Quantum Computing for Computer Scientists

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) : [this 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

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: [this video]

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,

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

> 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 [this 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]

> 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 [this 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