Quantum gates by adiabatic and superadiabatic probabilistic controlled evolutions

¹ Faculty of Information and Communication Technology, International Islamic University Malaysia Gombak, 53100, Malaysia
² Departamento de Física, Universidade Federal de São Carlos - Rod. Washington Luís, km 235, SP-310, 13565-905 São Carlos, São Paulo, Brazil
³ Research Center of Semiconductor Technology - Bd. Dr. Frantz Fanon, 16038, Algeria
⁴ Cybersecurity and Systems Unit, Islamic Science Institute, University Sains Islam Malaysia - Nilai, 71800, Malaysia

^(a) ab3@live.fr (corresponding author)

Received: 11 December 2020
Accepted: 4 June 2021

Abstract

Adiabatic and superadiabatic controlled evolutions are used as universal models for quantum computations, where an auxiliary system is used as the main resource in the theory. While the adiabatic case demands a slow dynamics (so that the adiabatic theorem is satisfied), the superadiabatic model can speed up such process by spending more energy than the adiabatic one. In this paper, we explore a hybrid scheme of controlled evolutions and measurement in order to optimize the thermodynamic cost of implementing quantum gates. By adjusting a free parameter of the theory of controlled evolutions, we show that we can improve the energy cost of the evolution. To this end, we used a model of computation based on adiabatic/superadiabatic evolution and post-selection measurement on the auxiliary qubit. In both cases, adiabatic and superadiabatic, the probabilistic model allows for optimizing the thermodynamics cost of implementing gates. When the system reservoir interaction is taken into account, we show that the superadiabatic probabilistic model is more robust than the adiabatic one.