# How powerful is adiabatic quantum computation?

@article{Dam2001HowPI, title={How powerful is adiabatic quantum computation?}, author={Wim van Dam and Michele Mosca and Umesh V. Vazirani}, journal={Proceedings 2001 IEEE International Conference on Cluster Computing}, year={2001}, pages={279-287} }

The authors analyze the computational power and limitations of the recently proposed 'quantum adiabatic evolution algorithm'. Adiabatic quantum computation is a novel paradigm for the design of quantum algorithms; it is truly quantum in the sense that it can be used to speed up searching by a quadratic factor over any classical algorithm. On the question of whether this new paradigm may be used to efficiently solve NP-complete problems on a quantum computer, we show that the usual query…

## 267 Citations

### A Universal Adiabatic Quantum Query Algorithm

- Computer Science, PhysicsTQC
- 2015

This work revisits the result that quantum adversary bound holds for continuous-time quantum computation, and uses for the first time in the context of quantum computation a version of the adiabatic theorem that does not require a spectral gap.

### How Does Adiabatic Quantum Computation Fit into Quantum Automata Theory?

- Physics, Computer ScienceDCFS
- 2019

A basic framework of adiabatic evolutionary quantum systems (AEQSs) with limited computational resources is laid out and their close connection to quantum finite automata theory is established.

### Quantum information processing in continuous time

- Physics
- 2004

Quantum mechanical computers can solve certain problems asymptotically faster than any classical computing device. Several fast quantum algorithms are known, but the nature of quantum speedup is not…

### Adiabatic Quantum State Generation

- Physics, Computer ScienceSIAM J. Comput.
- 2007

The ASG paradigm is defined and demonstrated by using it to turn a variety of (classical) approximate counting algorithms into efficient quantum state generators of nontrivial quantum states, including, for example, the uniform superposition over all perfect matchings in a bipartite graph.

### Quantum walks and ground state problems

- Physics
- 2007

Since the appearance of Shor's factoring algorithm in 1994, the search for novel quantum computer algorithms has proved surprisingly difficult. Two design approaches that have yielded some progress…

### Quantum Algorithmic Techniques for Fault-Tolerant Quantum Computers

- Computer Science, Physics
- 2019

This thesis introduces three sets of techniques that can be used by themselves or as subroutines in other algorithms for scalable, fault-tolerant quantum computers and presents a fully quantum Boltzmann machine.

### Adiabatic quantum computing with parameterized quantum circuits

- Physics, Computer Science
- 2022

This work analyzes how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states to propose a discrete version of adiabatic quantum computing that can be implemented with quantum devices identical with those of variational quantum algorithms, while being insensitive to the parameter initialization and other limitations that the optimization part of variations bring.

### Limits on Efficient Computation in the Physical World

- Computer ScienceArXiv
- 2004

This thesis attacks the common belief that quantum computing resembles classical exponential parallelism, by showing that quantum computers would face serious limitations on a wider range of problems than was previously known, and studies the relationship of the quantum computing model to physical reality.

### Different adiabatic quantum optimization algorithms

- Computer ScienceQuantum Inf. Comput.
- 2011

These AQO algorithms for Exact Cover and 3SAT are based on the polynomial reductions to the NP-complete Maximum-weight Independent Set (MIS) problem, and it is made clear that all these negative results are only for a specific AQO algorithm.

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