TY - JOUR T1 - Improved quantum algorithms for the ordered search problem via semidefinite programming JF - Physical Review A Y1 - 2007 A1 - Andrew M. Childs A1 - Andrew J. Landahl A1 - Pablo A. Parrilo AB - 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_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 ordered search in terms of a semidefinite program, we find new 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_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm. VL - 75 UR - http://arxiv.org/abs/quant-ph/0608161v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.75.032335 ER - TY - JOUR T1 - Quantum search by measurement JF - Physical Review A Y1 - 2002 A1 - Andrew M. Childs A1 - Enrico Deotto A1 - Edward Farhi A1 - Jeffrey Goldstone A1 - Sam Gutmann A1 - Andrew J. Landahl AB - We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution, in that the goal is to remain in the ground state of a time-varying Hamiltonian. Indeed, we show that the running times of the two algorithms are closely related. We also show how to achieve the quadratic speedup for Grover's unstructured search problem with only two measurements. Finally, we discuss some similarities and differences between the adiabatic and measurement algorithms. VL - 66 UR - http://arxiv.org/abs/quant-ph/0204013v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.66.032314 ER -