Decoherence in a dynamical quantum phase transition

TL;DR

This paper investigates how decoherence affects quantum phase transitions in Ising chains and compares it to adiabatic Grover search, revealing that second-order transitions are more susceptible to decoherence as system size grows.

Contribution

It provides a comparative analysis of decoherence effects on second-order and first-order quantum phase transitions in quantum algorithms.

Findings

Decoherence impact increases with system size in second-order transitions.

First-order transitions are less affected by decoherence.

Scalability of adiabatic algorithms may be limited by decoherence effects.

Abstract

Motivated by the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compare it to the adiabatic version of Grovers search algorithm, which displays a first order quantum phase transition. For site-independent and site-dependent coupling strengths as well as different operator couplings, the results show that (in contrast to first-order transitions) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins/qubits). This might limit the scalability of the corresponding adiabatic quantum algorithm.