Quantum Circuits for Collective Amplitude Damping in Two-Qubit Systems

Quantum computers have now appeared in our society and are utilized for the investigation of science and engineering. At present, they have been built as intermediate-size computers containing about fifty qubits and are weak against noise effects. Hence, they are called noisy-intermediate scale quantum devices. In order to accomplish efficient quantum computation with using these machines, a key issue is going to be the coherent control of individual and collective quantum noises. In this work, we focus on a latter type and investigate formulations of the collective quantum noises represented as quantum circuits. To simplify our discussions and make them concrete, we analyze collective amplitude damping processes in two-qubit systems. As verifications of our formalisms and the quantum circuits, we demonstrate digital quantum simulations of the collective amplitude damping by examining six different initial conditions with varying the number of execution of an overall operation for our quantum simulations. We observe that our results show good numerical matching with the solution of quantum master equation for the two-qubit systems as we increase such a number. In addition, we explain the essence of the way to extend our formalisms to analyze the collective amplitude damping in larger qubit systems. These results pave the way for establishing systematic approaches to control the quantum noises and designing large-scale quantum computers.