Question

How does a dynamical decoupling sequence like CPMG protect a qubit from low-frequency environmental noise?

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A qubit experiences environmental noise as a fluctuating magnetic or electric field that causes the qubit phase to drift over time, an effect known as dephasing. Low-frequency noise is characterized by fluctuations that change slowly relative to the timescale of the qubit operation. A CPMG sequence consists of applying a series of rapid pi-pulses, which are rotations that flip the state of the qubit by 180 degrees, at specific time intervals. Between these pulses, the qubit accumulates a phase error due to the environmental noise. When a pi-pulse is applied, the sign of the accumulated phase error is effectively inverted. If the noise is low-frequency, the noise value remains nearly constant during the interval between pulses. Consequently, the phase error accumulated before the pulse is canceled out by the phase error accumulated after the pulse. By repeating this sequence, the periodic pulses refocus the qubit state, ensuring that the phase errors do not build up over time. This process acts like a band-pass filter that suppresses the effects of noise at frequencies below the repetition rate of the pulses. Essentially, the CPMG sequence forces the qubit to periodically experience both the positive and negative aspects of the slow-moving noise, causing the net phase accumulation to average to zero.

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How does a dynamical decoupling sequence like CPMG protect a qubit from low-frequency environmental noise?

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