How powerful is adiabatic quantum computation?

  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},
  • W. V. DamM. MoscaU. Vazirani
  • Published 8 October 2001
  • Physics, Computer Science
  • Proceedings 2001 IEEE International Conference on Cluster Computing
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… 

A Universal Adiabatic Quantum Query Algorithm

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?

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

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

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

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

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.

4 – Quantum Computing

Adiabatic quantum computing with parameterized quantum circuits

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

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

  • V. Choi
  • Computer Science
    Quantum 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.



On the power of quantum computation

  • Daniel R. Simon
  • Computer Science
    Proceedings 35th Annual Symposium on Foundations of Computer Science
  • 1994
This work presents here a problem of distinguishing between two fairly natural classes of function, which can provably be solved exponentially faster in the quantum model than in the classical probabilistic one, when the function is given as an oracle drawn equiprobably from the uniform distribution on either class.

A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability

Numerical results on randomly generated instances of an NP-complete problem and of a problem that can be solved classically in polynomial time are presented.

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

For the small examples that the authors could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.

A fast quantum mechanical algorithm for database search

In early 1994, it was demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) .

Quantum Computation by Adiabatic Evolution

We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that

Algorithms for quantum computation: discrete logarithms and factoring

  • P. Shor
  • Computer Science
    Proceedings 35th Annual Symposium on Foundations of Computer Science
  • 1994
Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.

Analog analogue of a digital quantum computation

We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system with a Hamiltonian of the form $E|w〉〈w|$ where $|w〉$

Quantum search heuristics

An alternative quantum algorithm for combinatorial search, adjusting amplitudes based on number of conflicts in search states, performs well, on average, for hard random satisfiability problems near

Quantum mechanics

Quantum Mechanics for Organic Chemists.By Howard E. Zimmerman. Pp. x + 215. (Academic: New York and London, May 1975.) $16.50; £7.90.

Beweis des Adiabatensatzes

ZusammenfassungDer Adiabatensatz in der neuen Quantenmechanik wird für den Fall des Punktspektrums in mathematisch strenger Weise bewiesen, wobei er sich auch bei einer vorübergehenden Entartung des