Quantum Computing Algorithms Pdf

Quantum algorithm Wikipedia. In 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. Although all classical algorithms can also be performed on a quantum computer,3 the term quantum algorithm is usually used for those algorithms which seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement. Problems which are undecidable using classical computers remain undecidable using quantum computers. QuantumMachineLearningAlgorithms ReadtheFinePrint. Quantum Computer Simulation Using CUDA. Quantum Algorithms 15. The eld of quantum computing has its own vocabulary, most of the novel terms used in this paper are described in the glossary at the end. This is a set of lecture notes on quantum algorithms. Here we show that there is much more to quantum computing by exploring some of the. Quantum Computing Lecture Notes. These lecture notes were formed in small. Peter Shors very surprising discovery of ecient quantum algorithms for the. Of quantum computers and for the study of new quantum computer algorithms. Quantum Computing and Shors Algorithm. PDF document. Chapter 1 Quantum Computing Basics and. QUANTUM COMPUTING BASICS AND CONCEPTS quantum mechanical theory and. This section contains 23 lecture notes for the lecture sessions taught in class. The students in this class scribed the lecture notes. Quantum Computing How. Quantum Computing Algorithms Pdf' title='Quantum Computing Algorithms Pdf' />What makes quantum algorithms interesting is that they might be able to solve some problems faster than classical algorithms. The most well known algorithms are Shors algorithm for factoring, and Grovers algorithm for searching an unstructured database or an unordered list. Shors algorithms runs exponentially faster than the best known classical algorithm for factoring, the general number field sieve. Grovers algorithm runs quadratically faster than the best possible classical algorithm for the same task. OvervieweditQuantum algorithms are usually described, in the commonly used circuit model of quantum computation, by a quantum circuit which acts on some input qubits and terminates with a measurement. A quantum circuit consists of simple quantum gates which act on at most a fixed number of qubits, usually two or three. Quantum algorithms may also be stated in other models of quantum computation, such as the Hamiltonian oracle model. Quantum algorithms can be categorized by the main techniques used by the algorithm. Some commonly used techniquesideas in quantum algorithms include phase kick back, phase estimation, the quantum Fourier transform, quantum walks, amplitude amplification and topological quantum field theory. Quantum algorithms may also be grouped by the type of problem solved, for instance see the survey on quantum algorithms for algebraic problems. Algorithms based on the quantum Fourier transformeditThe quantum Fourier transform is the quantum analogue of the discrete Fourier transform, and is used in several quantum algorithms. The Hadamard transform is also an example of a quantum Fourier transform over an n dimensional vector space over the field F2. The quantum Fourier transform can be efficiently implemented on a quantum computer using only a polynomial number of quantum gates. DeutschJozsa algorithmeditThe DeutschJozsa algorithm solves a black box problem which probably requires exponentially many queries to the black box for any deterministic classical computer, but can be done with exactly one query by a quantum computer. If we allow both bounded error quantum and classical algorithms, then there is no speedup since a classical probabilistic algorithm can solve the problem with a constant number of queries with small probability of error. The algorithm determines whether a function f is either constant 0 on all inputs or 1 on all inputs or balanced returns 1 for half of the input domain and 0 for the other half. Simons algorithmeditSimons algorithm solves a black box problem exponentially faster than any classical algorithm, including bounded error probabilistic algorithms. This algorithm, which achieves an exponential speedup over all classical algorithms that we consider efficient, was the motivation for Shors factoring algorithm. My Wife Got Married Sub Indo. Quantum phase estimation algorithmeditThe quantum phase estimation algorithm is used to determine the eigenphase of an eigenvector of a unitary gate given a quantum state proportional to the eigenvector and access to the gate. The algorithm is frequently used as a subroutine in other algorithms. Shors algorithmeditShors algorithm solves the discrete logarithm problem and the integer factorization problem in polynomial time,6 whereas the best known classical algorithms take super polynomial time. These problems are not known to be in P or NP complete. It is also one of the few quantum algorithms that solves a nonblack box problem in polynomial time where the best known classical algorithms run in super polynomial time. Hidden subgroup problemeditThe abelianhidden subgroup problem is a generalization of many problems that can be solved by a quantum computer, such as Simons problem, solving Pells equation, testing the principal ideal of a ring R and factoring. There are efficient quantum algorithms known for the Abelian hidden subgroup problem. The more general hidden subgroup problem, where the group isnt necessarily abelian, is a generalization of the previously mentioned problems and graph isomorphism and certain lattice problems. Efficient quantum algorithms are known for certain non abelian groups. However, no efficient algorithms are known for the symmetric group, which would give an efficient algorithm for graph isomorphism8 and the dihedral group, which would solve certain lattice problems. Boson sampling problemeditThe Boson Sampling Problem in an experimental configuration assumes1. The problem is then to produce a fair sample of the probability distribution of the output which is dependent on the input arrangement of bosons and the Unitarity. Solving this problem with a classical computer algorithm requires computing the permanent of the unitary transform matrix, which may be either impossible or take a prohibitively long time. In 2. 01. 4, it was proposed1. In 2. 01. 5, investigation predicted1. Fock state photons and identified a transition in computational complexity from classically simulatable to just as hard as the Boson Sampling Problem, dependent on the size of coherent amplitude inputs. Estimating Gauss sumseditA Gauss sum is a type of exponential sum. The best known classical algorithm for estimating these sums takes exponential time. Since the discrete logarithm problem reduces to Gauss sum estimation, an efficient classical algorithm for estimating Gauss sums would imply an efficient classical algorithm for computing discrete logarithms, which is considered unlikely. However, quantum computers can estimate Gauss sums to polynomial precision in polynomial time. Fourier fishing and Fourier checkingeditWe have an oracle consisting of n random Boolean functions mapping n bit strings to a Boolean value. We are required to find n n bit strings z. Hadamard Fourier transform, at least 34 of the strings satisfyfzi1displaystyle lefttilde fleftzirightrightgeqslant 1and at least 14 satisfiesfzi2displaystyle lefttilde fleftzirightrightgeqslant 2. This can be done in BQP. Algorithms based on amplitude amplificationeditAmplitude amplification is a technique that allows the amplification of a chosen subspace of a quantum state. Applications of amplitude amplification usually lead to quadratic speedups over the corresponding classical algorithms. It can be considered to be a generalization of Grovers algorithm.