Date of Graduation

5-2025

Document Type

Thesis

Degree Name

Master of Science in Physics (MS)

Degree Level

Graduate

Department

Physics

Advisor/Mentor

Gea-Banacloche, Julio R.

Committee Member

Vyas, Reeta

Second Committee Member

Singh, Surendra

Keywords

quantum gates; cavity QED; field fluctuations; semiclassical approximation; Tavis-Cummings model; gate error scaling

Abstract

If we want to physically implement qubits by using two level atoms within a cavity, then certain single-qubit gates (such as the X-gate) can be performed by bathing the atoms in an electromagnetic field from a laser. If the average photon count n̄ of the field greatly exceeds the number of N qubits, then the slight fluctuations of the field's phase and amplitude are mostly negligible. However, such a strong field might require more energy than what is desirable for the setup. If a weaker field is used in which phase and amplitude fluctuations might be noticeable, then the gate implementation may be imperfect. This error means that the actual qubit state is different from what we would expect from a state created by a perfectly classical field. In this paper, we compare three different techniques to show how this error scales as 1/n̄ for any preferred system of X-gates or Rx(θ)-gates on N atoms. We use a semiclassical treatment of a fluctuating field in addition to the Tavis-Cummings model and second order perturbation. The second order perturbation gives excellent results for when the initial atomic state is in a Cat State or an average of all states. From this, we find equations for maximum and average gate errors, respectively. We show how this error can be reduced by squeezing the coherent source as well as adjusting the interaction time between the field and atoms to be different from what is classically expected.

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