Simulação de canais quânticos usando preparação variacional de estados

Abstract

Quantum computers still suffer from errors that keep them in the category of Noisy Intermediate-Scale Quantum (NISQ) computers. Among the various tools capable of circumventing some of the problems of NISQ computers, there is the Variational Quantum Algorithm (VQA). This algorithm can be useful in almost all sub-areas of quantum computing, such as error correction, compilation, combinatorial optimization, and dynamic simulations. These algorithms involve optimization processes in parametric rotation gates and can make use of well-founded optimizers in classical machine learning in computing. Some studies in the formalism of quantum mechanics lead us to possible experiments on a quantum computer, but due to its sensitivity, these experiments require daily calibration. When dealing with an external environment, the system behaves as an open system, governed by a unitary operator in the global state space and described by a completely positive trace-preserving map (CPTP) in the local state space. We call these processes quantum channels, which result in an evolved state over time. Through the formalism of the representation in terms of Kraus operators, we obtain the evolved states through analytical calculations and compare the coherence of this state with the coherence of the evolved state obtained through the protocol of simulating noisy quantum channels proposed in [M. S. Zanetti, D. F. Pinto, M. L. W. Basso, and J. Maziero, Simulating noisy quantum channels via quantum state preparation algorithms, J. Phys. B: At. Mol. Opt. Phys. 56, 115501 (2023)]. During a step of this protocol, state preparations are performed using functions from the Qiskit library. The present work performs state preparations using VQA. We simulate channels associated with bit-flip, phase-flip, bit-phase-flip, depolarizing, amplitude damping, phase damping, generalized amplitude damping, Lorentz, and Heisenberg-Weyl dephasing. The results of simulations with VQA are satisfactory, with the coherence of the simulated state approaching the analytical value. This demonstrates the usefulness of VQA in state preparation for this problem.