Hi all,
Tomorrow Timothée Dao will tell us about his master thesis conducted at IBM "Informationally Complete Measurements for Estimating Quantum Expectation Values". See below for the abstract. The talk will take place at 2pm in HIT E 41.1
Best,
Ladina
Title :
"Informationally Complete Measurements for Estimating Quantum Expectation Values"
Abstract :
A major bottleneck faced by many current quantum algorithms is the large number of measurements required to achieve a specified precision. This talk addresses the problem by exploring the use of generalized measurements – formally described by positive operator-valued measures (POVMs) – to estimate the expectation value of quantum observables. We present a framework for estimating expectation values using informationally complete POVMs, and apply this toolbox to find optimal measurements, in the sense of minimizing the number of measurements required to achieve a specified precision.
Firstly, we introduce a comprehensive formalism that naturally integrates generalized measurements and classical techniques for manipulating them, for instance via randomization of projective measurements. Leveraging elements from frame theory, our approach provides systematic and general procedures to analyze measurement outcomes and produce estimates. Notably, the well-known classical shadows method [1] is shown to be a special case of the presented framework.
Secondly, we apply our formalism to the problem of determining optimal measurement schemes given a quantum system and a collection of observables to estimate. We compare the performance of various classes of POVMs and outcome processing methods. The classes of POVMs considered range from measurements that are currently implementable in practical experiments, such as local Pauli measurements, to those that will likely be implementable in the near future, such as local dilation POVMs. We assess the trade-off between performance and difficulty of implementation of these classes. Finally, we propose concrete solutions to enhance the measurement process, which enables, among other applications, an improvement of the classical shadows technique.
[1] H.-Y. Huang, R. Kueng, and J. Preskill, “Predicting many properties of a quantum system from very few measurements”, Nature Physics 16, 1050–1057 (2020)."