# Can a classical limit of qubit emerge on a classical computer? [closed]

Hello,

I am uncertain; however, today at a toy museum, I might have captured a qubit on a classical computing structure, “ a broken 90-marble abacus,” as shown in the attached photos above.

I did not use it correctly, but if we set the first photo to be the state “0”, then the next one is “1”. You may say the third photo shows 0.5, but you can also say that it is a bit closer to 0 or 1. Thus, while we observe this purple marble positioned between 0 and 1, we cannot tell if it moves to 0 or 1 until we measure its displacement. Therefore, I wonder if it can be said that the classical limit of qubit emerged on classical computer in this third photo? Its probability of being 0 or 1 is fifty-fifty.

The picture below gives a further explanation with a chart of marble A's location. In abacus computing, the states of A are limited to four states, namely, resting at 0 or 1, or moving toward 0 or 1. A cannot rest between 0 and 1. Abacus computing is observed by taking two photographs during its sequence giving two locations of A. When taking the first shot, we can know A's location and not sure if it is moving or resting. Then we take a second shot and know how it moves. After all, we can tell or predict its outcome 0 or 1. Thus, when we observe the initial location of A, this is the state of the classical limit of qubit, which has fifty-fifty probability of becoming 0 or 1, until secondary observation.

This concept can be extended to tossing coin or tumbling dice. If the observer is unable to predict those outcomes by observing those motions, the observer can tell only classical probabilities.

Thank you,

Ryoji

• Your example can serve only as a model for explanation what a qubit is. But abacus is macroscopic entity, hence it cannot show a quantum behavior and it is not a quantum system. Dec 19 '19 at 19:45
• Dear Martine, all objects in the real world, small and large, are quantum systems in the sense of being subject to quantum mechanics at all times. Classical physics is always at most an approximation that may be more or less good for some purposes. The abacus doesn't effectively preserve quantum coherence and becomes complicated but that doesn't change the fact that the fundamental laws that govern it are still the laws of quantum mechanics. Dec 21 '19 at 9:23

A computer that may be visualized in this simple way, like abacus with moving marbles, where the locations of the marbles are continuous, including 0.5, is called an "analog computer" and it is a different, and much simpler, thing than a quantum computer.

What may be changed continuously in a quantum computers aren't the observable locations (or voltages) themselves but the probability amplitudes for each configuration. When it comes to allowed values of each qubit, each of them may still be just 0 or 1 and nothing in between. However, the quantum computer allows each qubit to be indeterminate, having some probability to be 0 and some probability to be 1.

In fact, each of the $$2^N$$ configuration of $$N$$ qubits may be given some probability that is independent from others. And quantum mechanics makes it more juicy. It's not just probabilities $$p_i$$, $$i=1 \dots 2^N$$, that specify the state of the quantum computer at the moment. Instead, it's complex numbers, the probability amplitudes, $$c_i$$ related to $$p_i$$ by $$p_i=|c_i|^2$$, that are needed to describe the state of the quantum computer at a given moment.

An operation performed by the quantum computer is some particular linear transformation (given by a matrix, $$2^N \times 2^N$$) of these $$2^N$$ complex numbers. This calculation involving $$2^N \times 2^N$$ continuous numbers could be simulated by a complicated classical computer with lots of memory and representation for the continuous numbers.

However, this operation that looks complicated in the simulation is achieved by the quantum computer's step that is basically comparably difficult to an operation of a classical computer with $$N$$ single bits that just maps some bits to a simple function of the neighbors.

The quantum computer doesn't allow "any" operation with the matrices to be done and it doesn't allow the complex numbers to be measured. Instead, just the bits themselves, with results either 0 or 1, may be measured by the quantum computer. So the class of quantum computers or quantum simulations is "more special" than the class of operations done on a classical computer with $$2^N$$ complex numbers. But despite this restriction, the quantum computer is capable of doing some things much more quickly than the classical computers.

A usable quantum compouter was first built by Google and, at least according to some precise definitions of the term, has achieved "quantum supremacy" which means quickly doing a calculation that could only be done very slowly at the world's fastest classical computers.

• Just note on the first quantum computer. I think that IBM Q was the first one. Additionally, "quantum supremacy" is fancy term used widely nowadays. I would be careful with general statements like "which means quickly doing a calculation that could only be done very slowly at the world's fastest classical computers" because speed-up depends on particular task (e.g. exponential speed-up for integer factoring - Shor while only quadratic for database searching - Grover). Dec 19 '19 at 19:20
• in the classical computing, the purple marble is allowed only 4 states. resting at 0 or 1, and moving from 0 to 1 and opposite direction (not allowed resting at 0.5). so when we take the picture like third one, we can obtain information of the marble's location and we are still not sure which direction it moves. then we take the second shot, we see it moved slightly to 0 or 1. Dec 19 '19 at 19:51
• Luboš Motl and Martin Vesely, thank you for your comments. I added further explanation with picture. I think qubit can be visualized in the classical limit on the classical computer. Dec 20 '19 at 12:05
• Dear Martine, the speedup surely depends on the task and people are careful about quantum supremacy - except for SJWs who find the term racist and not careful enough LOL. Quantum supremacy takes place when any kind of task is solved much more quickly by the quantum computer than the classical one. It is obvious that the speedup will be almost non-existent for some particular tasks. Preskill and the people who defined the quantum supremacy did so carefuly and if you are not careful, it's your fault, not theirs. Dec 21 '19 at 9:25
• Hi, I think the first gear up to any classical commands would come with existing voltage bit generated semiconductors by replacing logic gates to what I suggested at the latter part of my paper ryoji.info/cqc.pdf . Google also used semiconductors but with quantum spins as bit at nearly 0k environment. I guess the most stable quantum bit is plasmon generated on graphens or like these. Dec 22 '19 at 2:17