Quantum Divide and Compute: Exploring The Effect of Different Noise Sources

Our recent work (Ayral et al., 2020 IEEE Computer Society Annual Symposium on VLSI (ISVLSI)) showed the first implementation of the Quantum Divide and Compute (QDC) method, which allows to break quantum circuits into smaller fragments with fewer qubits and shallower depth. QDC can thus deal with the limited number of qubits and short coherence times of noisy, intermediate-scale quantum processors. This article investigates the impact of different noise sources -- readout error, gate error and decoherence -- on the success probability of the QDC procedure. We perform detailed noise modeling on the Atos Quantum Learning Machine, allowing us to understand tradeoffs and formulate recommendations about which hardware noise sources should be preferentially optimized. We describe in detail the noise models we used to reproduce experimental runs on IBM's Johannesburg processor. This work also includes a detailed derivation of the equations used in the QDC procedure to compute the output distribution of the original quantum circuit from the output distribution of its fragments. Finally, we analyze the computational complexity of the QDC method for the circuit under study via tensor-network considerations, and elaborate on the relation the QDC method with tensor-network simulation methods.