A Quantum Algorithm for the Hamiltonian NAND Tree
E. Farhi, J. Goldstone, S. Gutmann
TL;DR
This paper presents a quantum algorithm using continuous time quantum walks to solve the Hamiltonian NAND tree problem efficiently, achieving a runtime proportional to the square root of N, and establishes a matching lower bound.
Contribution
It introduces a quantum algorithm for the Hamiltonian NAND tree problem with optimal runtime and proves a matching lower bound in the Hamiltonian oracle model.
Findings
Quantum algorithm solves NAND tree problem in O(√N) time.
Lower bound of Ω(√N) established for the problem.
Algorithm matches the theoretical lower bound, demonstrating optimality.
Abstract
We give a quantum algorithm for the binary NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a run time proportional to sqrt N. We also show a lower bound of sqrt N for the NAND tree problem in the Hamiltonian oracle model.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Cloud Computing and Resource Management