Quantum simulation is one of the central discipline to demonstrate the power of quantum computing. 
In recent years, the theoretical framework of quantum superchannels has been developed and applied widely as the extension of quantum channels. 
In this work, we study the quantum circuit simulation task of superchannels.
We develop a quantum superchannel simulation algorithm based on the convex decomposition into sum of extreme superchannels.
We demonstrate the algorithm by numerical simulation of qubit superchannels with high accuracy, making it applicable to current experimental platforms.
Our study stands as an expansion of the superchannel theory to the field of quantum simulation and algorithm, as well as an extension of quantum simulation from channels and open-system dynamics to superchannels and processes with manifest quantum memory effects.
The existence of universal quantum computers has been theoretically well established. However, building up a real quantum computer system not only relies on the theory of universality, but also needs methods to satisfy requirements on other features, such as programmability, modularity, scalability, etc. To this end, here we study the recently proposed model of quantum von Neumann architecture by putting it in a practical and broader setting, namely, the hierarchical design of a computer system. We analyze the structures of quantum CPU and quantum control units and draw their connections with computational advantages. We also point out that a recent demonstration of our model would require less than 20 qubits.
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