bit entanglement and, thus, provide a class of universal quantum gates. Some physical attributes and issues related to their limitations, decoherence and measurement are also discussed.

DOI
10.1142/s0219749906001761

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Semiconductor quantum dots are a promising candidate for future quantum computer devices. Presently, there are three major proposals for designing quantum computing gates based on quantum dot technology: (i) electrons trapped in microcavity; (ii) spintronics; (iii) biexcitons. We survey these designs and show mathematically how, in principle, they will generate 1-bit rotation gates as well as 2-bit entanglement and, thus, provide a class of universal quantum gates. Some physical attributes and issues related to their limitations, decoherence and measurement are also discussed.
Quantum computing is the outcome of the size of semiconductor chips breaking the limits of classical physics, and is a landmark technology in the post-Moore's law era. Making use of the quantum properties of electrons in semiconductor quantum dots is believed to be one of the most promising candidates for the realization of quantum computing. In recent years, a series of breakthroughs have been made, including the preparation and readout of qubits, and the manipulation of quantum logic gates. This paper first introduces the background and significance of research on semiconductor quantum dot-based quantum computing and then provides an overview of the developments regarding spin-, charge-, and few-electron-based qubits, as well as the long distance coherent coupling of qubits. Finally, we discuss future trends in semiconductor-based quantum computing.
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Computations with a future quantum computer will be implemented through the operations by elementary quantum gates.It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any n-bit unitary operation can be carried out by concatenations of 1-bit and 2-bit elementary quantum gates.Three contemporary quantum devices-cavity QED, ion traps and quantum dots-have been widely regarded as perhaps the most promising candidates for the construction of elementary quantum gates.In this paper, we describe the physical properties of these devices, and show the mathematical derivations based on the interaction of the laser field as control with atoms, ions or electron spins, leading to the following:(i) the 1-bit unitary rotation gates; and(ii) the 2-bit quantum phase gates and the controlled-not gate.This paper is aimed at providing a sufficiently self-contained survey account of analytical nature for mathematicians, physicists and computer scientists to aid interdisciplinary understanding in the research of quantum computation.
Technological growth in the electronics industry has historically been measured by the number of transistors that can be crammed onto a single microchip. Unfortunately, all good things must come to an end; spectacular growth in the number of transistors on a chip requires spectacular reduction of the transistor size. For electrons in semiconductors, the laws of quantum mechanics take over at the nanometre scale, and the conventional wisdom for progress (transistor cramming) must be abandoned. This realization has stimulated extensive research on ways to exploit the spin (in addition to the orbital) degree of freedom of the electron, giving birth to the field of spintronics . Perhaps the most ambitious goal of spintronics is to realize complete control over the quantum mechanical nature of the relevant spins. This prospect has motivated a race to design and build a spintronic device capable of complete control over its quantum mechanical state, and ultimately, performing computations: a quantum computer. In this tutorial we summarize past and very recent developments which point the way to spin-based quantum computing in the solid state. After introducing a set of basic requirements for any quantum computer proposal, we offer a brief summary of some of the many theoretical proposals for solid-state quantum computers. We then focus on the Loss–DiVincenzo proposal for quantum computing with the spins of electrons confined to quantum dots. There are many obstacles to building such a quantum device. We address these, and survey recent theoretical, and then experimental progress in the field. To conclude the tutorial, we list some as-yet unrealized experiments, which would be crucial for the development of a quantum dot quantum computer.
Present-day computers are essentially non-quantum mechanical in operation. The logic gates of a classical computer are irreversible in nature. For easy understanding, elementary quantum mechanics is reviewed including the Schrödinger’s equation, the particle-in-a-box problem, state superposition and collapsing. Bloch sphere representation of a quantum bit is explained. The qubits display interesting properties of quantum superposition, entanglement and interference, characteristic of atomic and subatomic particles. Measurements carried out on qubits cause their wave functions to collapse forcing them into a definite 0 or 1 state. Qubit decoherence on interaction with the environment is a major problem in quantum computing Three types of quantum computing devices are discussed including silicon, superconducting and trapped qubit devices. Among silicon devices, gate-controlled silicon quantum dots and phosphorous donor implanted Si substrates are considered. Superconducting qubit archetypes and their realization techniques are explained. The transmon qubit design is preferred for charge noise mitigation. Under the trapped ion qubit devices, construction and operation of Paul ion traps is discussed, and the types of trapped ion qubits are elucidated.
Coupled quantum-dot system in semiconductor is considered to be one of the promising candidates of quantum computer. It will be most desirable that the quantum computing devices are implemented into the same substrate as the widely used LSI circuits. From this viewpoint, the quantum computer of coupled quantum dots of semiconductors is presented concentrating on the controlled-NOT-gate operation. The decoherence time of the quantum computation and the measurement procedure by field-effect-transistor structure are discussed.