3,781 research outputs found
Hamiltonian simulation with nearly optimal dependence on all parameters
We present an algorithm for sparse Hamiltonian simulation whose complexity is
optimal (up to log factors) as a function of all parameters of interest.
Previous algorithms had optimal or near-optimal scaling in some parameters at
the cost of poor scaling in others. Hamiltonian simulation via a quantum walk
has optimal dependence on the sparsity at the expense of poor scaling in the
allowed error. In contrast, an approach based on fractional-query simulation
provides optimal scaling in the error at the expense of poor scaling in the
sparsity. Here we combine the two approaches, achieving the best features of
both. By implementing a linear combination of quantum walk steps with
coefficients given by Bessel functions, our algorithm's complexity (as measured
by the number of queries and 2-qubit gates) is logarithmic in the inverse
error, and nearly linear in the product of the evolution time, the
sparsity, and the magnitude of the largest entry of the Hamiltonian. Our
dependence on the error is optimal, and we prove a new lower bound showing that
no algorithm can have sublinear dependence on .Comment: 21 pages, corrects minor error in Lemma 7 in FOCS versio
Energy-scales convergence for optimal and robust quantum transport in photosynthetic complexes
Underlying physical principles for the high efficiency of excitation energy
transfer in light-harvesting complexes are not fully understood. Notably, the
degree of robustness of these systems for transporting energy is not known
considering their realistic interactions with vibrational and radiative
environments within the surrounding solvent and scaffold proteins. In this
work, we employ an efficient technique to estimate energy transfer efficiency
of such complex excitonic systems. We observe that the dynamics of the
Fenna-Matthews-Olson (FMO) complex leads to optimal and robust energy transport
due to a convergence of energy scales among all important internal and external
parameters. In particular, we show that the FMO energy transfer efficiency is
optimum and stable with respect to the relevant parameters of environmental
interactions and Frenkel-exciton Hamiltonian including reorganization energy
, bath frequency cutoff , temperature , bath spatial
correlations, initial excitations, dissipation rate, trapping rate, disorders,
and dipole moments orientations. We identify the ratio of \lambda T/\gamma\*g
as a single key parameter governing quantum transport efficiency, where g is
the average excitonic energy gap.Comment: minor revisions, removing some figures, 19 pages, 19 figure
Hamiltonian Simulation by Qubitization
We present the problem of approximating the time-evolution operator
to error , where the Hamiltonian is the
projection of a unitary oracle onto the state created by
another unitary oracle. Our algorithm solves this with a query complexity
to both oracles that is optimal
with respect to all parameters in both the asymptotic and non-asymptotic
regime, and also with low overhead, using at most two additional ancilla
qubits. This approach to Hamiltonian simulation subsumes important prior art
considering Hamiltonians which are -sparse or a linear combination of
unitaries, leading to significant improvements in space and gate complexity,
such as a quadratic speed-up for precision simulations. It also motivates
useful new instances, such as where is a density matrix. A key
technical result is `qubitization', which uses the controlled version of these
oracles to embed any in an invariant subspace. A large
class of operator functions of can then be computed with optimal
query complexity, of which is a special case.Comment: 23 pages, 1 figure; v2: updated notation; v3: accepted versio
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