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
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
SIAM Journal on Computing
Efficient discrete-time simulations of continuous-time quantum query algorithms
Proceedings of the forty-first annual ACM symposium on Theory of computing
Simulating sparse Hamiltonians with star decompositions
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
On the efficiency of quantum algorithms for Hamiltonian simulation
Quantum Information Processing
Black-box hamiltonian simulation and unitary implementation
Quantum Information & Computation
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We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation algorithms based on product formulas and, most notably, scales better with the simulation error than any known Hamiltonian simulation technique. Our main tool is a general method to nearly deterministically implement linear combinations of nearby unitary operations, which we show is optimal among a large class of methods.