Quantum computingA quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.
Quantum logic gateIn quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. Unlike many classical logic gates, quantum logic gates are reversible. It is possible to perform classical computing using only reversible gates.
Quantum programmingQuantum programming is the process of designing or assembling sequences of instructions, called quantum circuits, using gates, switches, and operators to manipulate a quantum system for a desired outcome or results of a given experiment. Quantum circuit algorithms can be implemented on integrated circuits, conducted with instrumentation, or written in a programming language for use with a quantum computer or a quantum processor. With quantum processor based systems, quantum programming languages help express quantum algorithms using high-level constructs.
Quantum counting algorithmQuantum counting algorithm is a quantum algorithm for efficiently counting the number of solutions for a given search problem. The algorithm is based on the quantum phase estimation algorithm and on Grover's search algorithm. Counting problems are common in diverse fields such as statistical estimation, statistical physics, networking, etc. As for quantum computing, the ability to perform quantum counting efficiently is needed in order to use Grover's search algorithm (because running Grover's search algorithm requires knowing how many solutions exist).
Quantum algorithmIn quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer.
Quantum circuitIn quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly other actions. The minimum set of actions that a circuit needs to be able to perform on the qubits to enable quantum computation is known as DiVincenzo's criteria. Circuits are written such that the horizontal axis is time, starting at the left hand side and ending at the right.
Boolean functionIn mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form , where is known as the Boolean domain and is a non-negative integer called the arity of the function.
Quantum Fourier transformIn quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator, and algorithms for the hidden subgroup problem. The quantum Fourier transform was discovered by Don Coppersmith.
Grover's algorithmIn quantum computing, Grover's algorithm, also known as the quantum search algorithm, refers to a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just evaluations of the function, where is the size of the function's domain. It was devised by Lov Grover in 1996. The analogous problem in classical computation cannot be solved in fewer than evaluations (because, on average, one has to check half of the domain to get a 50% chance of finding the right input).
Quantum informationQuantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term. It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields.
Quantum supremacyIn quantum computing, quantum supremacy, quantum primacy or quantum advantage is the goal of demonstrating that a programmable quantum computer can solve a problem that no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem. The term was coined by John Preskill in 2012, but the concept dates back to Yuri Manin's 1980 and Richard Feynman's 1981 proposals of quantum computing.
Boolean algebraIn mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬.
Quantum complexity theoryQuantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as well as the relationship between quantum complexity classes and classical (i.e., non-quantum) complexity classes. Two important quantum complexity classes are BQP and QMA.
Graph coloringIn graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.
Quantum algorithm for linear systems of equationsThe quantum algorithm for linear systems of equations, also called HHL algorithm, designed by Aram Harrow, Avinatan Hassidim, and Seth Lloyd, is a quantum algorithm published in 2008 for solving linear systems. The algorithm estimates the result of a scalar measurement on the solution vector to a given linear system of equations. The algorithm is one of the main fundamental algorithms expected to provide a speedup over their classical counterparts, along with Shor's factoring algorithm, Grover's search algorithm, and the quantum fourier transform.
Edge coloringIn graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most k different colors, for a given value of k, or with the fewest possible colors.
AlgorithmIn mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.
Boolean differential calculusBoolean differential calculus (BDC) (German: Boolescher Differentialkalkül (BDK)) is a subject field of Boolean algebra discussing changes of Boolean variables and Boolean functions. Boolean differential calculus concepts are analogous to those of classical differential calculus, notably studying the changes in functions and variables with respect to another/others. The Boolean differential calculus allows various aspects of dynamical systems theory such as automata theory on finite automata Petri net theory supervisory control theory (SCT) to be discussed in a united and closed form, with their individual advantages combined.
Fractional coloringFractional coloring is a topic in a young branch of graph theory known as fractional graph theory. It is a generalization of ordinary graph coloring. In a traditional graph coloring, each vertex in a graph is assigned some color, and adjacent vertices — those connected by edges — must be assigned different colors. In a fractional coloring however, a set of colors is assigned to each vertex of a graph. The requirement about adjacent vertices still holds, so if two vertices are joined by an edge, they must have no colors in common.
Boolean expressionIn computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants true or false, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions. Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits.
