Environmentassisted analog quantum search
Abstract
Two main obstacles for observing quantum advantage in noisy intermediatescale quantum computers (NISQ) are the finiteprecision effects due to control errors, or disorders, and decoherence effects due to thermal fluctuations. It has been shown that dissipative quantum computation is possible in the presence of an idealized fully engineered bath. However, it is not clear, in general, what performance can be achieved by NISQ when internal bath degrees of freedom are not controllable. In this work, we consider the task of quantum search of a marked node on a complete graph of n nodes in the presence of both static disorder and nonzero coupling to an environment. We show that, given fixed and finite levels of disorder and thermal fluctuations, there is an optimal range of bath temperatures that can significantly improve the success probability of the algorithm. Remarkably for a fixed disorder strength σ , the system relaxation time decreases for higher temperatures within a robust range of parameters. In particular, we demonstrate that for strong disorder, the presence of a thermal bath increases the success probability from 1 /(n σ^{2}) to at least 1 /2 . While the asymptotic running time is approximately maintained, the need to repeat the algorithm many times and issues associated with unitary overrotations can be avoided as the system relaxes to an absorbing steady state. Furthermore, we discuss for what regimes of disorder and bath parameters quantum speedup is possible and mention conditions for which similar phenomena can be observed in more general families of graphs. Our work highlights that in the presence of static disorder, even nonengineered environmental interactions can be beneficial for a quantum algorithm.
 Publication:

Physical Review A
 Pub Date:
 August 2018
 DOI:
 10.1103/PhysRevA.98.022316
 arXiv:
 arXiv:1710.02111
 Bibcode:
 2018PhRvA..98b2316N
 Keywords:

 Quantum Physics
 EPrint:
 Phys. Rev. A 98, 022316 (2018)