Counting statistics of microwave photons in circuit QED

TL;DR

This paper investigates the photon counting statistics in circuit QED resonators used for quantum computing, analyzing how different approximations affect photon distribution overlaps and readout fidelity.

Contribution

It provides a detailed analysis of photon emission statistics beyond the dispersive approximation, highlighting the impact of nondispersive terms on readout fidelity.

Findings

Poissonian photon distributions in the dispersive limit with negligible relaxation

Nondispersive Hamiltonian terms cause squeezing and Purcell decay, affecting photon distribution overlap

Strategies to minimize overlap improve intensity-sensitive readout fidelity

Abstract

In superconducting circuit architectures for quantum computing, microwave resonators are often used both to isolate qubits from the electromagnetic environment and to facilitate qubit state readout. We analyze the full counting statistics of photons emitted from such driven readout resonators both in and beyond the dispersive approximation. We calculate the overlap between emitted-photon distributions for the two qubit states and explore strategies for its minimization with the purpose of increasing fidelity of intensity-sensitive readout techniques. In the dispersive approximation and at negligible qubit relaxation, both distributions are Poissonian, and the overlap between them can be easily made arbitrarily small. Nondispersive terms of the Hamiltonian generate squeezing and the Purcell decay with the latter effect giving the dominant contribution to the overlap between two distributions.