Into the Unknown
Quantum MechanicsUniversity of Colorado Boulder If you’re with mechanical or aerospace engineering backgrounds and looking for a course that presents an introduction to quantum mechanics, this course is right for you. The course covers the most fundamental concepts and plenty of stuff. I have to say the pace of this course is fast, you need…
Unfortunately, real atoms (including hydrogen atoms) are not very well described by the simple theory. There are more things contribute to the actual atomic structure: Higher order effects Spin-orbit coupling Relativistic Nuclear spin Zeman Identity particles, that leads to the Pauli exclusion principle. Multiple electrons, the electromagnetic fields associated with the electrons can interact. Spin-Orbit…
External Motion Particle in a box is the simplest problem in quantum mechanics. A particle is just translating back and forth between the walls of the box. If there is no external field acting on the particle, i.e. no force acting on the particle except at the walls, then you can decompose the problem into…
Quantum mechanics is the mathematics of atomic and molecular structure. We seek to determine allowed quantum states and their energies. A Short History A definite understanding that atoms are composed of separate particles (nuclei and electrons) did not really occur till toward the end of the 19th century. The development of quantum mechanics is strongly…
The Introduction to Quantum ComputingSaint Petersburg State University This wonderful, challenging and inspiring course covers lots of topics. You will find that in the path of becoming a quantum computing expert, not only quantum mechanics is required, but also the knowledge of thermodynamics, computer science, optics and many more are needed. The course starts with…
Brute-force is apparently applicable to any problem of NP, since if you have some candidate for an answer, you can easily check / verify this candidate (but finding a candidate is still hard). For example: given a phone number to find its owner in the phone book, you can easily check it, but you need…
Nowadays, probably Peter Shor’s algorithm for function period finding is the most significant achievement in the field of quantum computing. It allows us to factor big composite numbers in polynomial time. However for the classical computations, this problem is believed to be hard. For a big number N = p × q, where p and…
The first algorithm ever designed for a quantum computer, is the algorithm for solving Deutsch’s problem. The algorithm is an illustration for the mathematical model of quantum computing. Deutsch’s Problem Deutsch’s problem is about the function which maps one bit to another bit, i.e. f:{0,1} → {0,1}. There are only 4 types such functions: f(x)…
The mathematical model of quantum computing allows us to understand and design quantum algorithms without any background in quantum mechanics or physical implementation of quantum hardware. The most significant part of the whole theory of quantum computing is qubit, i.e. quantum bit, which is the minimum unit of quantum information. One qubit information can be…
The computation is a physical process, which is finite in time with fixed and distinguished set of states. It always consumes or transforms energy meanwhile keeps distinguishable states. Computations transform or process information. Information is actually an interpretation of the particular system states. Two different systems with different states can actually present the same information….
Physical Basics of Quantum ComputingSaint Petersburg State University It is challenging for lecturers to jam so much knowledge in one course, meanwhile equivalently challenging for learners to grasp the knowledge well. Don’t try this course until you have gotten a solid background in quantum mechanics. I have to admit the first week’s contents cost me…
Foundations of Quantum MechanicsUniversity of Colorado Boulder This is a challenging course. If you are serious about learning quantum mechanics, I highly recommend this course to you. Furthermore if you want to engage yourself with quantum computing, this course is an excellent choice to lay the foundations. Your quest starts here: the time-independent Schrödinger equation…
The real physical devices that implement computational models are always imperfect. It is not always possible to eliminate all of error sources in practice, however in many cases one could minimize the chances of their occurrence. Classical Error Correction Theory There are three main problems in classical error correction theory: Information channel is an important…
The essence of the quantum computations might not determine some particular result for a certain function, but establish the global properties of this function. For example, in the Deutsch problem, we don’t find the individual values of a function, but consider the whole superposition of the values and make conclusions about whether the function is…
Unlike the classical bit, as we already know the quantum bit is able to stay in superposition state. When measuring a qubit in superposition state, one obtains every basis state with a certain probability. The probabilistic behavior of quantum objects has its effect on the logical operations. No-cloning Theorem Classical element FANOUT (bit-copying) could be…