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Skip to 0 minutes and 3 seconds29 nuclear spin can be used as a qubit for quantum information processing, but sometimes we want to use other spins like electron spins for quantum information processing. What kinds of devices would we create that – that hold those state variables? Okay so let’s just say we, we do work on silicon. So, so in the case of silicon quantum computer, uh, in a case of electron spin qubit we use 28 silicon nuclear spin free silicon and then place electron spin one by one, into silicon. I see. Yeah. And we have two different ways. One is to place, for example other so-called donors; impurities like phosphorus, which actually provide extra spin into silicon lattice.

Skip to 0 minutes and 58 secondsSo you know by placing position of number of, let’s just say by forming an array of phosphorus on the, on the surface of silicon wafers, we can have – we can place a qubit one by one in a position we want. Okay. Let me. I have a model here, which I think represents the arrangement of the atoms in. yeah that’s a – this is silicon crystal lattice. Right. Okay.

Skip to 1 minute and 28 secondsSo tell me… So if we, each dot is the silicon atom, if this is silicon crystal, but we can replace one of the silicon atom with phosphorus, donor and basically phosphorus atom then this phosphorus atom provides one extra electron in vicinity of this phosphorus and this one extra electron has a nuclear – uh, electron spin… Okay. …so it works as electron spin qubit. I see, So tell me how do you, in a system like that, how do you control the single spin? How do you control the – the… Okay. So, if we have phosphorus here then what we can do is that, let’s just say, phosphorus is here about 1-2-3-4 atomic layers below the surface. Okay.

Skip to 2 minutes and 24 secondsUhm and there is actually electron spin attached to this. And we can actually put extra metal on top of this silicon and apply electric field by biasing the electrode. And that will actually change the state of the electron state – electron state. I see. So you are gonna build wires on top of the surface like this. Is that the same way that the circuits are built for computer chips? Slightly different manner bec – oh actually, okay correction. In a same way, yes. We can use the IC – state of art integrated circuit technology.

Skip to 3 minutes and 3 secondsWe can have wire of metal here, send current back and forth that will actually create magnetic field, clockwise and anti-clock – clockwise alternating magnetic field, that actually changes – that, that can – that actually controls the state of the electron spin, up or down. So we can actually change the state of the electron spin 0 or 1 by just simply sending current back, current back and forth on the – on the electrode on the top. Great thank you. So we have already discussed, electron spins as a type of state variable… Right. …nuclear spin as a type of a variable and you’re talking now about putting one of those atoms inside the – this chip. Or a piece of silicon....

Skip to 4 minutes and 2 secondsWhat other kinds of systems are you and your group working on? Okay. this, let me just talk about, one other thing, right. Sure. Okay. Uh, we can also – we can replace silicon atom with phosphorus electron. The other way of putting single electron into silicon is that we can simply put electrode and bias strongly in a positive manner and electron can actually be – one electron can be attached underneath the electrode. We make by, you know, lithography. So of course there are lots of electrons inside this material right. Because it’s… Actually no – it’s yes and no. Because all electrons are used up for making bonds, silicon bonds.

Skip to 4 minutes and 53 secondsBut with some trick and by putting bias – positive bias on top of silicon we can actually attract one electron underneath the... So we have one extra electron in here and we can keep that one extra electron and use that? Under – right. And, and as a spin cubit and this way we can actually, uh, choose the positioning very precisely by using standard IC, silicon IC technology. I see. So who is actually building these devices? Well you know Intel is now working very strong – Intel is working very hard on making such chips. then possibly we don’t know yet, but other semiconductor manufacturers might be working on it as well. Right.

Nuclear Spin

An atom is composed of the atomic nucleus and the electrons in orbitals around it. Earlier, we saw how an electron can be used to create our quantum state variable. But there is another choice: using the atom’s nucleus. Keio University’s Kohei Itoh describes how we can use nuclear spin as a qubit.

You know that each electron has a spin, and the spin can be either aligned with the surrounding magnetic field, which we call spin up, or anti-aligned with it, which we call spin down. The nucleus of some types of atoms also has a spin. You probably know that the nucleus is composed of protons and neutrons. Besides charge and mass, these can give a nucleus a spin. For a given type of atom (say, carbon), the number of protons is fixed, but there may be several options for the number of neutrons. We call each of these variants an isotope. The rules for nuclei are complicated, but for certain isotopes of different elements, we have a simple, clean system that we can also use as a qubit.

Nuclear spins were actually one of the first types of qubits used experimentally. Lieven Vandersypen, then a graduate student at Stanford University, performed experiments using a liquid containing molecules with ordinary hydrogen (\(^1\)H) and isotopes of flourine (\(^{19}\)F) and carbon (\(^{13}\)C) as qubits. For solid-state systems, a lot of work has been done on phosphorus (\(^{31}\)P), silicon (\(^{29}\)Si), and carbon in diamond.

Control versus Isolation

For our quantum state variable, we want something that has two characteristics: one, we want it to be easy to control; and two, we want it to be well isolated from the environment, so that different kinds of noise, such as the radiation from wireless LANs and microwave ovens, doesn’t affect the state very much. When we build a device, we build a lot of shielding around it to protect it from those kinds of things.

