Quantum computers can search arbitrarily large databases by a single query

This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database has to return a (YES/NO) answer). A classical algorithm will be limited to the information theoretic bound of at least O(log N) queries (which it would achieve by using a binary search).Comment: Several enhancements to the original pape

Quantum Mechanics helps in searching for a needle in a haystack

Quantum mechanics can speed up a range of search applications over unsorted data. For example imagine a phone directory containing N names arranged in completely random order. To find someone's phone number with a probability of 50%, any classical algorithm (whether deterministic or probabilistic) will need to access the database a minimum of O(N) times. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only O(sqrt(N)) accesses to the database.Comment: Postscript, 4 pages. This is a modified version of the STOC paper (quant-ph/9605043) and is modified to make it more comprehensible to physicists. It appeared in Phys. Rev. Letters on July 14, 1997. (This paper was originally put out on quant-ph on June 13, 1997, the present version has some minor typographical changes

Quantum computers can search rapidly by using almost any transformation

A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation called the Walsh-Hadamard (W-H) transform. This paper shows that this algorithm can be implemented by replacing the W-H transform by almost any quantum mechanical operation. This leads to several new applications where it improves the number of steps by a square-root. It also broadens the scope for implementation since it demonstrates quantum mechanical algorithms that can readily adapt to available technology.Comment: This paper is an adapted version of quant-ph/9711043. It has been modified to make it more readable for physicists. 9 pages, postscrip

Heisenberg chains cannot mirror a state

Faithful exchange of quantum information can in future become a key part of many computational algorithms. Some Authors suggest to use chains of mutually coupled spins as channels for quantum communication. One can divide these proposals into the groups of assisted protocols, which require some additional action from the users, and natural ones, based on the concept of state mirroring. We show that mirror is fundamentally not the feature chains of spins-1/2 coupled by the Heisenberg interaction, but without local magnetic fields. This fact has certain consequences in terms of the natural state transfer

The Phytoplankton of Two Artificial Lakes in Hendricks County, Indiana

The small artificial lake has become an important and increasingly popular project for conservation groups, sporting clubs, municipalities, farmers, and landowners. Its purpose is often defined as being for the propagation of fish, the prevention of soil erosion, the restoration of wildlife, and recreation. To this might be added: water conservation, flood control, and food production by fish-pond farming. The Conservation Department of the State of Iowa reports nearly 2000 artificial lakes having been constructed in that state since World War II. When one considers the many thousands of acres of fertile farm land save from flooding streams, the hours of leisure time spent by the factory or office worker on the banks of these ponds, and the havens provided for the wildlife, the worthiness of these projects can easily be realized

Nested quantum search and NP-complete problems

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting this standard search algorithm. The number of iterations required to find the solution of an average instance of a constraint satisfaction problem scales as $\sqrt{d^\alpha}$, with a constant $\alpha<1$ depending on the nesting depth and the problem considered. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, this constant $\alpha$ is estimated to be around 0.62 for average instances of maximum difficulty. This corresponds to a square-root speedup over a classical nested search algorithm, of which our presented algorithm is the quantum counterpart.Comment: 18 pages RevTeX, 3 Postscript figure

Quantum error correction of systematic errors using a quantum search framework

Composite pulses are a quantum control technique for canceling out systematic control errors. We present a new composite pulse sequence inspired by quantum search. Our technique can correct a wider variety of systematic errors -- including, for example, nonlinear over-rotational errors -- than previous techniques. Concatenation of the pulse sequence can reduce a systematic error to an arbitrarily small level.Comment: 6 pages, 2 figure