【メモ】 Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos (Seth Lloyd)

グッとくる文章だけ引用。

The quantum-computational nature of the universe dictates that the details of the future are intrinsically unpredictable. They can be computed only by a computer the size of the universe itself. Otherwise, the only way to discover the future is to wait and see what happens. (p.4)

After the first controlled-NOT, the demon's bit is perfectly correlated with the state of the gas bit. That is, the demon now "knows" the value of the gas bit. More precisely, as far as the demon is concerned, the entropy of the gas bit is zero, because it is conditioned on the state of the demon's bit after the operation, a state the demon knows. (pp.95-96)

マックスウェルのデーモンの思考実験では、デーモンを物理的なシステムとすると、必ず気体の系と相互作用しなければならなず、相互作用の過程（ここではcontrolled-NOTの演算）の前後を通して、気体粒子に関する情報が必然的に（デーモンの中で）保存される、ということ。だからデーモンを含めた系全体として見れば、エントロピーは減少していない。

Even if the underlying laws of physics were fully deterministic, however, the computational ability of simple systems such as colliding spheres implies that to perform the type of simulation Laplace envisaged, the calculating demon would have to have at least as much computational power as the universe as a whole. Since, as we shall see, computational power requires physical resources, Laplace's demon would have to use at least as much space, time, and energy as the universe itself. (p.98)

The reason [that bigger things tend to behave more "classically" and less quantum-mechanically] lies not so much with the physical size of the objects as with its visibility. The bigger something is, the more interactions it tends to have with its surroundings, thus the easier it is to detect. In order to go through both slits at once and produce the interference pattern, a particle must pass through the slits undetected. (p.107)

All that is required to destroy the interference pattern is for some system, no matter how small, to get information about the position of the particle. (...) It is now clear why big things tend to show up in one place or another, but not both. Pebbles, people, and planets are constantly interacting with their surroundings. Each interaction with an electron, a molecule of air, a particle of light tends to localize a system. Big things interact with lots of little things, each of which gets information about the location of the big thing. As a result, big things tend to appear here or there instead of here and there at the same time. (p.108)

The process by which the environment destroys the wavelike nature of things by getting information about a quantum system is called "decoherence." (p.108)

The information about which slit the particle went through infects first the detector, then me. If I write you a letter telling you whether or not I heard a click, then when you receive the letter your relative state will reflect what happened: |Seth wrote me to say he heard a click> or |Seth wrote me to say he didn't hear a click>. Now you have become entangled with the particle, the detector, and me. After the measurement, the information about its outcome spreads to infect whatever it comes into contact with. (p.122)

because the behavior of elementary particles can be mapped directly onto the behavior of qubits interacting via logic operations, a simulation of the universe on a quantum computer is indistinguishable from the universe itself. (p.154)

To look at this from another angle, numbers produced by short programs are more likely to appear as outputs of the [programming] monkey's computer than numbers that can be produced only by long programs. Many beautiful and intricate mathematical patterns - regular geometric shapes, fractal patterns, the laws of quantum mechanics, elementary particles, the laws of chemistry - can be produced by short computer programs. (...) Algorithmically probable things are just those things that exhibit large amounts of regularity, structure, and order. (p.184)

この説明が実際の宇宙で意味を成すためには、コンピュータと猿のそれぞれの対応物が必要だが、Lloydによると、コンピュータは量子力学の法則、猿は量子ゆらぎに対応しているらしい。ということは、宇宙の発生（計算の始まり）に先立って存在していなければならないのは、量子力学の法則（あるいは重力を織り込んだ量子重力理論？）に限る、ということだろう。しかし上の引用では、量子力学の法則も、ランダムなゆらぎの結果生じるかのように書いてある。何が計算に先立っていて、何が計算の結果生じるのか、はっきりしてよLlyodさん！