Scalable noisy quantum circuits for biased-noise qubits

Quantum error mitigation allows to reduce the impact of noise on quantum algorithms. Yet, it is not scalable as it requires resources scaling exponentially with the circuit size. In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard-tests involving entangling and certain non-Clifford gates, which can be conducted reliably with only a polynomial overhead in algorithm repetitions. On the flip side we also found a classical algorithm able to efficiently simulate our specific variants of Hadamard test. We propose to use this algorithm as a simple benchmark of the biasness of the noise at the scale of large and complicated quantum circuits. The strong noise-resilience of our circuits could motivate further research, to see if a quantum computational advantage could be reached for highly specific, yet noisy circuits.