Contents
What are the major topics in quantum algorithms?
These notes cover several major topics in quantum algorithms, divided into six parts: • InPart I, we discuss quantum circuits|in particular, the problem of expressing a quantum algorithm using a given universal set of quantum gates. • InPart II, we discuss quantum algorithms for algebraic problems.
Can a classical algorithm be performed on a quantum computer?
Quantum algorithm. 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, the term quantum algorithm is usually used for those algorithms which seem inherently quantum,…
What are the methods for proving lower bounds on quantum query complexity?
We cover the two main methods for proving lower bounds on quantum query complexity (the polynomial method and the adversary method), demonstrating limitations on the power of quantum algorithms.
How does a quantum computation begin in the j0istate?
A quantum computation begins in the j0istate, applies a sequence of one- and two-qubit gates chosen from the set of allowed gates, and \\fnally reports an outcome obtained by measuring in the computational basis. 2 Chapter 1. Preliminaries 1.3 Universal gate sets
Which is the fastest quantum algorithm for integer factorization?
The quantum algorithm of Peter Shor solves this in ˜O(n3) time [ 82, 125 ]. The fastest known classical algorithm for integer factorization is the general number field sieve, which is believed to run in time 2˜O ( n1 / 3) .
Which is faster Shor’s algorithm or a quantum algorithm?
A quantum algorithm even faster than Shor’s for the special case of factoring “semiprimes”, which are widely used in cryptography, is given in [ 271 ]. If small factors exist, Shor’s algorithm can be beaten by a quantum algorithm using Grover search to speed up the elliptic curve factorization method [ 366 ].