Quantum Algorithm Implementations for Beginners

The way this starts seems to tell a story that I feel is quite disconnected from reality:

> As quantum computers have become available to the general public, the need has arisen to train a cohort of quantum programmers

It seems to peddle the idea that in a few years we'll replace all normal computers with quantum computers. I don't think this is even remotely plausible.

It's still an open question whether quantum computers that do anything useful at all are feasible. But even if they are - we can safely assume that for a long time they will be expensive devices, running in complex physical experiments, that will be reserved for very special needs.

From all we know QCs aren't magically faster computers that are suitable to do everything better. There are just a few very special algorithms where QCs have an advantage. That's certainly interesting, but even if it would be possible - and that's a big if - it's unlikely anyone will add them to our smartphones anytime soon, simply because there's no need for that.

If quantum computers arrive we'll need a handful of specialized programmers that are familiar with their algorithms. But not masses of them.

This paper is a good example of how much progress we've had in quantum algorithm research since the dawn Quantum information science. Here is another good survey for people who want to learn more about quantum algorithms [0].

From the abstract, it seems like a resource I wish I had when I was starting to get into quantum computation.

[0]: https://math.nist.gov/quantum/zoo/

I like the idea, but I must admit that (with my background of a mathematics researcher, but almost completely ignorant of quantum physics and quantum physicists' notations) it is rather difficult to understand. In particular the bra-ket notation (which to me is already difficult due to its breaking the obvious way to match parentheses, but this might just require some time) seems to be used inconsistently across the paper (I believe that different authors wrote about the different algorithms, and the variations are rather evident and unhelpful). There are some formulas of which I cannot make any sense (last example I found: in the definition of QFT inside Shor's algorithm, the k inside the ket ranges from 0 to N-1, while according to the introduction it should range on all the combinations of a certain number of qubits).

Also, some authors seem to take for granted some concepts (such as the properties of the quantum gates) that are not explained anywhere and not obvious to me.

Still, an interesting read.

I've started reading some quantum computing texts, and dabbled a bit with IBM's quantum computing experience, and this is where I get stuck:

I can follow the basics at the level of "gates" or circuits -- a lot of what's out there is essentially quantum assembly language or something of that sort.

But what about interfacing classical and quantum computing? Is the idea that you just run something from start to finish on a quantum computer? Or that you take the output from a classical system and input into a quantum system?

Some of the things I'd be most interested in with a quantum computer seem to require an interface with a classical computer, or at least raise the issue, which generally isn't addressed by these sorts of pieces. It's sort of assumed that you're programming whatever it is you're interested in at the level of machine/assembly code.

Page 9-10:

"Fig. 2 shows the circuit that was designed to fit the ibmqx4 quantum computer. The circuit consists of state preparation (first two time slots), a Toffoli gate (the next 13 time slots), followed by the 2 | ψ 〉〈 ψ |− I operator (7 time slots), and measurement (the final 2 time slots). We use q [0] (in the register notation from Fig. 2) as the ancillary bit, q , and q [1] and q [2] as x 1 and x 2 . Note that the quantum computer imposes constraints on the possible source and target of CNOT gates. Some care must be taken to choose the appropriate qubits to represent each variable so that the necessary CNOT gates can be implemented. It is possible to circumvent some of the limitations in the source and target of the CNOT gates (i.e., the source and target can be reversed), but this requires increasing the depth of the circuit. Our initial implementation utilized a Toffoli gate that used such an approach, but the circuit was significantly deeper and the results were inferior to the results with the circuit in Fig. 2.

"Using the simulator, this circuit produces the correct answer x = (1 , 1) every time. We executed 1,024 shots using the ibmqx4 and x = (1 , 1) was obtained 662 times with (0 , 0) , (0 , 1) , and (1 , 0) occurring 119, 101, and 142 times respectively. This indicates that the probability of obtaining the correct answer is approximately 65%. The deviation between the simulator and the quantum computer is apparently due to the depth of the circuit combined with the approximate nature of the quantum computer. We note that our first implementation of this algorithm which used a Toffoli gate with a depth of 23 (compared to a depth of 13 here) obtained the correct answer 48% of the time."

"We designed a circuit that implements an instance of Grover’s algorithm for an IBM 5-qubit quantum computer. The outcome was successful in the sense that the quantum computer successfully completed the search with a probability that is appreciably greater than 50%. However, the 65% success rate that was obtained is much lower than the 100% that is obtained by the simulator. Deeper and more complex oracles would likely produce less satisfactory results, and this is in line with our experience implementing the oracle with a deeper implementation of the Toffoli gate."

I'm still not sure how measurement of quantum computing results works, and this isn't helping.

this isn't related to the paper's content but why in the world are there so many authors? i mean if it were an experimental paper i wouldn't be surprised but this is theory (or at the least exposition).