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We introduce an efficient algorithm based on the quantum noise framework forsimulating open quantum systems on quantum devices. We prove that the opensystem dynamics can be simulated by repeatedly applying random unitary gatesacting on the system qubits plus a single ancillary bath qubit representing theenvironment. This algorithm represents a notable step forward compared tocurrent approaches, not only beacause the ancilla overhead remains alwaysconstant regardless of the system size, but also because it provides aperturbative approximation of the full Lindblad equation to first order in theenvironment coupling constants, allowing to reach a better target accuracy withrespect to first order approximation in the time step, thus reducing the totalnumber of steps. When the perturbative approximation does not hold one can takesmaller time steps and the approach reduces to the solution to first order inthe time step. As a future perspective, this framework easily accomodatesnon-Markovian effects by relaxing the reset of the bath qubit prescription.

Efficient quantum algorithm to simulate open systems through the quantum noise formalism