# Quantum algorithms for the ordered search problem via semidefinite programming

## Abstract

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log{sub 2} N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for the ordered search problem in terms of a semidefinite program, we find quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log{sub 605} N{approx_equal}0.433 log{sub 2} N queries, which improves upon the previously best known exact algorithm.

- Authors:

- Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)
- Center for Advanced Studies, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131 (United States)
- Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

- Publication Date:

- OSTI Identifier:
- 20982281

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032335; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; PROGRAMMING; QUANTUM COMPUTERS; QUANTUM INFORMATION; QUANTUM MECHANICS

### Citation Formats

```
Childs, Andrew M., Landahl, Andrew J., and Parrilo, Pablo A.
```*Quantum algorithms for the ordered search problem via semidefinite programming*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032335.

```
Childs, Andrew M., Landahl, Andrew J., & Parrilo, Pablo A.
```*Quantum algorithms for the ordered search problem via semidefinite programming*. United States. doi:10.1103/PHYSREVA.75.032335.

```
Childs, Andrew M., Landahl, Andrew J., and Parrilo, Pablo A. Thu .
"Quantum algorithms for the ordered search problem via semidefinite programming". United States.
doi:10.1103/PHYSREVA.75.032335.
```

```
@article{osti_20982281,
```

title = {Quantum algorithms for the ordered search problem via semidefinite programming},

author = {Childs, Andrew M. and Landahl, Andrew J. and Parrilo, Pablo A.},

abstractNote = {One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log{sub 2} N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for the ordered search problem in terms of a semidefinite program, we find quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log{sub 605} N{approx_equal}0.433 log{sub 2} N queries, which improves upon the previously best known exact algorithm.},

doi = {10.1103/PHYSREVA.75.032335},

journal = {Physical Review. A},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}