# Information content of queries in training Parameterized Quantum Circuits

## TL;DR

This paper investigates the information content in training parameterized quantum circuits, highlighting a significant disparity between the information in exact evaluations and that in single-run samples, from an information theoretic perspective.

## Contribution

It provides an information theoretic analysis of the sample complexity in training PQCs, revealing the disparity between exact evaluations and single-run samples.

## Key findings

- Single exact evaluations contain large information content.
- Single quantum circuit runs provide exponentially less information.
- Implications for the efficiency of training PQCs.

## Abstract

Parameterized quantum circuits (PQC, aka, variational quantum circuits) are among the proposals for a computational advantage over classical computation of near-term (not fault tolerant) digital quantum computers. PQCs have to be "trained" -- i.e., the expectation value function has to be maximized over the space of parameters. This paper deals with the number of samples (or "runs" of the quantum computer) which are required to train the PQC, and approaches it from an information theoretic viewpoint. The main take-away is a disparity in the large amount of information contained in a single exact evaluation of the expectation value, vs the exponentially small amount contained in the random sample obtained from a single run of the quantum circuit.