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Computation and Quantum Chemistry/計算と量子化学

Computation and Quantum Chemistry/計算と量子化学
3.5
Feynman recognized that doing the calculations for quantum chemistry, understanding how atoms behave and how they bond into molecules. Topics like that was difficult for a classical computer and so he proposed that maybe we could build a machine that operates on quantum principles that would solve those same kinds of problems. That’s what we call a quantum computer today. So, quantum chemistry is actually really important and difficult field in a lot of ways, and we have with us today one of the world’s experts on how you might actually solve quantum chemistry problems on a quantum computer, Dr. James Whitfield who is a Professor of Physics at Dartmouth College. James! Welcome. Thank you. Thank you for the invitation. I’m glad to be here.
53.7
First I just gave a rough definition of quantum chemistry. Let me hear your definition of quantum chemistry. What are the kinds of things we are trying to solve or learn when we’re solving quantum chemistry problems? Right so, quite often chemistry; you have a lot of these things, molecules and atoms, and we are interested in how they behave, but because they are so tiny the underlying physics and the underlying rules for how they behave is quantum mechanical. And thus you need quantum mechanics describe them; this allows us to understand many things, right. For instance the electronic behavior of these how the electrons moving around, molecular orbitals and things like this.
90.4
What the electrons actually form is actually dictates a large part of the vibrational motion, the rotational motion, the other various motions that can occur. And it turns out in quantum chemistry, quite often we’re interested in the ground state electronic potential. Because it turns out that the electronic excitations, because we can see things around us, have colors. Great. So.. Tell me why is solving these problems actually hard for a computer? Well the problem size grows exponentially, as you pointed out in some of the earlier articles inside the course, the size of the Hilbert space, the problem space grows very large with the number of qubits that you have. The same thing is true with the number of electrons that you have.
135.2
So more electrons that you have the larger the problem becomes and then it becomes exponentially hard to approach with most or all known classical algorithms. Every time we are talking about a molecule when we add another atom to the molecule, it gets twice as hard to calculate the behavior of the system or some factor like that? Right, or you could even think, even if it didn’t get too much harder, right. You can think–if you’re talking about proteins and we scale up to the entire cell. There is a large, large, large number of electrons that are dictating the behavior of everything inside that cell.
168.5
But to take into account all of those electrons, we are going to need a very large computational machines. And if the scaling is very poor then we’re not going to be able to go past very small atoms, molecules inside of the system. Great so. Who actually solves quantum chemistry problems and why. What are they trying to learn, or do, or build? In particular, I work on electronic structure.
191.3
And quantum chemistry is very broad, so there are a lot of different aspects to it, there’s vibrational structure, people are interested in how these things are vibrating and this would dictate, say thermal properties if you want to know what happens for an infrared camera for instance and this would be all dictated by the vibrational properties. If you want to know what things look like, how they respond to optical frequencies, optical wavelengths would be what color they give off, what color they absorb at, and thinks like this would all be important things, so the detection of helium, for instance, was done just looking at the sun and seeing what spectrum lines came through.
223.2
To understand why these things occur is where the quantum mechanics comes in, the quantum chemistry, the quantum physics, where they start to play a role in understanding the world around us. Great. So at a practical level, does it affect how we do material design or drugs or some other sort of chemistry? Yeah it’s a good point, yes of course it does. With material design and a lot of these things, and especially nowadays where this is a large, large scale computational projects where we just have tremendous amounts of computational power around us. You can really do the screening studies. Where you really start looking at just random instances to try and find something that matches what you’re looking for.
264.3
So drug design for instance, if you want to know something that binds to a particular site, you just try everything and see which one actually fits the best. The idea of quantum computing, is that we can try these things faster, we can try larger sets of things, and we can try them as quickly as possible and really make better screening techniques for doing these material designs. Let me ask you a question. What’s your favorite problem that you’re hoping someone will solve using a quantum computer? Me personally, I’m very interested in the computational aspects of the problem.
294.7
Then I would like to solve the problem quite generically, that if you think about a pharmaceutical company or a material design company, they are really interested in particular instances in application areas, right! In the idea of what we’re trying to do with quantum computation and largely with electronic structure packages in general is to make general-purpose tools that work well, that work better over a wide range of systems. They give back better answers with lower error bars and faster. Really optimizing the toolset, so if you want to know what building you could build, you just need the tools. So we are working on the tools side. I really focus on how I can really scale up problems.
336.8
To understand what’s the best format to put data in, in order to understand the problem. I find is much more exciting, the mathematical problem than the actual physical problems. But when your research then is successful then lots of other people will be able to use it for…? That’s the goal that it should be widely applicable to anybody doing electronic structure methods or using computers to understand chemistry or physics. Just help everybody. Sounds good. Microsoft research is fond of talking about the Haber-Bosch process, which is used for making fertilizers and they’ve pointed out that 1% to 2% of all of the world’s energy that’s consumed today is actually used in this process for making fertilizer for agriculture.
384.1
How can a quantum computer actually help us with that particular problem? I believe this is catalytic problem. So with catalysis what happens is that you really want something to help you get over your reaction pathway faster. In catalysis quite often you have perhaps some metal complex inside the center, so it’s iron-sulfur complexes and things like this where you end up with these very large atoms that will provide a lot of intermediate states, and distinguishing between these different states is very difficult for the methods that we typically employ, So with this, it really requires a better physical description and that’s where the quantum computation comes in.
426.9
So it’s a nice problem that’s difficult to approach from a classic computer that also has a nice application area and like you said nitrogen fixation, your fertilizers and things like this it’s very important problem. Great. So when we succeed with quantum chemistry, which is the area that Feynman first proposed for working on quantum computers it’s going to have a real positive impact on society in many different ways. Yeah. Medicine for instance. Understanding how better drug discovery, drug designs as you mentioned earlier, material design, making stronger paints and things like this, less scratch resistance glasses for instance things like this, all these things people want to understand both computationally as well as engineering wise. Is that a word? So that’s great.
479.4
James, thank you for that description of how we can use quantum computers to solve quantum chemistry problems and we will have you back later in the course to actually talk about some of the algorithms. Excellent, thank you.

