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## Keio University

NOAA's Tide Predicting Machine No. 2( 24 April 2017, at 10:15). In Wikipedia

# Are Qubits just analog?

Qubits carry information in superposition and entangled states, which gives them capabilities that analog systems do not have.

## Analog classical data

We can build computers using continuous variables, giving us an analog computer. Analog classical computers were built up through the 1960s, and researchers such as Caltech’s Carver Mead continued working on them using VLSI in the 1980s. They can be mechanical or electrical systems, or a combination of the two. (I (Van Meter) actually took a class from Carver Mead on analog VLSI in that era, at Caltech; I learned a tremendous amount about both the technology and what it means to be a researcher, but I flunked the class!)

Analog computers work well on certain kinds of differential equations, performing integration and differentiation directly, making them useful for tasks such as predicting the tides. Some current-day researchers believe we will ultimately move back to such analog systems for many computational tasks that today are done digitally.

## Quantum data

A common question that comes up when beginners (especially if they are experienced computer people) learn about the phase of qubits and the fact that they can be “partly” in the zero state and “partly” in the one state is, “Doesn’t that just mean that qubits are analog? We’ve been building analog computers for a long time…”

We have already talked about superposition of quantum states, so at first glance it might seem that superposition is the key. But, in fact, an analog system can also carry signals with multiple frequencies at the same time, so superposition alone is not the answer.

Two factors distinguish quantum bits from classical analog data: measurement collapse and entanglement. We saw just a few Steps ago that a qubit, when measured, always collapses into either 0 or 1, with a probability based on the square of the size of the quantum amplitudes. This may seem to be a dubious feature, or even negative, given that it allows us to only extract a single bit out of the state. In an analog computer, in contrast, with appropriately sensitive measuring devices we could directly measure the amount of zero and one, and even the phase. Isn’t that more information?

In a sense, the collapse of the qubit does destroy some information about the superposition of the state. However, once we have learned how to make good quantum algorithms, that collapse also helps us, by taking away parts of the superposition that we didn’t want. This effect will be seen very clearly in Shor’s algorithm for factoring large numbers, in particular.

That’s still only half of the answer, however. Entanglement is a key feature of quantum systems in which two (or more) parts of the system show a type of correlation that cannot occur in classical systems. This entanglement, among other things, helps us keep separate terms of the superposition of multi-qubit systems in a way that a classical analog computer cannot.

In the next Activity, we will learn much more about entanglement.

# 量子ビットはアナログか？

## 従来のアナログデータ

アナログコンピュータは、特定の微分方程式の解を求めたり、微分積分や潮位を予測したりする上で非常に効果的でした。 そういった理由から、一部の研究者たちは、デジタル計算の一部をアナログ処理に戻していく必要性が将来出てくるであろうと予測しています。

## 量子データ

ある意味で、測定による量子ビットの崩壊は、もとの重ね合わせにあった量子状態を部分的に破壊してしまっているとも言えます。 ところが、こういった情報の破壊にメリットが一切ないわけではありません。 量子ビットの崩壊を逆手に取って、必要ない重ね合わせ状態をシステムから取り除いてあげることで、量子アルゴリズムの効率が上がり、結果役に立つことがあります。 この有効性は、特にShorの素因数分解アルゴリズムにおいて明確に確認することができます。

ですが、これはアナログと量子の違いの答えの半分に過ぎません。 従来型のシステムには存在しないもう１つの重要な特徴が、「量子もつれ」で、２つ以上の量子ビットが、ある種の相互関係の状態になるという現象です。 こういった量子もつれや、重ね合わせ状態の崩壊等の特徴が、量子コンピュータと従来のアナログコンピュータとの違いを生んでいます。