Quantum Computing for Computer Scientists

I'll try to give here a crash course on how simulating quantum systems on a quantum computer works - not for the actual computer type in the article (D-Wave's quantum annealer) but on a traditional gate-based quantum computer. So, we have this thing called the Schrodinger equation. For our purposes, all you need to know is that it's an equation which can perfectly describe the behavior of a quantum system as it evolves in time. Examples of quantum systems include a single electron sitting in a magnetic field, photons going through closely-placed slits, or entire biomolecules doing biomolecule things. Simulating things on computers is great because of how darn easy & cheap it is compared to running the same scenario in the real world. We want to simulate quantum systems on computers. We simulate quantum systems by trying to mimic the action of the Schrodinger equation on the quantum system. However, (as Feynman famously pointed out in Simulating Physics with Computers [0]), classical computers are very bad at this. They take exponential resources to simulate a quantum system. Now, if you have a computer that obeys the same physical laws as the quantum system it's simulating - a quantum computer - we might be able to simulate the system with only linear resources. Let's take a very simple quantum system. Consider a single electron, sitting in a magnetic field. Electrons have a property called spin which is affected by magnetic fields. Electrons can have their spin be up, down,

The Quantum Computing for Computer Scientists video by Microsoft Research ( [VIDEO] ) really hammered it home for me. It goes slowly and the presenter, in his own words "shuts up and does the math".

Here is a video of a researcher at Microsoft Quantum lecturing on this: [VIDEO] "Quantum Computing for Computer Scientists.". However, even with understanding how a Quantum Computer works at its most basic level I still have difficulty understanding the more useful Quantum Algorithms: [LINK] [LINK]

I’ve begun to put together useful resources for learning more here: [LINK] I’d like to really flesh out that page; I’ve now come across so many folks that are amazing at explaining this stuff... It’s just a time crunch to juggle all this as you might imagine ;) These two videos in particular helped me get started: 1. What is a physical quantum computer? [LINK] 2. How might one compute using it? [VIDEO]

I will answer this question in two ways: one, I will tell you how I learned, and two I will tell you how I would have liked to have learned with the benefit of hindsight. Different people will value one more than the other, but both are more valuable than a giant list of resources with zero guidance where to start. How I learned: I started out like you, in possession of an undergraduate education in computer science. I began reading Quantum Computer Science: An Introduction [0] by N. David Mermin. This is a very good textbook, but I absolutely could not skim it. I had to ensure I understood every single line before moving onto the next. I had the impression I wasn't learning very quickly, when in fact (due to the textbook's density) I was taking in a huge amount of information. After a few weeks with the Mermin textbook, I bought Quantum Computing for Computer Scientists [1] by Yanofsky & Mannucci. This is a much softer introduction than Mermin, almost too soft: I skipped the first few chapters on linear algebra and complex numbers. However, in combination with the Mermin textbook, I acquired a good understanding of quantum computing basics. It was at this point I reached my own personal threshold for feeling I "understood" quantum computing. People often recommend Quantum Computation and Quantum Information by Nielsen & Chuang (also called "Mike & Ike") for beginners. I believe this is not good advice. Had I tried to learn from that textbook, I would have failed. However, it

Learning Quantum Computing based on skill level (math is the biggest friction point, suggested pdf should save you lots of time) (Recc is personal recommendations, Hi-Recc is look at ASAP) # QC Main Ideas - Rotate, Compute, Rotate - Think in Amplitude Interference # Beginner: -(Hi-Recc) Quantum Computing Primer (1.5hr) : [VIDEO] -(Hi-Recc) Math Primer for Quantum Computing (easiest intro/primer I found on the topic; Highly Recommend ) : [LINK] -- understand Bra Ket notation [<Bra|Ket>] (Ket as Column vector, Bra (Row vector) as Complex Conjugate of Ket (denoted as dagger) ) -- understand Kronecker product ( for multi-qubit systems) - Quantum Computing for Computer Scientists book - [LINK] - Quantum Math Primer (Faculty of Khan) (found a bit hard the first time around, pretty dense) : [LINK] # Intermediate -(Recc) Ryan O'Donnell CMU course [is the best if you want to really understand the capabilities of quantum computing, get practice with math, intuition] (algos connection to Fourier, Quantum Complexity Theory, Math best practices, learning multi-quibit systems) -- Quantum Computation and Information at CMU : [LINK] -- Lecture Notes (use as reference in case video is not clear, or camera shot lags/changes) [LINK] - Mermin's Textbook [LINK] - Nielsen & Chuang's Textbook [LINK] -- Nielsen's Lectures [LINK] # Advanced -(Recc) Scott Aaronson Graduate Course [LINK] -(Recc) Scott Aaronson Papers (really interesting) [LINK] - Complexity Zoo - List of Algorithms [LINK] -(Recc) Machi

If anyone is interested I've also created a short 1.5 hour lecture on quantum computing aimed specifically at software engineers & computer scientists, which has proven popular: [VIDEO] I'd love to answer any questions people have. In quantum computation, state behaves like a vector and logic gates behave like matrices that multiply the vector to get a new state value. It doesn't get too much more complicated than that.

