Simulating noisy quantum channels via quantum state preparation algorithms

Abstract

In Refs. [Phys. Rev. A 96, 062303 (2017)] and [Sci. China Phys. Mech. Astron. 61, 70311 (2018)], the authors reported an algorithm to simulate, in a circuit-based quantum computer, a general quantum channel (QC). However, the application of their algorithm is very limited because it entails the solution of intricate non-linear systems of equations in order to obtain the quantum circuit to be implemented for the simulation. Motivated by this issue, in this article we identify and discuss a simple way to implement the simulation of QCs on any d-level quantum system through quantum state preparation algorithms, that have received much attention in the quantum information science literature lately. We exemplify the versatility of our protocol applying it to most well known qubit QCs, to some qudit QCs, and to simulate the effect of Lorentz transformations on spin states. We also regard the application of our protocol for initial mixed states. Most of the given application examples are verified experimentally using IBM's quantum computers.

Quantum simulation of Pauli channels and dynamical maps: Algorithm and implementation

“…As in the one qubit case, Pauli channels for N qubits attenuate the components r ã of the density matrix. This can be seen by substituting Eq (11) in Eq (12) and using the property of Eq (5):…”

“…Since their inception, quantum computers were proposed as powerful tools for the simulation of quantum systems [1]. Being open quantum systems of fundamental [2,3] and practical [4] interest, there has been efforts towards the simulation of the evolution of open quantum systems [5][6][7] and specifically for quantum channels [8][9][10][11], which can be used to study and model decoherence. Such quantum algorithms can be represented using what is known as a quantum circuit [12], which we will study in section 3.…”