One of the comments on my previous post about the physical representation of qubits prompted me to dig a little deeper into existing resources, to see if I could better understand how quantum computers reach low-level states naturally, and how that affects the programming aspect. While doing research on that, I think I’ve clarified a couple of things for myself.
First, I found this great D-Wave whitepaper on how you would approach programming a quantum computer to solve a map coloring problem, compared to traditional computing. As they say, instead of explicitly programming the steps of the algorithms, you instead program in what I think of as the “error function” — the thing you want minimized. I find quite a lot of similarities here to machine learning, and I can see why people say that quantum computing could really help solve machine learning problems. Like in many machine learning algorithms, you try to minimize some error function (i.e. root-mean-squared error on a test data set). Even Figure 3 of a quantum cell (page 6) looks kind of like a neural network, especially if you squint. But one thing that I didn’t understand very well was the use of qubits in the cells. People talk about ~50 qubits as being able to perform things traditional computing cannot. Yet according to this whitepaper, if you extend the problem to all 13 Canadian states, solving this relatively straightforward problem would require 104 qubits (13 provinces * 1 cell per province * 8 qubits per cell), which seems excessive…so not quite clear if that is because this is a simplified example or dependent on the D-Wave architecture.
Second, I came across this great 2013 article from Scientific American that addresses some of the questions I brought up in my previous post about quantum parity. Apparently for at least two types of quantum systems (superconducting circuits and trapped ions), they seem to solve simple calculations similarly, though there are differences in speed and error propagation. With Microsoft introducing topological qubits, it will be interesting to see if it performs similarly to the other two technologies. One new term that I learned from the article is “quantum volume”, which encapsulates the idea that the published number of qubits does not reflect the actual processing power (what I referred to as quantum parity)! So increasing quantum volume will actually help solve more complex problems, instead of just the “raw” number of qubits.
So overall I think +1.5 for understanding this week.