2 research outputs found
A universal adiabatic quantum query algorithm
Quantum query complexity is known to be characterized by the so-called
quantum adversary bound. While this result has been proved in the standard
discrete-time model of quantum computation, it also holds for continuous-time
(or Hamiltonian-based) quantum computation, due to a known equivalence between
these two query complexity models. In this work, we revisit this result by
providing a direct proof in the continuous-time model. One originality of our
proof is that it draws new connections between the adversary bound, a modern
technique of theoretical computer science, and early theorems of quantum
mechanics. Indeed, the proof of the lower bound is based on Ehrenfest's
theorem, while the upper bound relies on the adiabatic theorem, as it goes by
constructing a universal adiabatic quantum query algorithm. Another originality
is that we use for the first time in the context of quantum computation a
version of the adiabatic theorem that does not require a spectral gap.Comment: 22 pages, compared to v1, includes a rigorous proof of the
correctness of the algorithm based on a version of the adiabatic theorem that
does not require a spectral ga
A Universal Adiabatic Quantum Query Algorithm
Quantum query complexity is known to be characterized by the so-called quantum adversary bound. While this result has been proved in the standard discrete-time model of quantum computation, it also holds for continuous-time (or Hamiltonian-based) quantum computation, due to a known equivalence between these two query complexity models. In this work, we revisit this result by providing a direct proof in the continuous-time model. One originality of our proof is that it draws new connections between the adversary bound, a modern technique of theoretical computer science, and early theorems of quantum mechanics. Indeed, the proof of the lower bound is based on Ehrenfest\u27s theorem, while the upper bound relies on the adiabatic theorem, as it goes by constructing a universal adiabatic quantum query algorithm. Another originality is that we use for the first time in the context of quantum computation a version of the adiabatic theorem that does not require a spectral gap