Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
Matrix computations (3rd ed.)
Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds
SIAM Journal on Matrix Analysis and Applications
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
Accelerating Simulated Annealing for the Permanent and Combinatorial Counting Problems
SIAM Journal on Computing
On the hitting times of quantum versus random walks
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices
SIAM Journal on Matrix Analysis and Applications
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Efficient circuits for quantum walks
Quantum Information & Computation
Quantum walks: a comprehensive review
Quantum Information Processing
Decoherence in quantum Markov chains
Quantum Information Processing
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The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is bounded from above by the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.