# Informationally complete measurements and tensor networks for high-precision measurements

- Institution: CERN
- Department: QTI Seminars
- Speaker: Stefano Mangini
- Year: 2025
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3022497)
- Licence: [CERN](http://copyright.web.cern.ch)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Abstract:

Accurate estimation of quantum observables is a fundamental challenge in quantum computing. In this talk, we explore a novel approach to providing unbiased estimators of multiple observables with low statistical error by leveraging informationally (over)complete measurements and tensor networks. The technique involves an observable-specific classical optimization of measurement data using tensor networks, leading to low-variance estimations. Compared to other observable estimation protocols based on classical shadows and measurement frames, our approach offers several advantages: (i) it can be optimized to achieve lower statistical error, reducing the measurement budget required for a given estimation precision; (ii) it scales efficiently to large numbers of qubits due to the tensor network structure; (iii) it applies to any measurement protocol with operators that admit an efficient tensor network representation. We benchmark the method through various numerical examples, including spin and chemical systems in both infinite- and finite-statistics scenarios, and demonstrate how optimal estimation can be achieved even with tensor networks of low bond dimension. .

0:00:00 Slide 1

0:02:06 Slide 2

0:04:51 Slide 3

0:06:15 Slide 4

0:08:18 Slide 5

0:10:56 Slide 6

0:13:11 Slide 7

0:15:15 Slide 8

0:17:56 Slide 9

0:19:21 Slide 10

0:21:31 Slide 11

0:23:36 Slide 12

0:25:11 Slide 13

0:27:09 Slide 14

0:29:05 Slide 15

0:30:41 Slide 16

0:32:56 Slide 17

0:36:08 Slide 18

0:44:15 Slide 19

0:46:33 Slide 20

0:48:37 Slide 21

0:52:27 Slide 22

0:54:06 Slide 23

0:57:38 Slide 24

0:58:56 Slide 25

1:00:16 Slide 26

1:02:19 Slide 27

1:05:28 Slide 28

## Lectures

1. [Informationally complete measurements and tensor networks for high-precision measurements](https://invisiblenetwork.ai/learn/cern/3022497/b41864c4ec39), 1 h 8 min (CERN's player)