IQC Student Seminar Featuring Sarah Li

We introduce an improved CNOT synthesis algorithm that considers nearest-neighbour interactions and CNOT gate error rates in noisy intermediate-scale quantum (NISQ) hardware. Our contribution is twofold. First, we define a \Cost function by approximating the average gate fidelity Favg. According to the simulation results, \Cost fits the error probability of a noisy CNOT circuit, Prob = 1 - Favg, much tighter than the commonly used cost functions. On IBM's fake Nairobi backend, it fits Prob with an error at most 10^(-3). On other backends, it fits Prob with an error at most 10^(-1). \Cost accounts for the machine calibration data, and thus accurately quantifies the dynamic error characteristics of a NISQ-executable CNOT circuit. Moreover, it circumvents the computation complexity of calculating Favg and shows remarkable scalability. 

Second, we propose an architecture-aware CNOT synthesis algorithm, NAPermRowCol, by adapting the leading Steiner-tree-based synthesis algorithms. A weighted edge is used to encode a CNOT gate error rate and \Cost-instructed heuristics are applied to each reduction step. Compared to IBM's Qiskit compiler, it reduces \Cost by a factor of 2 on average (and up to a factor of 8.8). It lowers the synthesized CNOT count by a factor of 13 on average (up to a factor of 162). Compared with algorithms that are noise-agnostic, it is effective and scalable to improve the fidelity of CNOT circuits. Depending on the benchmark circuit and the IBM backend selected, it lowers the synthesized CNOT count up to 56.95% compared to ROWCOL and up to 21.62% compared to PermRowCol. It reduces the synthesis \Cost up to 25.71% compared to ROWCOL and up to 9.12% compared to PermRowCol. NAPermRowCol improves the fidelity and execution time of a synthesized CNOT circuit across varied NISQ hardware. It does not use ancillary qubits and is not restricted to certain initial qubit maps. It could be generalized to route a more complicated quantum circuit, and eventually boost the overall efficiency and accuracy of quantum computing on NISQ devices. 

Joint-work with: Dohun Kim, Minyoung Kim, and Michele Mosca