Hari Krovi

Anderson localization makes adiabatic quantum optimization fail

Understanding NP-complete problems is a central topic in computer science (NP stands for nondeterministic polynomial time). This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NP-complete problems using a quantum computer. The efficiency of this approach is limited by small spectral gaps between the ground and excited states of the quantum computer’s Hamiltonian. We show that the statistics of the gaps can be analyzed in a novel way, borrowed from the study of quantum disordered systems in statistical mechanics. It turns out that due to a phenomenon similar to Anderson localization, exponentially small gaps appear close to the end of the adiabatic algorithm for large random instances of NP-complete problems. This implies that unfortunately, adiabatic quantum optimization fails: The system gets trapped in one of the numerous local minima.

Rate-distance tradeoff and resource costs for all-optical quantum repeaters

We present a resource-performance tradeoff of an all-optical quantum repeater that uses photon sources, linear optics, photon detectors and classical feedforward at each repeater node, but no quantum memories. We show that the quantum-secure key rate has the form

Rate-loss analysis of an efficient quantum repeater architecture

R(\eta) = D\eta^s

Convolutional entanglement distillation

bits per mode, where

Hitting time for the continuous quantum walk

\eta

Practical quantum repeaters with parametric down-conversion sources

is the end-to-end channels transmissivity, and the constants

Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups

D

BQP-completeness of scattering in scalar quantum field theory

and

Efficiency of an enhanced linear optical Bell-state measurement scheme with realistic imperfections

s

Quantum Walks Can Find a Marked Element on Any Graph

are functions of various device inefficiencies and the resource constraint, such as the number of available photon sources at each repeater node. Even with lossy devices, we show that it is possible to attain