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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Published on: August 2, 2019

Optimal Complexity of Parameterized Quantum Circuits.

Guilherme I Correr^1,2, Pedro C Azado^1,3, Diogo O Soares-Pinto¹

¹Instituto de Física de São Carlos, Universidade de São Paulo, IFSC-USP, São Carlos 13566-590, SP, Brazil.

Entropy (Basel, Switzerland)

|January 28, 2026

Summary

This summary is machine-generated.

Parameterized quantum circuits offer faster convergence for quantum algorithms by generating expressive states. Circuit topology significantly impacts entanglement and complexity growth, with majorization criteria providing valuable insights.

Keywords:

entanglement expressibility majorization parameterized quantum circuits

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Area of Science:

Quantum Computing
Quantum Information Theory

Background:

Parameterized quantum circuits are essential for variational quantum algorithms in the Noisy Intermediate-Scale Quantum (NISQ) era.
Their expressibility, the ability to generate diverse quantum states, is key to approximating solutions for complex problems.
Assessing expressibility via random parameter sampling relates to fundamental concepts of quantum complexity.

Purpose of the Study:

To compare the convergence rate of different parameterized quantum circuits towards the Haar measure (asymptotic complexity).
To investigate the role of circuit topology in entanglement generation and quantum complexity.
To evaluate the utility of majorization-based measures in understanding random quantum state generation.

Main Methods:

Comparison of various parameterized quantum circuit classes against universal random circuits.
Quantification of circuit expressibility using random parameter sampling.
Application of majorization-based complexity measures.
Analysis of qubit connection topology's impact on entanglement.

Main Results:

Parameterized circuits demonstrate faster convergence to asymptotic complexity compared to universal random circuits, requiring fewer gates.
Qubit connectivity topology significantly influences entanglement generation and the growth of quantum complexity.
The majorization criterion provides a complementary perspective on random state generation dynamics.

Conclusions:

Parameterized quantum circuits are efficient for achieving high expressibility and complexity in NISQ algorithms.
Optimizing qubit topology is critical for maximizing entanglement and computational power.
Majorization measures offer a valuable tool for analyzing quantum state ensembles and complexity.