Here is a long-ish video that explains quantum computers without using pop-science hand-wavy terminology [VIDEO]

There is absolutely no way to understand quantum mechanics without learning the math. All metaphors are faulty and will lead you to incorrect conclusions. Fortunately the advent of quantum computing has made the math quite easy - it's just linear algebra of the type one would pick up within the first week of an undergraduate course. I made a video aimed at computer scientists which you might find useful: [VIDEO]

I think this talk is an excellent 'foot in the door' intro. Should provide a solid foundation, and plenty of insider jargon to follow up on! [VIDEO]

For those who are interested, this lecture was sent to me as an overview of quantum computation for people like me: people who know how to code and know some basic linear algebra. It goes deeper than the pop-sci articles about "doing all combinations at once" but remains accessible and by the end you understand entanglement and can read some Q# code. [VIDEO]

> one can literally write down a matrix of numbers in a program to define a new mathematical function, and later use that function to manipulate the contents of the computer's RAM[1]. This "Quantum Computing for Computer Scientists" video [VIDEO] explains classical and quantum operators as just matrices. What are other good references? Quantum state: [LINK] Quantum logic; quantum logical operators: [LINK] > All this business about energy levels, evolution, etc. are distractions, just as the electrodynamics of a transistor are distractions from what it means to program a computer. But a classical simulator - like e.g. qiskit - for a quantum circuit/experiment/function must run the experiment very^very^very many times to even probabilistically approximate a sufficient quantum system; because of the combinatorial probabilistic explosion that results from adding just one more basis state. What are the fundamental limitations of quantum simulators? Maybe it's possible. Quantum simulator: [LINK] - [ ] Maybe Twistor theory has insight into a classical geometrical formulation that could be run on a non-QC? Amplituhedron: [LINK] [Photon] wave-particle constructive superpositions approximate which operators, which may form a neat topology like this: - [ ] > A research question for a new school year: > The classical logical operators form a neat topology. Should we expect there to be such symmetry and structure amongst the quantum operators as well? [LINK]

The videos by Microsoft Research[1] and PBS[2] are perhaps the most accessible and yet accurate explanations of quantum computing I have found so far. [1] [VIDEO] [2] [LINK]

The shortest possible answer is that qubit states are modeled as two-dimensional vectors on the complex unit sphere. We arbitrarily designate two orthonormal vectors on this sphere as corresponding to classical states 0 and 1. If the qubit vector isn't in the 0 or 1 state, it's in some linear combination of them. This is called superposition. Since most people don't know what linear combination means, superposition is explained as "sort of both at the same time". Upon measurement the qubits are collapsed to 0 or 1 with some probability proportional to how close they are to the 0 and 1 states. The precise probabilities are given by something called the Born rule. I gave a longer talk aimed at computer scientists if you're interested beyond this explanation: [VIDEO]

> Instead [of the Bohr model], Morello uses a real-world example in his teaching — a material called a quantum dot, which is used in some LEDs and in some television screens. “I can now teach quantum mechanics in a way that is far more engaging than the way I was taught quantum mechanics when I was an undergrad in the 1990s,” he says. > Morello also teaches the mathematics behind quantum mechanics in a more computer-friendly way. His students learn to solve problems using matrices that they can represent using code written for the Python programming language, rather than conventional differential equations on paper. From [LINK] : >> This "Quantum Computing for Computer Scientists" video [VIDEO] explains classical and quantum operators as just matrices. What are other good references? Unfortunately the QuantumQ game doesn't yet have the matrix forms of the quantum logical operators in the (open source) game docs. Would be a helpful resource, in addition to the Quantum logic wikipedia page and numpy and/or SymPy without cirq: A Manim presentation demonstrating that quantum logical operator matrices are Bloch sphere rotations, are reversible, and why we restrict operators to the category of unitary transformations > His colleagues at the UNSW are also developing laboratory courses to give students hands-on experience with the hardware in quantum technologies. For example, they designed a teaching lab to convey the fundamental concept of quantum spin, a property of electrons and

> what is programming a quantum computer like? You compose a series of gates that manipulate the state qbits to perform calculation. My understanding is that these gates can be abstracted in a somewhat familiar programming language environment. I've got a very rudimentary understanding, my crude summary would be: it's basically applied linear algebra, leveraging the properties of superposition to perform some types of computations more efficiently. Namely, reducing some search spaces to sqrt n. This video is a good hands on intro: [VIDEO]

[VIDEO] This video is the simplest explanation that I have found for Quantum Computing which doesn't do the whole pop-sciency "is both zero and one at the same time" nonsense.

Start here: [VIDEO] You don't need to know quantum theory necessarily, but you will need to know some maths. Specifically linear algebra. There are a few youtube courses on linear algebra For a casual set of video: - [LINK] For a more formal approach: - [LINK] And the corresponding open courseware - [LINK] Linear algebra done right comes highly recommended - [LINK]

MSR has a very clear and accessible tutorial on quantum computing for anyone interested in getting up to speed with the fundamentals: [VIDEO] .

This talk [1] helped me at the start. The only prerequisite is knowing basic linear algebra. Now, if you're interested in how quantum computers operate, well good luck. That's a whole other beast. [1] [VIDEO]