Coins make quantum walks faster
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum verification of matrix products
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Proceedings of the 24th international conference on Machine learning
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
Claw finding algorithms using quantum walk
Theoretical Computer Science
Quantum random walks - new method for designing quantum algorithms
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Quantum walks with multiple or moving marked locations
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
The quantum complexity of group testing
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Can quantum search accelerate evolutionary algorithms?
Proceedings of the 12th annual conference on Genetic and evolutionary computation
A note on the search for k elements via quantum walk
Information Processing Letters
Finding is as easy as detecting for quantum walks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Any AND-OR Formula of Size $N$ Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
SIAM Journal on Computing
Efficient circuits for quantum walks
Quantum Information & Computation
Quantum walks on directed graphs
Quantum Information & Computation
Graph embedding using a quasi-quantum analogue of the hitting times of continuous time quantum walks
Quantum Information & Computation
Eigenpath traversal by phase randomization
Quantum Information & Computation
Quantum Information & Computation
Quantum Information & Computation
Quantum property testing for bounded-degree graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
SIAM Journal on Computing
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Quantum complexity of testing group commutativity
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Faster quantum algorithm for evaluating game trees
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Reflections for quantum query algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Exact Quantum Algorithms for the Leader Election Problem
ACM Transactions on Computation Theory (TOCT)
Spatial search using the discrete time quantum walk
Natural Computing: an international journal
Black-box hamiltonian simulation and unitary implementation
Quantum Information & Computation
Time averaged distribution of a discrete-time quantum walk on the path
Quantum Information Processing
Quantum walks: a comprehensive review
Quantum Information Processing
The quantum query complexity of algebraic properties
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
An improved claw finding algorithm using quantum walk
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Span programs and quantum algorithms for st-connectivity and claw detection
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Hitting time of quantum walks with perturbation
Quantum Information Processing
Quantum speed-up for unsupervised learning
Machine Learning
Quantum phase estimation with arbitrary constant-precision phase shift operators
Quantum Information & Computation
Time-Efficient quantum walks for 3-distinctness
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Decoherence in quantum Markov chains
Quantum Information Processing
Selecting efficient phase estimation with constant-precision phase shift operators
Quantum Information Processing
| Hi-index | 0.00 |
We develop a generic metho d for quantizing classical algorithms based on random walks. We show that under certain conditions, the quantum version gives rise to a quadratic speed-up. This is the case, in particular,when the Markov chain is ergodic and its transition matrix is symmetric. This generalizes the celebrated result ofGrover [G96] and a number of more recent results, including the element distinctness result of Ambainis [Amb03] and the result of Ambainis, Kempe and Rivosh [AKR] that computes properties of quantum walks on the d-dimensional torus.Among the consequences is a faster search for multiple marked items. We show that the quantum escape time, just like its classical version, depends on the spectral properties of the transition matrix with the marked rows and columns deleted.