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Quantum Dots

Quantum Dots

An atom has a nucleus and electrons in orbitals around the nucleus. We can create artificial atoms known as quantum dots using our ability to manipulate electrical fields and create material barriers to the movement of electrons.

Real atoms

The nucleus of an atom creates an electrical potential centered around itself that attracts the electrons, with the lowest energy at the center. One of the central problems with classical mechanics, which drove researchers to create quantum mechanics, is the fact that the electron doesn’t fall into that center well, but instead maintains its distance from the nucleus.

It turns out that the electrons can only take certain discrete energy levels that correspond to standing waves around the nucleus. The electron’s position is a quantum probability amplitude, rather than a single fixed point, and is known as an orbital. The shape and size of these orbitals depend on the strength of the electrical potential created by the nucleus.

Artificial atoms

Of course, with real atoms, we have only a very limited ability to influence the electrical field. But if we can confine one or a few electrons in ways that are similar to the electrons in ordinary atomic orbitals, we can create artificial atoms known as quantum dots. We confine the electrons using a combination of the material structure and electrical fields created using voltages. An electron won’t normally move past the physical edge of the device. With a junction made of certain types of materials, it takes substantial energy to cross the boundary. When a positive voltage is applied to a wire, it attracts electrons, and conversely a negative charge repels electrons. Using these characteristics carefully, we can confine an electron tightly in either a disk-shaped area or a small volume.

Quantum dots can be either self-assembled or gate-defined. Self-assembled quantum dots are made of materials that clump together. In one approach, small amounts of a certain type of semiconductor are grown on top of a substrate (chip surface) of another type of semiconductor, and differences in the spacing between the atoms cause the new material to bead up, like water on a good rain jacket. In the vertical direction, our electron will then be confined to the boundary where the materials meet, and horizontally, it will be limited to the disk-shaped footprint of the dot.

Gate-defined quantum dots are made like computer chips, with microscopic wires laid on top of a material such as silicon using a process known as photolithography. But there is an additional twist: different layers of material are deposited before the wires are created on top. The electrons are then confined in the vertical dimension by the material boundary, and in the horizontal directions by electrical fields created by voltage on the wires.


So how do we use this ability to confine individual electrons to create a qubit? With a single electron, we can use the spin of the electron as our qubit, as we discussed in the video on electron spin as our state variable. Because spin is a magnetic effect, we need to use magnetic fields to define “up” and “down” for the electron, and to control its spin. For some designs, we can also control the spin optically, using laser pulses.

Changing the spin of an electron requires careful dynamic control of magnetic fields, which tends to be slow and is difficult to target to a single quantum dot. Quantum dot designs have evolved over the last two decades to work around this problem. Several proposals actually use more than one quantum dot to hold a qubit, sometimes with more than one electron. If the magnetic field differs slightly from place to place, this difference can be used to control the spin. With two electrons, we can also define our qubit to be the difference in their states. With a careful choice of qubit representation, we can eliminate the need to modify the magnetic field, instead controlling the exchange of electrons between two dots to execute single-qubit and two-qubit gates.


Quantum dots rely on fabrication techniques that have been developed over a half century of silicon photolithography. The ability to couple some designs to photons makes them attractive for communications, as well. Especially for the exchange-oriented designs, the time to execute a gate is very fast, meaning that performance will be excellent if the system can be scaled up.

The biggest weakness in quantum dots has been memory lifetime, which is hurt by stray electrons, stray magnetic fields, and interaction with the nuclei of nearby atoms. Recent work has made tremendous progress in this area. Also, like some other technologies, quantum dots require temperatures near absolute zero, so the experimental setup is complex, if well understood. Finally, while in theory it is possible to put many quantum dots on a single chip, the wires necessary for controlling them clutter the arrangement, and finding an architecture for many qubits has been challenging.




原子核は電子を自身へ近づけるために、エネルギーがもっとも低い中心方向への電気的な力を持っています。量子力学を創った研究者にとって、 古典力学の中心的な問題は、どうして電子は原子核に衝突せず、距離を保っているのかと言う点でした。




量子ドットは、自己組織化型のものか、ゲート定義型のものになります。自己組織化した量子ドットは、物質が集まったものから作られています。一つのアプローチとしては、少量のある種の半導体が基盤上で別の種類に代わり、原子同士の空間が、雨の中で非常に役立つレインコートなどの新しい素材の開発に役立ちます。垂直方向において、物質がぶつかる部分に境界を設けることで電子を閉じ込め、水平方向において、円形に動きが制限されます。 ゲート定義型の量子ドットは、コンピュータのチップのように、フォトリソグラフィという手法を用いて基盤上でケイ素を微細な線状に繋いでいきます。しかしここに一捻りあります。それは、異なる層が、基盤が線で繋がれる前に、用意されているということです。



電子のスピンを変化させるためには、慎重に磁場を動的制御する必要であり、これは時間がかかる上に、単一の量子ドットを対象として行うことは困難です。 量子ドットの設計は、この問題を回避するために、過去20年間に進化してきました。 いくつかの提案は実際に量子ビットを保持するために複数の量子ドットを使用し、時にはさらに複数の電子も使用します。

磁場が場所によって若干異なる場合、この差を用いてスピンを制御することができます。 2つの電子を用いることで、その状態の*:違い**を量子ビットとして定義することもできます。 量子ビットにする状態を慎重に選択することで、磁場を変化させる必要性を排除し、代わりに2つのドット間の電子交換を制御すれば、単一量子ビットゲートおよび2量子ビットゲートを実行できます。


量子ドットは、シリコンフォトリソグラフィーによって半世紀にわたり開発された製造技術に立脚している。 量子ドットの設計のいくつかを結合して光子にする能力は、量子ドットを通信にとっても魅力的なものとしています。 特に、交換指向型設計の場合、ゲート実行時間は非常に高速です。つまり、システムを拡張することができれば、パフォーマンスが優れています。

量子ドットの最大の弱点は、漂遊電子、漂遊磁場、および近くの原子核との相互作用によって傷ついてしまうメモリの寿命でした。 最近の研究はこれらの分野で驚異的な進歩を遂げました。 また、いくつかの他の技術と同様に、量子ドットは絶対零度に近い温度を必要とするため、実験設定は複雑になってしまいます。 最後に、理論的には単一のチップ上に多くの量子ドットを配置することが可能であるが、それらを制御するために必要なワイヤは配置を乱雑にしてしまい、多量子ビットのアーキテクチャをつくることは困難でした。

© Keio University
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Understanding Quantum Computers

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