Quantum algorithm

Quantum mechanics

Algorithm

Root (linguistics)

Linguistics

Quantum computer

Philosophy

Discrete mathematics

Node (physics)

Time complexity

Computation

Computer science

Polynomial

Physics

Quantum walk

Mathematics

Mathematical analysis

Artificial intelligence

Quantum

Decision tree

Tree (set theory)

Combinatorics

State (computer science)

Physical Review A

Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root. We devise a quantum mechanical algorithm that evolves a state, initially localized at the root, through the tree. We prove that if the classical strategy succeeds in reaching level n in time polynomial in n, then so does the quantum algorithm. Moreover, we find examples of trees for which the classical algorithm requires time exponential in n, but for which the quantum algorithm succeeds in polynomial time. The examples we have so far, however, could also be solved in polynomial time by different classical algorithms.

Quantum computation and decision trees