Improving the Fidelity of CNOT Circuits on NISQ Hardware

We introduce an improved CNOT synthesis algorithm that considers nearest-neighbour interactions and CNOT gate error rates in noisy intermediate-scale quantum (NISQ) hardware. Compared to IBM's Qiskit compiler, it improves the fidelity of a synthesized CNOT circuit by about 2 times on average (up to 9 times). It lowers the synthesized CNOT count by a factor of 13 on average (up to a factor of 162). 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 matches Prob to within 10⁻³. On other backends, it fits Prob to within 10⁻¹. Cost accurately quantifies the dynamic error characteristics and shows remarkable scalability. Second, we propose a noise-aware CNOT routing algorithm, NAPermRowCol, by adapting the leading Steiner-tree-based connectivity-aware CNOT synthesis algorithms. A weighted edge is used to encode a CNOT gate error rate and Cost-instructed heuristics are applied to each reduction step. NAPermRowCol does not use ancillary qubits and is not restricted to certain initial qubit maps. Compared with algorithms that are noise-agnostic, it improves the fidelity of a synthesized CNOT circuit across varied NISQ hardware. 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. Our method can be extended to route a more general quantum circuit, giving a powerful new tool for compiling on NISQ devices.