Nuclear spins are actually already naturally protected. The electrons around the nucleus serve as a kind of shield, keeping the radio waves away from the nucleus. This makes it very hard to control, and very slow to act and measure. But the advantage is that we can keep the state exactly the way we want it for a long time, so nuclear spins can make good memories, for example, for quantum networks or long computations where some of the data isn’t used for a long time.

3-D Printing

If you would like to print your own copy of the 3-D model of silicon atoms shown in this video, you can use either of these two files:

  • STL file Most 3-D printing software will take this file for printing. You will probably want to adjust the scale to suit your printer. For your printer settings, we recommend printing this with a raft, but without support.
  • OpenSCAD file If you would like to modify the shape and are willing to do a little programming, this was created in a language called OpenSCAD.

The face that prints diagonally (the largest face) is known in crystallography terms as the (111) face. For silicon computer chips, this is the surface on top of which transistors are built.

If you would like a smaller model with fewer atoms, this one is a smaller cube, and includes a scale bar on the side that represents one nanometer at the scale of silicon.

  • STL file Most 3-D printing software will take this file for printing. You will probably want to adjust the scale to suit your printer. For your printer settings, we recommend printing this with a raft, but without support.
  • OpenSCAD file If you would like to modify the shape and are willing to do a little programming, this was created in a language called OpenSCAD.

By the way, diamond has the same crystal structure as pure silicon, though of course it is made of carbon atoms instead of silicon. The atoms are also packed more tightly in diamond.




核スピン

原子は原子核と電子から成り電子は核の周りを周回しています。前回までに、電子がどのように量子状態変数を作るのに利用されているのかを学んできました。実はこの方法以外にも原子核を利用するという方法があります。慶應義塾大学の伊藤公平教授がどのように核スピンを量子ビットとして利用するのかについて説明してくださいました。

電子にはスピンがあり、周囲の磁場によって同じ方向に向けることができ、スピンアップと反対方向を向くスピンダウンがあるというのは前回までに学んできました。原子核は陽子と中性子によって構成されていることはご存知かと思いますが、それらは電荷や質量だけではなく核スピンも持っています。原子(たとえば炭素)は陽子の数は決まっていますが中性子の個数によっていくつかの種類が存在します。これを同位体(アイソトープ)と呼びます。原子核の性質は非常に複雑ですが、特定の原子の同位体については非常にシンプルに扱えるため、それらを量子ビットとして利用することができるのです。

実は量子ビットの実験に核スピンは初期から用いられてきました。スタンフォード大学でLieven Vandersypen 氏が開始し、今は大学院生が受け継いでいるチームでは、普通の水素(\(^1\)H)とフッ素系の同位体(\(^{19}\)F)、炭素の同位体(\(^{13}\)C)が含まれた液体を用いて量子ビットを作る実験を行いました。他にもリン (\(^{31}\)P)やケイ素(\(^{29}\)Si)、ダイヤモンドなどを用いた実験も行われています。

制御と隔離

理想的な状態変数であるには2つの条件を満たしている必要があります。1つは容易に操作ができること。もう1つは放射線や無線LAN、マイクロ波などによって状態が壊れないように環境からうまく隔離できることです。実際にデバイスを作る時には環境から隔離するための機構が非常に重要になってきます。

しかしながら核スピンというのは、その性質から、守られているといってもよい状況です。核の周りに存在する複数の電子がシールドの役割を果たし、ラジオの電波など環境からの影響を受けづらくなっています。一方で同時にこれは操作が難しく、動作や測定にも時間がかかることを意味しています。ただ、長所として量子状態を正確に長期間保つことができるので、核スピンは量子ネットワークや長時間の計算時に有用な記憶装置としての利用が期待されています。

3-Dプリンティング

この動画内で登場した3-Dシリコンモデルが必要であれば、以下の2つのファイルをダウンロードしてください。

  • ほとんどの3-Dプリンティングソフトの場合STLファイルを利用できると思います。ご自身でサイズを調整してご利用ください。プリンターのセッティングの際はサポート材は使わずラフトを利用することをお勧めします。
  • もしご自身で整形したければ、OpenSCADファイルをご利用ください。

斜めに印刷される表面(最も大きな面)は、結晶学の用語でミラー指数が(111)と表されます。半導体コンピュータチップのトランジスタはこの構造上に構築されます。

より少ない数の原子を用いてもっと小さいモデル作りたいければ、以下の小さな立方体をご利用ください。サイドバーに1ナノメートルのスケールが表示されています。

  • ほとんどの3-Dプリンティングソフトの場合STLファイルを利用できると思います。ご自身でサイズを調整しご利用ください。プリンターのセッティングの際はサポート材は使わずラフトを利用することをお勧めします。
  • もしご自身で整形したければ、OpenSCADファイルをご利用ください。

ちなみに、ダイヤモンドは純粋なシリコンの結晶と同じ構造を持っており、もちろんダイヤモンドはシリコンではなく、炭素の原子でできています。また、ダイヤモンドの方が、より高密度に原子が並べられています。

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This video is from the free online course:

Understanding Quantum Computers

Keio University