hershkumar

le mois dernierdiscuss

I find it strange that it’s so often framed as a competition between classical and quantum computation, when in practice the development for quantum algorithms has led to many advances in classical computing; quantum algorithms require large systems, and the struggle to represent those large systems classically has led to many different frameworks (tensor networks, neural quantum states, etc) which are interesting even separated from the context of quantum computation.

hershkumar

il y a 6 moisdiscuss

Most of what I use day to day in research is either specialized to my subfield or can be found in Nielsen and Chuang, so I've actually never looked at any other textbooks specifically for quantum computation. If you're interested in more of the information theory aspect, I have heard that "The Theory of Quantum Information" by John Watrous is a good text, but I have not personally read any of it.

As for Modern Physics, if you have the math prerequisites and you want a broad overview, the series of textbooks by Landau and Lifshitz would be my go-to. However, the problems are quite challenging and the text is relatively terse. I think the only other textbook that I've used personally would be Halliday, Resnick, and Krane. I didn't read a great deal of the textbook, but I do recall finding it relatively well-written.

hershkumar

il y a 6 moisdiscuss

1) Generally the two models of QC are the digital/circuit model (analogous to digital logic gates, with some caveats, such as reversibility of operations, no-cloning theorem), and analog computation (tuning the parameters of a continuous-time quantum system in your lab such that the system produces useful output)

2) The physics/architecture/organization depends heavily on the type of computer being discussed. In classical computing, one "type" of computer has won the arms race. This is not yet the case for quantum computers, there are several different physical processes through which people are trying to generate computation, trapped ions, superconducting qubits, photonics, quantum dots, neutral atoms, etc.

3) There are several ways that you can simulate quantum computation on classical hardware, perhaps the most common would be through something like IBM's Qiskit, where you can keep track of the degrees of freedom of the quantum computer throughout the computation, and apply quantum logic gates in circuits. Another, more complicated method, would be something like tensor network simulations, which are efficient classical simulators of a restricted subset of quantum states.

4) In terms of research, one particularly interesting (although I'm biased by working in the field) application is quantum algorithms for nuclear/high energy physics. Classical methods (Lattice QCD) suffer from extreme computational drawbacks (factorial scaling in the number of quarks, NP-Hard Monte Carlo sign problems), and one potential way around this is using quantum computers to simulate nuclear systems instead of classical computers ("The best model of a cat is another cat, the best model of a quantum system is another quantum system")

If you're interested in learning more about QC, I would highly recommend looking at Nielsen and Chuang's "Quantum Computation and Quantum Information", it's essentially the standard primer on the world of quantum computation.

hershkumar

il y a 7 moisdiscuss

simulation of quantum systems: quantum chemistry, nuclear physics, high energy physics, condensed matter physics, to name the most promising ones off the top of my head.

hershkumar

il y a 7 moisdiscuss

“Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the ﬁrst room, and it’s dark, completely dark. One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and ﬁnally, after six months or so, you ﬁnd the light switch. You turn it on, and suddenly, it’s all illuminated. You can see exactly where you were.” - Andrew Wiles

hershkumar

il y a 8 moisdiscuss

The hardware very much lags behind the algorithmic advances, much of the current push for new features in quantum hardware (midcircuit measurement/feedforward, phonon mode coupling, etc) often comes from theorist colleagues pestering experimentalists about whether their hardware can run their algorithms yet.

In fact, this is analogous to the original motivation for the development of classical supercomputers, physicists wanted to run expensive non-perturbation Lattice QCD calculations, so they co-designed some of the earliest supercomputer architectures.

hershkumar

il y a 8 moisdiscuss

I think the more convincing argument is that most known applications of quantum computers (sidestepping any hardware practicalities), are for niche problems (in my wheelhouse, quantum simulation), the average person has no (practically advantageous) reason to own a quantum computer.

hershkumar

il y a 9 moisdiscuss

If you prefer python, tenpy is quite nice for tensor networks as well.

hershkumar

il y a 9 moisdiscuss

Yeah this seems like a very useful technique for ground state properties, I’m also surprised in retrospect, having never heard of TWA before now.

hershkumar

il y a 9 moisdiscuss

Reading their paper, it does seem like this method is significantly simpler than using something like MPS, my main concern is the practical coupling regime for which this method works, I would imagine that it would fail closer to critical points in theories with phase transitions?

hershkumar

il y a 10 moisdiscuss

Practically speaking, QM can be taught without the assumption that students understand the Hamiltonian formalism, simply by starting with Hilbert spaces and operators on Hilbert spaces. In fact, I would claim that having taken a class on basic linear algebra would better prepare you to understand quantum mechanics than mastering classical mechanics. QM is generally taught by referencing classical mechanics, but I believe that's more reflective of the fact that most universities require classical mechanics as a core course, and students coming in to QM will have generally taken it.

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