Maintaining quantum coherence in the presence of noise through state monitoring

Abstract

Unsharp measurements allow the estimation and tracking of quantum wave functions in real time with minimal disruption of the dynamics. Here we demonstrate that high-fidelity state monitoring, and hence quantum control, is possible, even in the presence of classical dephasing and amplitude noise, by simulating such measurements on a two-level system undergoing Rabi oscillations. Finite estimation fidelity is found to persist indefinitely after the decoherence times set by the noise fields in the absence of measurement.

Quantum evolution in the stroboscopic limit of repeated measurements

“…which generalize Eq. (11). Restricting ourselves to the subspace suppC i , we see that the operator C i acts as the identity operator on all vectors |ξ ∈ suppC i .…”

“…Since the conditional output state is non-linearly related with the input density operator, other non-trivial dynamics is possible including the emerging chaotic behavior [9,10]. Repetitive measurements enable maintenance of quantum coherence in the presence of noise [11] or acceleration of decoherence [12]. Repeated selective measurements are applicable in ground state cooling [13].…”

Implementation schemes for unsharp measurements with trapped ions

“…We have also shown earlier [8], that it is possible, in principle, to monitor (approximately) the dynamics (Rabi oscillations) of a single two-level quantum system in real time using unsharp measurements, or to estimate the Rabi frequency [9], while only weakly influencing the original dynamics. By using unsharp measurement estimation in conjunction * Electronic address: choudhary@ukzn.ac.za † Electronic address: konradt@ukzn.ac.za ‡ Electronic address: huys@csir.co.za with feedback, Vijay et al recently demonstrated stabilization of Rabi oscillations in a superconducting qubit at a desired frequency [10].…”

“…However, to fulfill condition Eq. (22) excess of F = 0.999 [8]. However, several further imperfections need to be considered.…”

Equation of motion for estimation fidelity of monitored oscillating qubits

“…The state estimate * konradt@ukzn.ac.za † hermann.uys@gmail.com is sequentially updated based on the outcome of each measurement on the actual quantum state with the same propagator as the system. Numerical simulations have demonstrated the convergence of the state estimate when all parameters in the Hamiltonian are precisely known [4,14] and even for the case of process tomography, treating the Hamiltonian parameters as state variables of a hybrid system [15][16][17].…”