Adiabatic quantum computation

  title={Adiabatic quantum computation},
  author={Tameem Albash and Daniel A. Lidar},
  journal={Reviews of Modern Physics},
Adiabatic quantum computing (AQC) started as an approach to solving optimization problems, and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical and quantum complexity theory and condensed matter physics. In this review we give an account of most of the major theoretical developments in the field, while focusing on the closed-system setting. The review is organized around a series of topics that are… 

Simulating quantum circuits by adiabatic computation: Improved spectral gap bounds

This paper provides two simplified proofs that the gap is inverse polynomial of the adiabatic Hamiltonian, and suggests that it may be possible to use these methods to find bounds for spectral gaps of Hamiltonians in other scenarios.

Limitations of optimization algorithms on noisy quantum devices

This work presents a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that include optimization problems and approximations to the ground state energy of Hamiltonians.

Adiabatic quantum computation with spin ensembles

In the standard approach to adiabatic quantum computing (AQC), quantum information stored on qubits are adia- batically evolved to find the lowest energy state of a problem Hamiltonian. Here we

Quantum Chemistry in the Age of Quantum Computing.

This Review provides an overview of the algorithms and results that are relevant for quantum chemistry and aims to help quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

Learning adiabatic quantum algorithms over optimization problems

This paper proposes a hybrid quantum-classical algorithm that, by solving optimization problems with an adiabatic machine, determines a problem Hamiltonian assuming restrictions on the class of available problem Hamiltonians.

Improving the Variational Quantum Eigensolver Using Variational Adiabatic Quantum Computing

Empirical evidence is provided that VAQC, combined with other techniques, can provide more accurate solutions than “plain” VQE, for the same amount of effort.

Low-Depth Mechanisms for Quantum Optimization

This work focuses on developing a language and tools connected with kinetic energy on a graph for understanding the physical mechanisms of success and failure to guide algorithmic improvement, and unveil many pitfalls and mechanisms in quantum optimization using a physical perspective.

Quantum search with hybrid adiabatic–quantum-walk algorithms and realistic noise

This work carries out a detailed examination of adiabatic and quantum-walk implementation of the quantum search algorithm, using the more physically realistic hypercube connectivity, rather than the complete graph, for the base Hamiltonian.

Quantum Algorithms for Scientific Computing and Approximate Optimization

The performance of the quantum approximate optimization algorithm (QAOA) is studied, and a generalization of QAOA is shown, particularly suitable for constrained optimization problems and low-resource implementations on near-term quantum devices.



A study of heuristic guesses for adiabatic quantum computation

This work introduces a simple form of heuristics: the ability to start the quantum evolution with a state which is a guess to the solution of the problem, and explains the viability of this approach and the needed modifications to the conventional AQC (CAQC) algorithm.

Probing entanglement in adiabatic quantum optimization with trapped ions

It is shown that a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem, and a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol.

Quantum Hamiltonian Complexity

This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems, and provides a novel information theoretic presentation of Bravyi's polynomial time algorithm for Quantum 2-SAT.

The Power of Quantum Systems on a Line

The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Some illegal configurations cannot be ruled out by local checks, and are instead ruled out because they would, in the future, evolve into a state which can be seen locally to be illegal.

From quantum circuits to adiabatic algorithms

  • M. Siu
  • Physics, Computer Science
  • 2005
This paper shows a way that directly maps any arbitrary circuit in the standard quantum-computing model to an adiabatic algorithm of the same depth and looks for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state.

Schedule path optimization for adiabatic quantum computing and optimization

This work investigates a strategy for increasing the minimum gap and success probability by introducing intermediate Hamiltonians that modify the evolution path between initial and final Hamiltonians and empirically finds that random Hamiltonians have a significant probability of increasing the success probability, but only by a modest amount.

Quantum Supremacy through the Quantum Approximate Optimization Algorithm

It is argued that beyond its possible computational value the QAOA can exhibit a form of Quantum Supremacy in that, based on reasonable complexity theoretic assumptions, the output distribution of even the lowest depth version cannot be efficiently simulated on any classical device.

Universality of entanglement and quantum-computation complexity

We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete exact cover problem

Local Hamiltonians in quantum computation

In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show

Period finding with adiabatic quantum computation

An efficient quantum-adiabatic algorithm is proposed that solves Simon's problem, in which one has to determine the “period”, or xor mask, of a given black-box function, and is exponentially faster than its classical counterpart and has the same complexity as the corresponding circuit-based algorithm.