Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0512066 · Canadian Journal of Physics

Entanglement and adiabatic quantum computation

Daria Ahrensmeier

Published Jan 15, 2006• 3 citations
arXivHTMLPDF

Abstract

Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a resource is discussed.PACS Nos.: 03.67.–a, 03.67.Lx, 03.67.Mn
DOI
10.1139/p06-033

Related papers

The dynamics of entanglement in the adiabatic search and Deutsch algorithms

K Choy, G Passante, D Ahrensmeier +4 more

The goal of this paper is to study the effect of entanglement on the running time of a quantum computation. Adiabatic quantum computation is suited to this kind of study, since it allows us to explicitly calculate the time evolution of the entanglement throughout the calculation. On the other hand, however, the adiabatic formalism makes it impossible to study the roles of entanglement and fidelity separately, which means that results have to be interpreted carefully. We study two algorithms: the search algorithm and the Deutsch–Jozsa algorithm. We find some evidence that entanglement can be considered a resource in quantum computation. PACS Nos.: 03.67.Mn, 03.67.Lx

arXiv:quant-ph/0605040•Canadian Journal of Physics•Oct 1, 2007•2 citations

The Dynamics of Entanglement in the Adiabatic Search and Deutsch Algorithms

K. Choy, Gina Passante, Daria Ahrensmeier +4 more

The goal of this paper is to study the effect of entanglement on the running time of a quantum computation. Adiabatic quantum computation is suited to this kind of study, since it allows us to explicitly calculate the time evolution of the entanglement throughout the calculation. On the other hand however, the adiabatic formalism makes it impossible to study the roles of entanglement and fidelity separately, which means that results have to be interpreted carefully. We study two algorithms: the search algorithm and the Deutsch-Jozsa algorithm. We find some evidence that entanglement can be considered a resource in quantum computation.

•May 3, 2006•3 citations

Alternative adiabatic quantum dynamics with algorithmic applications

Joseph Cunningham, Jérémie Roland

In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the adiabatic theorem. We propose several alternative processes that achieve the same goal, but can easily be implemented on a gate-based quantum computer without the overhead of simulating time-dependent Hamiltonian evolution. We give a general framework for deriving `adiabatic' theorems for these processes. As an application, we give various algorithms for solving the Quantum Linear Systems Problem (QLSP) with optimal scaling in the condition number. One of these algorithms was previously developed in [Cunningham, Roland 2024] and another can be seen as a randomised version of the discrete adiabatic algorithm of [Costa et al. 2022]. We also describe versions of Trotterisation in our framework, which allows several results from [An et al. 2025] to be reproduced in a randomised setting. In particular, bounds on the Trotter error in terms of the fidelity are obtained that are asymptotically better than the standard bounds.

quant-pharXiv:2605.30110•May 29, 2026•0 citations

Adiabatic quantum computation and Deutsch’s algorithm

Saurya Das, Randy Kobes, G. Kunstatter

We show that by a suitable choice of a time-dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both global and local adiabatic evolutions.

arXiv:quant-ph/0111032•Physical Review A•Jun 5, 2002•48 citations

ENTANGLEMENT IN ADIABATIC QUANTUM SEARCHING ALGORITHMS

Wen Jiayan, Daowen Qiu

Quantum entanglement is widely considered as one of the key resources for quantum-computational power. However, present interpretations of entanglement in speeding up of quantum algorithms remain far from complete. We analyze and compare the behaviors of entanglement during the adiabatic evolution of Grover's quantum search algorithms with complexity [Formula: see text] and O(1), respectively. Our results show that entanglement has a significant impact on the computational efficiency of both algorithms. That is, the greater the entanglement, the higher is the quantum computation, and vice versa. Furthermore, the correlations between entanglement and energy are discussed. It is observed that for the algorithm with complexity O(1), its entanglement degree becomes larger when the energy input into the quantum system increases, thus making the algorithm more efficient.

International Journal of Quantum Information•Oct 1, 2008•9 citations

From quantum circuits to adiabatic algorithms

M. Stewart Siu

This paper explores several aspects of the adiabatic quantum-computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum-computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an $n$-local Hamiltonian, we will study whether approximation is possible using previous results on ground-state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.

arXiv:quant-ph/0409024•Physical Review A•Jun 14, 2005•35 citations
The goal of this paper is to study the effect of entanglement on the running time of a quantum computation. Adiabatic quantum computation is suited to this kind of study, since it allows us to explicitly calculate the time evolution of the entanglement throughout the calculation. On the other hand, however, the adiabatic formalism makes it impossible to study the roles of entanglement and fidelity separately, which means that results have to be interpreted carefully. We study two algorithms: the search algorithm and the Deutsch–Jozsa algorithm. We find some evidence that entanglement can be considered a resource in quantum computation. PACS Nos.: 03.67.Mn, 03.67.Lx
The goal of this paper is to study the effect of entanglement on the running time of a quantum computation. Adiabatic quantum computation is suited to this kind of study, since it allows us to explicitly calculate the time evolution of the entanglement throughout the calculation. On the other hand however, the adiabatic formalism makes it impossible to study the roles of entanglement and fidelity separately, which means that results have to be interpreted carefully. We study two algorithms: the search algorithm and the Deutsch-Jozsa algorithm. We find some evidence that entanglement can be considered a resource in quantum computation.
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the adiabatic theorem. We propose several alternative processes that achieve the same goal, but can easily be implemented on a gate-based quantum computer without the overhead of simulating time-dependent Hamiltonian evolution. We give a general framework for deriving `adiabatic' theorems for these processes. As an application, we give various algorithms for solving the Quantum Linear Systems Problem (QLSP) with optimal scaling in the condition number. One of these algorithms was previously developed in [Cunningham, Roland 2024] and another can be seen as a randomised version of the discrete adiabatic algorithm of [Costa et al. 2022]. We also describe versions of Trotterisation in our framework, which allows several results from [An et al. 2025] to be reproduced in a randomised setting. In particular, bounds on the Trotter error in terms of the fidelity are obtained that are asymptotically better than the standard bounds.
Quantum entanglement is widely considered as one of the key resources for quantum-computational power. However, present interpretations of entanglement in speeding up of quantum algorithms remain far from complete. We analyze and compare the behaviors of entanglement during the adiabatic evolution of Grover's quantum search algorithms with complexity [Formula: see text] and O(1), respectively. Our results show that entanglement has a significant impact on the computational efficiency of both algorithms. That is, the greater the entanglement, the higher is the quantum computation, and vice versa. Furthermore, the correlations between entanglement and energy are discussed. It is observed that for the algorithm with complexity O(1), its entanglement degree becomes larger when the energy input into the quantum system increases, thus making the algorithm more efficient.
This paper explores several aspects of the adiabatic quantum-computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum-computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an nnn-local Hamiltonian, we will study whether approximation is possible using previous results on ground-state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.