This paper presents two ways to improve the Real-Time Iterative Spectrogram Inversion (RTISI) algorithm. The standard RTISI phase estimator with look-ahead processes the buffered frames in reverse order. We show that better results are achieved by controlling this order according to frame energy. Another improvement is to initialize the last row of the phase estimator buffer by progressing the ...

This paper discusses the implementation of a two-phase procedure to construct confidence intervals for a simulation estimator of the steady-state quantiles of stochastic processes. We compute sample quantiles at certain grid points and use Lagrange interpolation to estimate the p quantile. The algorithm dynamically increases the sample size so that quantile estimates satisfy the proportional pr...

By using a systematic optimization approach, we determine quantum states of light with definite photon number leading to the best possible precision in optical two-mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse th...

We introduce a new method called rejection filtering that we use to perform adaptive Bayesian phase estimation. Our approach has several advantages: it is classically efficient, easy to implement, achieves Heisenberg limited scaling, resists depolarizing noise, tracks time-dependent eigenstates, recovers from failures, and can be run on a field programmable gate array. It also outperforms exist...

We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine its scaling in circuit depth and width. We show that the use of purely random measurements requires a number of measurements that is optimal up to constant ...