We study the quantum walk search algorithm of Shenvi, Kempe, and Whaley [PRA 67 052307 (2003)] on data structures of one to two spatial dimensions, on which the algorithm is less efficient than in three or more spatial dimensions. Our aim is to understand why the quantum algorithm is dimension dependent whereas the best classical algorithm is not, and to find in more detail how the efficiency o...

By studying the diffusion operator in Grover’s quantum search algorithm, we find a mathematical analogy between quantum searching and classical, elastic two-body collisions. We exploit this analogy using a thought experiment involving multiple collisions between two-bodies to help illuminate why Grover’s quantum search algorithm works. Related issues are discussed. PACS numbers: 03.67. Quantum ...

Quantum walks are quantum counterparts of random walks. In the last 5 years, they have become one of main methods of designing quantum algorithms. Quantum walk based algorithms include element distinctness, spatial search, quantum speedup of Markov chains, evaluation of Boolean formulas and search on ”glued trees” graph. In this talk, I will describe the quantum walk method for designing search...

Consider the unstructured search of an unknown number I of items in a large unsorted database of size N. The multi-object quantum search algorithm consists of two parts. The first part of the algorithm is to generalize Grover’s single-object search algorithm to the multiobject case, and the second part is to solve a counting problem to determine /. In this paper we study the multi-object quantu...

quantum circuits are promising choices for future quantum computing technology, since the multiple-valued quantum system is more compact than the corresponding binary quantum system. Grover's quantum search algorithm requires a sub-circuit called oracle, which takes a set of inputs and gives an output stating whether a given search condition on the inputs is satisfied or not. Equality, less-tha...

In this paper, we will define a quantum operator that performs the inversion about the mean only on a subspace of the system (Partial Diffusion Operator). This operator is used in a quantum search algorithm that runs in O( √ N/M) for searching an unstructured list of size N with M matches such that 1 ≤ M ≤ N . We will show that the performance of the algorithm is more reliable than known fixed ...

We describe a quantum algorithm for computing the intersection of two sets and its application to associative memory. The algorithm is based on a modification of Grover’s quantum search algorithm (Grover, 1996). We present algorithms for pattern retrieval, pattern completion, and pattern correction. We show that the quantum associative memory can store an exponential number of memories and retr...

A quantum algorithm for combinatorial search is presented that provides a simple framework for utilizing search heuristics. The algorithm is evaluated in a new case that is an unstructured version of the graph coloring problem. It performs significantly better than the direct use of quantum parallelism, on average, in cases corresponding to previously identified “phase transitions” in search di...

This paper proposes a new artificial bee colony algorithm with quantum theory and the chaotic local search strategy (QCABC), and uses it to solve the optimal power flow (OPF) problem. Under the quantum computing theory, the QCABC algorithm encodes each individual with quantum bits to form a corresponding quantum bit string. By determining each quantum bits value, we can get the value of the ind...