Divide-and-Conquer Simulation of Open Quantum Systems

One of the promises of quantum computing is to simulate physical systems efficiently. However, simulation of open quantum systems remains challenging, as their evolution involves non-unitary operators. The Stinespring dilation can simulate an open dynamic using a logarithmic number of auxiliary qubits, but requires a high circuit depth, which is impractical for NISQ devices. An alternative approach is parallel probabilistic block-encoding methods, such as the Sz.-Nagy and Singular Value Decomposition dilations. These methods implement the action of a single Kraus operator on quantum hardware and require one auxiliary qubit for each operator. They also result in shallower circuits but are hybrid methods, and do not simulate the complete quantum dynamic on the quantum computer. In this work, we describe a divide-and-conquer strategy to combine the output of each Kraus operator dilation and obtain the complete dynamic on quantum hardware with a lower circuit depth. We also introduce a balanced strategy that groups the Kraus operators into an expanded operator, leading to a trade-off between circuit depth, CNOT count, and number of qubits. We perform a computational analysis to demonstrate the advantages of the method and present a simulation of the Fenna-Matthews-Olson dynamic on current hardware.