Learn Invest About

Where Understanding Creates Value. Open education — built by a family, for everyone.

Learn

Quantum Engineering
All Curricula

Company

About SIIEA
Investment Hub
Contact

Legal

Terms of Service
Privacy Policy
Disclaimer

© 2026 SIIEA Innovations, LLC. All rights reserved.

Educational content licensed under CC BY-NC-SA 4.0. Content is AI-assisted — see disclaimer.

Quantum Engineering Year 1: Quantum Mechanics Core Month 21Day 572

This content was created with AI assistance and may contain errors or inaccuracies. Always verify against authoritative academic sources.

Full disclaimer

Year 1·Month 21·Week 2

Day 572: Gate Identities and Circuit Equivalences

Day 572 of 2,016~15 min read

Learning Objectives

•**Derive key CNOT identities** including HXH = Z conjugation rules
•**Swap control and target** using Hadamard gates
•**Commute gates** through CNOT in circuit optimization
•**Apply gate identities** to simplify quantum circuits
•**Understand circuit equivalences** for different gate sets
•**Use identities** for practical circuit compilation

Today's Schedule (7 hours)

Previous dayNext day

On this page

1 Fundamental CNOT Identities 2 The HXH Z Identity 3 Control-Target Swap Identity 4 CNOT-CZ Conversion 5 Pauli Gate Propagation Through CNOT 6 Summary Pauli Propagation Rules 7 CNOT Cancellation 8 Triple CNOT SWAP 9 CZ Identities 10 Circuit Equivalences for Common Patterns 11 Useful Commutation Relations 12 Applications to Circuit Optimization Quantum Computing Connection

Day 571Day 572 of 2,016Day 573