Exact Equivalence between Quantum Adiabatic Algorithm and Quantum Circuit Algorithm

Computational equivalence between quantum Turing machines and quantum circuit families

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 discretetime model of quantum computation, it also holds for continuous-time (or Hamiltonianbased) quantum computation, due to a known equivalence between these two query complexity models. In this work, we revisit this result by providing a direct pr...

Adiabatic quantum search algorithm for structured problems

The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speedup over a classical search, just as Grover’s algorithm. In this paper, we study how the structure of the search...

An optimal adiabatic quantum query algorithm

The quantum adversary method was originally introduced by Ambainis [Amb02] for lower-bounding the quantum query complexity Q(f) of a function f . It is based on optimizing a matrix Γ assigning weights to pairs of inputs. It was later shown by Høyer et al. [HLŠ07] that using negative weights also provides a lower bound, which is stronger for some functions. A series of works [RŠ12, Rei09, Rei11]...

Speedup in Quantum Adiabatic Evolution Algorithm

Quantum adiabatic evolution algorithm suggested by Farhi et al. was effective in solving instances of NP-complete problems. The algorithm is governed by the adiabatic theorem. Therefore, in order to reduce the running time, it is essential to examine the minimum energy gap between the ground level and the next one through the evolution. In this letter, we show a way of speedup in quantum adiaba...