Finding cliques by quantum adiabatic evolution

@article{Childs2002FindingCB,
  title={Finding cliques by quantum adiabatic evolution},
  author={Andrew M. Childs and E. Farhi and J. Goldstone and S. Gutmann},
  journal={Quantum Inf. Comput.},
  year={2002},
  volume={2},
  pages={181-191}
}
Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph. An n-vertex random graph has each edge included with probability 1/2, and a clique is a completely connected subgraph. There is no known classical algorithm that finds the largest clique in a random graph… Expand
An Alternative Adiabatic Quantum Algorithm for the Hamiltonian Cycle Problem
We put forward an alternative quantum algorithm for finding Hamiltonian cycles in any N-vertex graph based on adiabatic quantum computing. With a von Neumann measurement on the final state, one mayExpand
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
TLDR
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. Expand
Quantum speedup in solving the maximal-clique problem
The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electricalExpand
Quantum adiabatic algorithms and large spin tunnelling
We study the quantum adiabatic evolution algorithm with different evolution paths that correspond to different control Hamiltonians H({tau}) sampled from a random ensemble. The algorithm is appliedExpand
Adiabatic quantum algorithms as quantum phase transitions: First versus second order
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higherExpand
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 notExpand
Total suppression of a large spin tunneling barrier in quantum adiabatic computation
We apply a quantum adiabatic evolution algorithm to a combinatorial optimization problem where the cost function depends entirely on the of the number of unit bits in a n-bit string (Hamming weight).Expand
Solving Set Cover with Pairs Problem using Quantum Annealing
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, andExpand
Adiabatic Quantum State Generation
TLDR
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. Expand
Adiabatic Quantum Algorithms for the NP-Complete Maximum-Weight Independent Set, Exact Cover and 3SAT Problems
  • V. Choi
  • Computer Science, Physics
  • ArXiv
  • 2010
TLDR
It is shown that by choosing the parameters appropriately in the problem Hamiltonian for MIS on CK graphs, the adiabatic quantum algorithm can prevent the first order quantum phase transition and significantly change the minimum spectral gap. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 15 REFERENCES
A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability
TLDR
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. Expand
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
TLDR
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. Expand
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 thatExpand
Large Cliques Elude the Metropolis Process
  • M. Jerrum
  • Mathematics, Computer Science
  • Random Struct. Algorithms
  • 1992
TLDR
It is shown that the Metropolis process takes super-polynomial time to locate a clique that is only slightly bigger than that produced by the greedy heuristic, which is one step above the greedy one in its level of sophistication. Expand
Quantum annealing in the transverse Ising model
We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions betweenExpand
Reversible arithmetic coding for quantum data compression
TLDR
A simple-to-implement quantum algorithm for projecting, with high probability, the block quantum state onto the typical subspace spanned by the lending eigenstates of its density matrix is presented. Expand
On the evolution of random graphs
(n) k edges have equal probabilities to be chosen as the next one . We shall 2 study the "evolution" of such a random graph if N is increased . In this investigation we endeavour to find what is theExpand
Schumacher's quantum data compression as a quantum computation.
  • Cleve, DiVincenzo
  • Physics, Medicine
  • Physical review. A, Atomic, molecular, and optical physics
  • 1996
TLDR
An explicit algorithm for performing Schumacher's noiseless compression of quantum bits is given, based on a combinatorial expression for a particular bijection among binary strings, expressed in a high-level pseudocode language. Expand
Algorithmic theory of random graphs
TLDR
There has been increasing interest in using random graphs as models for the average case analysis of graph algorithms, and some of the results are surveyed. Expand
Hiding Cliques for Cryptographic Security
TLDR
It is demonstrated how a well studied combinatorial optimization problem may be used as a new cryptographic primitive by “hiding” large cliques in random graphs by exploiting the conjecture that no polynomial-time algorithm exists which finds a clique of size. Expand
...
1
2
...