High School Quantum Computers and their special properties?

[LightningInAJar]

I believe at the current time quantum computers can't get as much done as fast as normal computers, but do quantum computers have access to information by its own nature that allows it to run special calculations that normal computers can't?

In particular physics or biology simulations using input from the physical world itself versus a normal computer which is basically entirely internalized?

 

[gentzen]

In particular physics or biology simulations using input from the physical world itself versus a normal computer which is basically entirely internalized?

Yes, they do have access to such information. And with currently existing quantum memory technology (stable for 10 seconds), they should already be able to exploit it. Quadratic improvement is definitively possible. There are also theoretical scenarios where exponential improvement seems possible, but it is still unclear how practically relevant they are.

 

[LightningInAJar]

I remember during the pandemic there were labs asking people to volunteer their PCs to help do processing to help speed along the research into the first vaccines, but I assume currently it isn't considered ethical to try anything on humans that hasn't been tested biological. They can't simply trust the calculations. But maybe with quantum computers a virtual human can be tested on someday? Or is that science fiction?

 

[Grelbr42]

I remember during the pandemic there were labs asking people to volunteer their PCs to help do processing to help speed along the research into the first vaccines, but I assume currently it isn't considered ethical to try anything on humans that hasn't been tested biological. They can't simply trust the calculations. But maybe with quantum computers a virtual human can be tested on someday? Or is that science fiction?

No.

The advantage of quantum computers is not related to total volume of throughput or total amount of memory or any such thing. For the ordinary run-of-the-mill type calculations, QC is actually not as good as the type of computers we have now.

Rather, there are certain types of tasks they are (potentially) good at that are incredibly difficult with standard computers. Here is an example. Consider multiplication.

So you are no doubt used to being able to input the x's and get the R = x1 * x2 * x3 * ... * xn. But along comes the QC. And a QC is reversible. You don't have to put in the x's. You can put in any combination of the "wires" attached to this device, and it will solve for the non-supplied. (Or tell you there is no solution.) So, you can input the R and get the x's. And you can get it in microseconds. That is, it can do factorization.

Now, if you know anything about cryptography, you know that this is a big deal. There are important cryptography schemes that involve multiplying by large prime numbers to get an encrypted sequence. So, in principle, a QC can crack such encryption. Ordinarily, with normal computers, this is thought to be intractable, hence why it is considered a fairly strong form of encryption.

At present the better QC don't have enough bits to do any serious such calcs. But people are working on it.

There are a bunch of other problems of this nature. There a lot of ways to set up an arithmetic problem so that it is fairly easy to go in one direction, and very hard in the other. For example, it might saturate bitcoin because it might make it possible to do the "mining" calculation at a rate that produced a new coin on every cycle of the CPU.

 

[.Scott]

So you are no doubt used to being able to input the x's and get the R = x1 * x2 * x3 * ... * xn. But along comes the QC. And a QC is reversible. You don't have to put in the x's. You can put in any combination of the "wires" attached to this device, and it will solve for the non-supplied. (Or tell you there is no solution.) So, you can input the R and get the x's. And you can get it in microseconds. That is, it can do factorization.

You are referring to Shaw's Algorithm. Shaw's Algorithm does factorization, and if you wish to skip the details it is OK to say that it "reverses multiplication".

But if you do go into the details (as provided in the wiki link above), you will discover that there is no actual "reverse multiplication". Instead there is some preliminary classical computations that either screen out certain easy solutions or find a suitable coprime integer to probe for the answer. The quantum part of the algorithm then finds an exponent for that coprime that yields 1 modulo N (N is the number to be factored). Then its back to classical computations. If that exponent is even, it is used to compute the factors. Otherwise, new coprime probes are generated until one is found that produces an even exponent.