Characterizing quantum circuits with qubit functional configurations

TL;DR

This paper introduces a new theoretical framework for characterizing quantum circuits through qubit functional configurations, enabling a systematic understanding of their properties and behaviors, especially in variational quantum algorithms.

Contribution

It proposes a novel theory that decomposes quantum circuits into functional configuration layers, facilitating the classification and analysis of circuit types and their properties.

Findings

Demonstrates application to hardware-efficient variational quantum algorithms

Provides a method to classify quantum circuits by configuration layers

Enables systematic understanding of quantum algorithm development

Abstract

We propose a theory of characterizing quantum circuits with qubit functional configurations. Any quantum circuit can be decomposed into alternating sequences of 1-qubit unitary gates and CNOT gates. Each CNOT sequence prepares the current quantum state into a layer of qubit functional configuration to specify the rule for the next 1-qubit unitary sequence on how to collectively modify the state vector entries. All the functional configuration layers on a quantum circuit define its type which can include many other circuits sharing the same configuration layers. Studying the functional configuration types allows us to collectively characterize the properties and behaviors of many quantum circuits. We demonstrate the theory's application to the hardware-efficient ansatzes of variational quantum algorithms. For potential applications, the functional configuration theory may allow systematic understanding and development of quantum algorithms based on their functional configuration types.