Exact Equivalence between Quantum Adiabatic Algorithm and Quantum Circuit Algorithm

Yu, Hongye; Huang, Yuliang; Wu, Biao

doi:10.1088/0256-307x/35/11/110303

Cited by 21 publications

(14 citation statements)

References 10 publications

(30 reference statements)

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“…An important discovery by Yu et al (2018) shows that the adiabatic and gate systems offer effectively the same potential for achieving the gains inherent in quantum computing processes, with a mathematical demonstration that the quantum circuit algorithm can be transformed into the quantum adiabatic algorithm with the exact same time complexity. This has useful implications for the relevance of QUBO models that have been implemented in an adiabatic quantum annealing setting, disclosing that analogous advances associated with QUBO models may ultimately be realized through quantum circuit systems.…”

Section: Y = 2588mentioning

confidence: 99%

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

Glover

Kochenberger²,

Du³

2019

4OR-Q J Oper Res

201

139

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The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and Fujitsu's digital annealing, and has become a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart of experimentation carried out with quantum computers developed by D-Wave Systems and neuromorphic computers developed by IBM. The consequences of these new computational technologies and their links to QUBO models are being explored in initiatives by organizations such as Google, Amazon and Lockheed Martin in the commercial realm and Los Alamos National Laboratory, Oak Ridge National Laboratory, Lawrence Livermore National Laboratory and NASA's Ames Research Center in the public sector. Computational experience is being amassed by both the classical and the quantum computing communities that highlights not only the potential of the QUBO model but also its effectiveness as an alternative to traditional modeling and solution methodologies.

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Section: Y = 2588mentioning

confidence: 99%

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

Glover

Kochenberger²,

Du³

2019

4OR-Q J Oper Res

201

139

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“…Como o teorema da equivalência entre os dois paradigmas de computação quântica prevê que os dois são análogos [30,44], foi encontrado uma versão adiabática para o algoritmo de busca, que chamaremos de algoritmo de Grover adiabático [45,46]. Nele, a análise de complexidade, se dá no tempo de evolução do Hamiltoniano, queé proporcionalà raiz quadrada do número de itens no banco de dados, assim τ max ∝ √ N .…”

Section: Algoritmo De Grover Adiabáticounclassified

Computação Quântica Adiabática: Do Teorema Adiabático ao Computador da D-Wave

Souza

Mendonça

Oliveira

et al. 2021

Rev. Bras. Ensino Fís.

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Neste artigo descrevemos os fundamentos da computação quântica adiabática, que consiste na interpolação de diferentes Hamiltonianos, desde um Hamiltoniano inicial, com autoestados e autoenergias conhecidos, até um Hamiltoniano final, onde é codificada a solução de um dado problema. Em particular, discutimos o método do annealing quântico, que é utilizado pela empresa canadense D-Wave, pioneira nessa área. Primeiramente apresentamos uma das demonstrações do teorema adiabático quântico e de uma condição de adiabaticidade para evolução de sistemas quânticos. Para exemplificar, descrevemos a implementação do algoritmo de Grover via computação quântica adiabática, discutindo os impactos da escolha da forma de interpolação dos Hamiltonianos inicial e final na complexidade do algoritmo. Em seguida, mostramos um algoritmo para o problema do caixeiro viajante executável na plataforma da D-Wave. Por fim, apresentamos aspectos físicos importantes da tecnologia dos computadores quânticos da D-Wave, expondo suas vantagens e desvantagens, além de descrever qualitativamente a engenharia de seu processador quântico.

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“…In the adiabatic algorithm, the quantum computer follows the ground state of a time-dependent Hamiltonian. It has been shown that every quantum circuit algorithm can be converted into a quantum adiabatic algorithm, whose time complexity is exactly the same [6,7]. A quantum Hamiltonian algorithm for independent-set problems has some advantages over other known quantum algorithms and classical algorithms [8].…”

Section: Introductionmentioning

confidence: 99%

Resonant Quantum Search with Monitor Qubits

Wilczek,

Hu,

2020

Preprint

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We present an algorithm for the generalized search problem (searching k marked items among N items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity O( N/k) as the Grover algorithm. A natural extension of the algorithm, incorporating auxiliary "monitor" qubits, can determine k precisely, if it is unknown.The time complexity of our counting algorithm is O( √ N ), similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.

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Exact Equivalence between Quantum Adiabatic Algorithm and Quantum Circuit Algorithm

Cited by 21 publications

References 10 publications

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

Computação Quântica Adiabática: Do Teorema Adiabático ao Computador da D-Wave

Resonant Quantum Search with Monitor Qubits

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