Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum circuits with mixed states
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Lifting Markov chains to speed up mixing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
An Example of the Difference Between Quantum and Classical Random Walks
Quantum Information Processing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Analysis of Absorbing Times of Quantum Walks
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
One-Dimensional Continuous-Time Quantum Walks
Quantum Information Processing
One-dimensional quantum walks with absorbing boundaries
Journal of Computer and System Sciences
Quantum Information Processing
Coins make quantum walks faster
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Proof rules for the correctness of quantum programs
Theoretical Computer Science
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Optimal computation with non-unitary quantum walks
Theoretical Computer Science
The Quantum Complexity of Markov Chain Monte Carlo
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
On the hitting times of quantum versus random walks
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graph matching using the interference of continuous-time quantum walks
Pattern Recognition
Graph matching using the interference of discrete-time quantum walks
Image and Vision Computing
Coined quantum walks lift the cospectrality of graphs and trees
Pattern Recognition
Characteristic Polynomial Analysis on Matrix Representations of Graphs
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Characterization of ergodic hidden Markov sources
IEEE Transactions on Information Theory
On analytic properties of entropy rate
IEEE Transactions on Information Theory
Continuous-time quantum walks on semi-regular spidernet graphs via quantum probability theory
Quantum Information Processing
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
A note on the search for k elements via quantum walk
Information Processing Letters
On the von neumann entropy of certain quantum walks subject to decoherence†
Mathematical Structures in Computer Science
A hybrid classical-quantum clustering algorithm based on quantum walks
Quantum Information Processing
Tree search and quantum computation
Quantum Information Processing
Limit theorems and absorption problems for quantum random walks in one dimension
Quantum Information & Computation
On mixing in continuous-time quantum walks on some circulant graphs
Quantum Information & Computation
Quantum algorithms for subset finding
Quantum Information & Computation
Mixing and decoherence in continuous-time quantum walks on cycles
Quantum Information & Computation
Quantum walks on directed graphs
Quantum Information & Computation
Universal mixing of quantum walk on graphs
Quantum Information & Computation
Exploring scalar quantum walks on Cayley graphs
Quantum Information & Computation
Graph embedding using a quasi-quantum analogue of the hitting times of continuous time quantum walks
Quantum Information & Computation
Quantum Information & Computation
Mixing of quantum walk on circulant bunkbeds
Quantum Information & Computation
QI'11 Proceedings of the 5th international conference on Quantum interaction
SIAM Journal on Computing
Towards unitary representations for graph matching
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
Coined quantum walks lift the cospectrality of graphs and trees
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Spatial search using the discrete time quantum walk
Natural Computing: an international journal
Entanglement for discrete-time quantum walks on the line
Quantum Information & Computation
Time averaged distribution of a discrete-time quantum walk on the path
Quantum Information Processing
Asymptotic distributions of quantum walks on the line with two entangled coins
Quantum Information Processing
Quantum walks: a comprehensive review
Quantum Information Processing
Mixing-time and large-decoherence in continuous-time quantum walks on one-dimension regular networks
Quantum Information Processing
Intricacies of quantum computational paths
Quantum Information Processing
| Hi-index | 0.12 |
We set the ground for a theory of quantum walks on graphs-the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible. However, by suitably relaxing the definition, we can obtain a measure of how fast the quantum walk spreads or how confined the quantum walk stays in a small neighborhood. We give definitions of mixing time, filling time, dispersion time. We show that in all these measures, the quantum walk on the cycle is almost quadratically faster then its classical correspondent. On the other hand, we give a lower bound on the possible speed up by quantum walks for general graphs, showing that quantum walks can be at most polynomially faster than their classical counterparts.