Deterministic coin tossing with applications to optimal parallel list ranking
Information and Control
Parallel symmetry-breaking in sparse graphs
SIAM Journal on Discrete Mathematics
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Quantum information processing in continuous time
Quantum information processing in continuous time
Some simple distributed algorithms for sparse networks
Distributed Computing
Limitations on the simulation of non-sparse hamiltonians
Quantum Information & Computation
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Black-box hamiltonian simulation and unitary implementation
Quantum Information & Computation
Hamiltonian simulation using linear combinations of unitary operations
Quantum Information & Computation
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
Efficient algorithms for universal quantum simulation
RC'13 Proceedings of the 5th international conference on Reversible Computation
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We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts for time t, this algorithm uses (d2(d+log* N) ∥Ht∥)1+o(1) queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d4(d+log* N) ∥Ht∥)1+o(1) To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces.