Translating classical math and code to quantum math and code

Question

I am starting to see a lot of classical quantitative problems such as linear regression being represented in quantum math, which suggests that almost anything based on frequentist statistics could be upgraded to the fancy 'braket' notation found in quantum math, in the same way that Bayesian interpretations of classical math models are currently abundant on the side line.

Ignoring the fact that anyone without a Masters in physics does not have the background to grasp or make a career out of quantum programming applied to their own discipline, at least what fundamental tenets, principles, and approaches, beyond just the qubit and circuitry theory, would help with the practical translation of existing classical math and Python code to their quantum counterparts? And is there a foreseeable demand in this sort of work, assuming that the quantumification of maths and code for some antiquated problem specific to some discipline at least generates a small speed-up over classical formulas and code?

Any holistic sources that discuss the impending migration from the classical to quantum paradigm math-wise would be great as well.

Answer 1

Bra-ket notation is not necessarily tied to "quantum math," it's simply a convenient notation in many circumstances. It may seem intimidating at first, but once you understand the basics (ket = vector, bra = covector) it's straightforward to grasp, as long as you have a solid understanding of Linear Algebra. If you are shaky on Linear Algebra, different notation is unlikely to help.

Quantum algorithms on the other hand are entirely different. These involve deep insights that may span several fields (particularly Math, CS and Physics), and I doubt that understanding them is easy for anybody (including physicists). Anybody from one of these three fields will certainly have a head start, but anyone with a STEM background and sufficient motivation should be able to learn the material. Nielsen and Chuang cite "mathematical maturity" as the key prerequisite.

Once the hardware is available to run meaningful quantum algorithms, I have no doubt that demand will vastly exceed supply of people capable of applying quantum algorithms to domain specific tasks. There is, however, a fair amount of uncertainty as to when that day will come.

I don't really know any references that match your request well, but you might find John Preskill's keynote address on NISQ era quantum computing helpful.

Answer 2

At least currently, most of the translations being made are in extraordinarily specialized areas - for example, quantum chemistry / computational chemistry. A lot of the math involves mapping domain math to quantum computers - ab initio molecular simulations need to map their traditional annihilation/creation operators to the X, Y, Z gates in quantum computers (https://arxiv.org/abs/1001.3855).

There likely will be demand for people who are able to effectively create new domain-specific quantum algorithms / apply existing quantum algorithms to solve new problems.

A big point is that quantum computers will not be stronger at all operations! We will likely not need to mitigate over much common classical code; instead, quantum computers will act as accelerators for specific operations (much like GPUs for graphical operations).