Impact of realistic noise on quantum metrological advantage using BECs

Understanding the limits set by realistic errors is crucial to the unleashing o practical applications of quantum technologies. Among the most promising applications of quantum technologies is quantum metrology. In this work, we consider an implementation of a metrology protocol under the digital quantum computation with one clean qubit (DQC1) scheme [1] and study its resilience to experimental errors. The DQC1 protocol can be implemented using a single-atom trapped in a tweezer and a Bose-Einstein Condensate.

We consider three sources of error affecting a DQC1 circuit (i) impurity of the initial state, (ii) decay and loss of atoms, causing a Markovian error and (iii) fluctuation of external magnetic fields causing a non-Markovian error. We model the impurity of the initial state using an incoherent mixture of a pure state and the uniformly mixed state. We show that the quantum advantage remains, for any non-zero proportion of the pure state in the mixture. Along with a light assisted decay of the single qubit, we also consider loss of atoms in the BEC. We show that the sensitivity of the metrology protocol is exponential in the decay rate, and we show a threshold value of the number of qubits below which the quantum advantage persists. Finally, we model external fluctuations of the field using a gaussian distribution. Like Markovian errors, we show a threshold for the number of qubits which scales inversely with the waist of the gaussian, below which the quantum advantage persists [2].

[1] H. Cable et al, Power of one bit of quantum information in quantum metrology, PRA, 93, 040304 (R)

[2] Philip Martin et al., Manuscript under preparation.