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 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 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.
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.
Boolean satisfiability problemIn logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable.
Computational problemIn theoretical computer science, a computational problem is a problem that may be solved by an algorithm. For example, the problem of factoring "Given a positive integer n, find a nontrivial prime factor of n." is a computational problem. A computational problem can be viewed as a set of instances or cases together with a, possibly empty, set of solutions for every instance/case. For example, in the factoring problem, the instances are the integers n, and solutions are prime numbers p that are the nontrivial prime factors of n.
NP-hardnessIn computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem H is NP-hard when every problem L in NP can be reduced in polynomial time to H; that is, assuming a solution for H takes 1 unit time, Hs solution can be used to solve L in polynomial time.
Computational complexity theoryIn theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.
Shor's algorithmShor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (that is, non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future.
Trapped ion quantum computerA trapped ion quantum computer is one proposed approach to a large-scale quantum computer. Ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. Qubits are stored in stable electronic states of each ion, and quantum information can be transferred through the collective quantized motion of the ions in a shared trap (interacting through the Coulomb force).
Computational complexityIn computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.
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).
2-satisfiabilityIn computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible values, in order to satisfy a system of constraints on pairs of variables. It is a special case of the general Boolean satisfiability problem, which can involve constraints on more than two variables, and of constraint satisfaction problems, which can allow more than two choices for the value of each variable.
Function problemIn computational complexity theory, a function problem is a computational problem where a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem. For function problems, the output is not simply 'yes' or 'no'. A functional problem is defined by a relation over strings of an arbitrary alphabet : An algorithm solves if for every input such that there exists a satisfying , the algorithm produces one such , and if there are no such , it rejects.
Maximum satisfiability problemIn computational complexity theory, the maximum satisfiability problem (MAX-SAT) is the problem of determining the maximum number of clauses, of a given Boolean formula in conjunctive normal form, that can be made true by an assignment of truth values to the variables of the formula. It is a generalization of the Boolean satisfiability problem, which asks whether there exists a truth assignment that makes all clauses true. The conjunctive normal form formula is not satisfiable: no matter which truth values are assigned to its two variables, at least one of its four clauses will be false.
NP-completenessIn computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution. The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions.
Quantum phase estimation algorithmIn quantum computing, the quantum phase estimation algorithm is a quantum algorithm to estimate the phase corresponding to an eigenvalue of a given unitary operator. Because the eigenvalues of a unitary operator always have unit modulus, they are characterized by their phase, and therefore the algorithm can be equivalently described as retrieving either the phase or the eigenvalue itself. The algorithm was initially introduced by Alexei Kitaev in 1995.
Decision problemIn computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.
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 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.
