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Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H.Expand
Simulating Hamiltonian dynamics with a truncated Taylor series.
A simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification. Expand
Hamiltonian Simulation with Nearly Optimal Dependence on all Parameters
An algorithm for sparse Hamiltonian simulation whose complexity is optimal (up to log factors) as a function of all parameters of interest is presented, and a new lower bound is proved showing that no algorithm can have sub linear dependence on tau. Expand
Exponential improvement in precision for simulating sparse Hamiltonians
The algorithm is based on a significantly improved simulation of the continuous- and fractional- query models using discrete quantum queries, showing that the former models are not much more powerful than the discrete model even for very small error. Expand
Black-box hamiltonian simulation and unitary implementation
We present general methods for simulating black-box Hamiltonians using quantum walks. These techniques have two main applications: simulating sparse Hamiltonians and implementing black-box unitaryExpand
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introducedExpand
Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit that does not require adaptive measurements. ThatExpand
Optimal input states and feedback for interferometric phase estimation
We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2Expand
Higher order decompositions of ordered operator exponentials
We present a decomposition scheme based on Lie–Trotter–Suzuki product formulae to approximate an ordered operator exponential with a product of ordinary operator exponentials. We show, using aExpand
How to perform the most accurate possible phase measurements
We present the theory of how to achieve phase measurements with the minimum possible variance in ways that are readily implementable with current experimental techniques. Measurements whoseExpand