Dartmouth大学のJames Whitfield助教授が量子化学の概念や、解決することのできる問題について解説してくださいます。以下の文章では、これらの問題が現代社会においてなぜ問題なのかということについて解説していきます。先にビデオを見ても、この文章を読んでくださっても構いません。

20世紀に起きた緑の革命によって、世界の食糧生産率は格段に上昇しました。多くの国における飢餓の原因は、十分な食べ物が生産できないことではなく、むしろ経済的格差や貧困、ガバナンスの弱体化に起因しています。この世界的な食糧自給を支えている一つの大きな要因が、空気中の窒素を固定し植物が取り込みやすい形にした、合成肥料の存在です。この手法はハーバー・ボッシュ法として知られ、人類が生産する全エネルギーの約1~2パーセントをも利用しています。この手法に代わる、より省エネルギーで実現可能な手法を見つけることは、人類にとって非常に大きな利益となるのです。

化学者たちは、分子の構造やそれにかかるエネルギーの大きさなど様々な分野に関して研究を行なっています。これらの情報から彼らは、異なる状態下において分子がどのような形状をとるのか、より大きな構造を持った時にどのような形となるかなど、化学反応がどのようにして起こっているかや、特定の反応でエネルギーが放出されているのか、吸収されているのかということを理解する上で重要な現象について推測を行なっています。

これらの計算ができることによって、肥料などがより効率的に生産されうる可能性があり、量子コンピュータはこの計算に一役買うのではないかと考えられています。またそのような過程の中で、植物の光合成の詳しい仕組みの理解や、強度、柔軟性などに優れた新たな材料の開発に繋がっていく可能性もあります。

それらの計算は、量子化学として知られ、量子コンピュータを用いることでより発展しうる分野であると考えられています。量子コンピュータを理解する上で重要である、量子力学の重要な概念について議論を行う時に見ていきますが、分子などのように、正確に量子系を記述しようとした場合、関与している電子や原子の数に応じて、指数関数的に計算が複雑になっていきます。これは古典コンピュータにとっては莫大な計算量となってしまいます。

幸運にも、私たちが分析したい状態が指数関数的に増えてしまうこの問題には、ある解決策があります。それは量子コンピュータを用いることです。多くの場合、私たちが求めたいのは、平均のエネルギーや、全ての可能な振動が同時に起こった場合などの可能性のある状態を集計したものや、最も低いエネルギー状態などの特定の状態などです。

この分野での計算の難しさは、どこまでの精度を答えに求めるかに依存しています。すでに議論したような素因数分解のような問題であれば、必ず特定の解が存在しています。しかし、多くの計算は、現実世界においてどのようなことが起こるか推測するために行われており、非常に複雑な値であったり、理想的なモデルとは必ずしも一致しません。従って、ある程度十分な値が出てきた段階で、計算を止めるべきポイントを見極める必要があるのです。

そのような疑問はさておき、量子化学は量子コンピュータにおける問題の基準を理想的に満たしているのです。全てのデータを用意したり、読み書きにかかるメモリーが小さく、分子の大きさが大きくなるにつれ、可能性のある答えは指数関数的に増大していくからです。

実際、量子化学は、ノーベル賞受賞者であるCaltech(カリフォルニア工科大学)のRichard Feynman氏によって、1980年代初頭に現在の量子コンピュータのようなものが提唱された時に、同時に提唱された量子コンピュータへの応用が可能な学問分野です。比較的に扱いやすい点と、人類への利益の大きさから、現在では最も期待される量子コンピュータへの応用分野の一つとされています。

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量子コンピュータ入門

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