Generalized quantum search Hamiltonian

2001/10/31 by Joonwoo Bae, Younghun Kwon · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Hamiltonian (control theory) #Hamiltonian path #Hamiltonian path problem #Initialization #Mathematical optimization #Mathematical physics #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #Quantum mechanics #Theoretical physics #quant-ph

paper · pdf · doi:10.1103/physreva.66.012314

published as Phys. Rev. A 66, 012314(2002) · 5 pages, Latex

arxiv created 2002/02/03 · openalex publication_date 2002/07/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

There are Hamiltonians that solve the search problem of finding one of N items in O(√(N)) steps. These are Hamiltonians describing an oscillation between two states. In this paper we propose a generalized search Hamiltonian H_g. Then the known search Hamiltonians become special cases of H_g. For the generalized search Hamiltonian, we present the remarkable result that searching with 100% success is subject only to the phase factor in H_g and independent of the number of states or initialization.

Citations

• An intuitive Hamiltonian for quantum search
• Searching in Grover's Algorithm
• An Exponentially Fast Quantum Search Algorithm

Cited by

• Lattice patch structure for fixed-frequency transmon quantum computer with high-fidelity CNOT gates
• Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes
• Quantum computers can search rapidly by using almost any selective transformation