Quantum computing is an emerging technology that could revolutionize how computations are performed in the future. It operates based on the law of quantum mechanics—a radically different law of physics from the one our current computers are based on. A quantum computer may be able to solve problems that are difficult to solve using current computers, such as breaking encryption, simulating a quantum system or enhancing machine learning algorithms.

This Study Group provides an introductory review of quantum computing using the Wolfram Quantum Computation Framework. We shall review basic concepts of quantum computation, such as quantum states, transformations, operators, gates, circuits and algorithms. The Wolfram Quantum Computation Framework performs high-level analytic and numeric computations in quantum information theory, allowing the simulation of quantum circuits and quantum algorithms. Starting from discrete quantum mechanics, this framework can work with quantum states and operators, implement measurements, perform basis manipulation, compute measure entanglement and more. The semantics are very intuitive and the framework is equipped with various named states and operators, including Bell states, Pauli operators, universal quantum gates and others, thus making it easy for people to simulate a quantum computer using the Wolfram Language.