23 research outputs found
Quantum search on structured problems
This paper shows how a basic property of unitary transformations can be used
for meaningful computations. This approach immediately leads to search-type
applications, where it improves the number of steps by a square-root - a simple
minded search that takes N steps, can be improved to O(sqrt(N)) steps. The
quantum search algorithm is one of several immediate consequences of this
framework. Several novel search-related applications are presented.Comment: To be presented at the 1st NASA QCQC conference in Palm Springs,
California, Feb. 17-20, '98. 12 pages, postscrip
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 , where is the dimension of the
search space, whereas any classical algorithm necessarily scales as . 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 , with
a constant 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 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
A quantum genetic algorithm with quantum crossover and mutation operations
In the context of evolutionary quantum computing in the literal meaning, a
quantum crossover operation has not been introduced so far. Here, we introduce
a novel quantum genetic algorithm which has a quantum crossover procedure
performing crossovers among all chromosomes in parallel for each generation. A
complexity analysis shows that a quadratic speedup is achieved over its
classical counterpart in the dominant factor of the run time to handle each
generation.Comment: 21 pages, 1 table, v2: typos corrected, minor modifications in
sections 3.5 and 4, v3: minor revision, title changed (original title:
Semiclassical genetic algorithm with quantum crossover and mutation
operations), v4: minor revision, v5: minor grammatical corrections, to appear
in QI
Quantum Associative Memory
This paper combines quantum computation with classical neural network theory
to produce a quantum computational learning algorithm. Quantum computation uses
microscopic quantum level effects to perform computational tasks and has
produced results that in some cases are exponentially faster than their
classical counterparts. The unique characteristics of quantum theory may also
be used to create a quantum associative memory with a capacity exponential in
the number of neurons. This paper combines two quantum computational algorithms
to produce such a quantum associative memory. The result is an exponential
increase in the capacity of the memory when compared to traditional associative
memories such as the Hopfield network. The paper covers necessary high-level
quantum mechanical and quantum computational ideas and introduces a quantum
associative memory. Theoretical analysis proves the utility of the memory, and
it is noted that a small version should be physically realizable in the near
future