Optimal and robust error filtration for quantum information processing

Error filtration is a hardware scheme that mitigates noise by exploiting auxiliary qubits and entangling gates. Although both the signal and ancillae are subject to local noise, constructive interference and postselection allow us to reduce the noise level in the signal qubit. Here we highlight the relation between error filtration and error detection codes and determine the optimal codes that make the qubits interfere most effectively. We examine our optimized scheme under imperfect implementation, where ancillary qubits may be noisy or subject to crosstalk. Even with these imperfections, we find that adding more ancillary qubits helps to protect quantum information. We benchmark our approach against figures of merit that correspond to different applications, including entanglement fidelity, quantum Fisher information (for applications in quantum sensing), and the Clauser-Horne-Shimony-Holt value (for cryptographic applications), with one, two, and three ancillary qubits. By using the entanglement fidelity as a figure of merit, we suggest a general condition for error filtration, and for one and two ancillae, we obtain some explicit expressions for the optimal codes. We also compare our method with the recently introduced superposed quantum error mitigation (SQEM) scheme based on superposition of causal orders and show that, for a wide range of noise strengths, our approach may outperform SQEM in terms of effectiveness and robustness.