Coherent Qubit Measurement in Cavity-Transmon Quantum Systems

TL;DR

This paper extends quantum jump measurement theory to cavity-transmon systems, enabling faster qubit readout by analyzing non-exponential photon statistics and the effects of heterodyne detection.

Contribution

It develops a theoretical framework for measuring quantum jumps in cavity-transmon systems, incorporating cavity quantum states and non-Hermitian evolution, to improve readout speed and accuracy.

Findings

Next photon statistics are highly non-exponential.

Faster readout possible on timescales shorter than cavity decay.

Intrinsic error for jump detection tends to zero at short times with large dispersion.

Abstract

A measurement of the time between quantum jumps implies the capability to measure the next jump. During the time between jumps the quantum system is not evolving in a closed or unitary manner. While the wave function maintains phase coherence it evolves according to a non-Hermitian effective Hamiltonian. So under null measurement the timing of the next quantum jump can change by very many orders of magnitude when compared to rates obtained by multiplying lifetimes with occupation probabilities obtained via unitary transformation. The theory developed in 1987 for atomic fluorescence is here extended to transitions in transmon qubits. These systems differ from atoms in that they are read out with a harmonic cavity whose resonance is determined by the state of the qubit. We extend our analysis of atomic fluorescence to this infinite level system by treating the cavity as a quantum system. We find that next photon statistics is highly non exponential and when implemented will enable faster readout, such as on time scales shorter than the decay time of the cavity. Commonly used heterodyne measurements are applied on time scales longer than the cavity lifetime. The overlap between the next photon theory and the theory of heterodyne measurement which are described according to the Stochastic Schroedinger Equation is elucidated. In the limit of large dispersion the intrinsic error for next jump detection -- at short time -- tends to zero. Whereas for short time dyne detection the error remains finite for all values of dispersion.