Error analysis of bit-flip qubits under random telegraph noise for low and high temperature measurement application

Abstract

Achieving small error for qubit gate operations under random telegraph noise (RTN) is of great interest for potential applications in quantum computing and quantum error correction. I calculate the error generated in the qubit driven by $\pi$, CORPSE, SCORPSE, symmetric and asymmetric pulses in presence of RTN. For a special case when pulse acts in x-direction and RTN in z-direction, I find that for small value of noise correlation time, $\pi$-pulse has small error among all the other pulses. For large value of noise correlation time, possibly white noise, symmetric pulse generates small error for small energy amplitudes of noise strength, whereas CORPSE pulse has small error for large energy amplitudes of noise strength. For the pulses acting in all the three directions, several pulse sequences were identified that generate small error in presence of small and large strength of energy amplitudes of RTN. More precisely, when $\pi$ pulse acts in x direction, CORPSE pulse acts in y direction and SCORPSE pulse acts in z-direction then such pulse sequences induces small error and may consider for better candidate in implementing of bit-flip quantum error correction. Error analysis of small energy amplitudes of RTN may be useful for low temperature measurements, whereas error analysis of large energy amplitudes of RTN may be useful for room temperature measurements of quantum error correction codes.