The official hello world is documented at: qiskit.org/documentation/intro_tutorial1.html and contains a Bell state circuit.

Our version at qiskit/hello.py.

Functional equations are equations in which the unknowns are functions rather than simple variables. These equations relate the values of a function at different points in its domain and often involve operations on those functions, such as addition, multiplication, or composition. They are used to determine the forms of functions that satisfy certain conditions.

Functions and mappings are fundamental concepts in mathematics, often used interchangeably, though they can have slightly different connotations depending on the context. ### Functions A **function** is a specific type of relation between two sets that assigns exactly one output from a set (the codomain) to each input from another set (the domain).

Infinite products are an extension of the concept of finite products, where instead of multiplying a finite number of terms together, an infinite sequence of terms is multiplied. The general form of an infinite product is: \[ P = \prod_{n=1}^{\infty} a_n \] where \( a_n \) are the terms in the sequence.

In the context of Wikipedia and similar collaborative knowledge platforms, "stubs" refer to short or incomplete articles that provide only a basic overview of a topic but lack comprehensive detail or coverage. Mathematical analysis stubs are articles related to the field of mathematical analysis that may not contain extensive information or may need additional contributions to improve their content. Mathematical analysis itself is a branch of mathematics that deals with limits, continuity, differentiation, integration, sequences, series, and functions.

Mathematical relations refer to the ways in which different mathematical entities are connected or associated with one another. In mathematics, a relation is essentially a set of ordered pairs that describe a relationship between two sets of elements. Here are some key concepts related to mathematical relations: 1. **Definition**: A relation from a set \( A \) to a set \( B \) is a subset of the Cartesian product \( A \times B \).

Lecture notes that were apparently very popular at Cornell University. In this period he was actively synthesizing the revolutionary bullshit Richard Feynman and Julian Schwinger were writing and making it understandable to the more general physicist audience, so it might be a good reading.

Oh yes, see also: Dirac equation vs quantum electrodynamics.

Probability fallacies are misconceptions or errors in reasoning related to probabilities, often leading individuals to draw incorrect conclusions based on how they interpret statistical information or probability outcomes. These fallacies stem from human intuition and cognitive biases, which can distort understanding of probability and risk. Here are some common examples of probability fallacies: 1. **Gambler's Fallacy**: This fallacy involves the belief that past independent events affect the likelihood of future independent events.

Formal systems are structured frameworks used in mathematics, logic, computer science, and other fields to rigorously define and manipulate symbols and statements according to a set of rules. Here are the main components of a formal system: 1. **Alphabet**: This consists of a finite set of symbols used to construct expressions or statements in the system. 2. **Syntax**: Syntax defines the rules for constructing valid expressions or statements from the symbols in the alphabet.