book

Superconducting Qubit Design Using Qiskit Metal: Engineering of Superconducting Quantum Architecture

Name: Superconducting Qubit Design Using Qiskit Metal: Engineering of Superconducting Quantum Architecture
ISBN: 9798868815041

by Subhojit Halder, Kinjal A. Chauhan, Muhamad Bagher Barfar, Srinjoy Ganguly, Shalini Devendrababu

July 2025

Intermediate to advanced

337 pages

19h 6m

English

Apress

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Superconducting Qubit Design Using Qiskit Metal
Introduction
Acknowledgments
Contents
About the Authors
About the Technical Reviewer
1. Introduction: Superconducting Qubits and Their Realizations
1.1 Quantum Computing and History1.2 Introduction to Qubits1.3 Timeline of Quantum Computing and Superconducting Circuits1.4 Quantum Computing Fundamentals1.5 Classical and Quantum Circuits1.6 Lagrangian Models1.7 Pauli Matrices1.8 Hamiltonian Model1.9 Superconducting Circuits1.9.1 What Is Superconductivity?1.10 Terms and Definitions of Some Important Concepts1.11 Superconducting Qubits1.12 Advantages and Disadvantages of Superconducting Systems1.13 Realizing Superconducting Circuits1.14 Conclusion
2. Theory of Superconducting Qubit
2.1 Harmonic Oscillator2.1.1 Classical Harmonic Oscillator2.1.1.1 Newtonian Analysis2.1.1.2 Lagrangian Formulation2.1.1.3 Hamiltonian Formulation2.1.2 Quantum Harmonic Oscillator2.1.3 Can a Harmonic Oscillator Serve As a Qubit?2.2 Classical Electrodynamics of an LC Oscillator Circuit2.2.1 Generating Hamiltonian of the Circuit2.3 Quantum Hamiltonian of an LC Oscillator Circuit2.4 Superconducting Qubits2.4.1 Basic Types of Superconducting Qubits2.4.1.1 Phase Qubit2.4.1.2 Charge Qubit2.4.1.3 Flux Qubit2.5 Transmon Qubit2.5.1 Classical Hamiltonian of Transmon Qubit2.5.1.1 Classical Hamiltonian2.5.1.2 Energy Landscape in a 2D Plane2.5.2 Quantum Hamiltonian of Transmon Qubit2.6 Other Refinements of Superconducting Qubit2.6.1 Xmon Qubit2.6.1.1 Circuit Design and Functionality2.6.1.2 Advantages and Applications2.6.2 Quantronium Qubit2.6.2.1 Design Features2.6.2.2 Operational Principles2.6.3 Fluxonium Qubit2.6.3.1 Design Features2.6.3.2 Operational Characteristics2.6.3.3 Advantages2.6.4 Gmon Qubit2.6.4.1 Circuit Design2.6.4.2 Advantages and Features2.6.5 Coaxmon Qubit2.6.5.1 Circuit Design2.6.5.2 Advantages2.7 Conclusion
3. Qiskit and Introduction to Qiskit Metal
3.1 Writing Basic Code3.2 Logic Gates3.3 Important Quantum Circuits3.4 Qiskit Metal3.4.1 Designing Quantum Chips3.4.2 Typical Quantum Processor Structure3.5 Qiskit Metal Installation Steps3.6 Conclusion
4. Qiskit Metal and Introduction to Chip Design
4.1 Qiskit Metal and Python4.2 Quantum Pins: QPins4.3 Routing Between the Qcomponents4.3.1 Straight Routing4.3.2 Any Direction Routing4.3.3 Routing at Bent Angles4.3.4 CPW Route Meander4.4 Types of Qubit4.4.1 Xmon Qubit4.4.2 Concentric Transmon4.4.3 Interdigitated Transmon Qubit4.5 Designing a Full-Fledged Chip in Qiskit Metal4.6 Josephson Junction4.6.1 Manhattan Style4.6.2 Dolan Style4.7 Qubit Coupler4.7.1 Direct Coupler (Transmon-Transmon)4.7.2 Tunable Couplers4.7.3 Bus Resonator Coupler (Transmon-Transmon)4.8 Electromagnetic Analysis and Quantization and Qiskit Metal4.9 Conclusion

5. Lumped Oscillator Model Analysis
5.1 Elements in Classical Lumped Model5.1.1 LC Tank Circuit5.1.2 Amplifier5.1.3 Oscillator Frequency and Stability Response5.2 Lumped Oscillator Model Analysis (LOM)5.3 Matrices5.3.1 Capacitance Matrix5.3.2 Resistance Matrix5.3.3 Impedance Matrix5.3.4 Admittance Matrix5.3.5 Mutual Inductance Matrix5.3.6 Inverse Inductance Matrix5.3.7 Scattering Matrix (S-Matrix)5.4 Capacitance Matrix and Lumped Oscillator Model Analysis5.5 Two Transmons Coupled by a Direct Coupler5.6 Advantages of Lumped Oscillator Model Analysis5.7 Conclusion
6. Energy-Participation Ratio Method for Quantization and Analysis
6.1 The EPR Method for Quantization of Superconducting Circuit6.1.1 Simple Circuit Quantization: Coupled Qubit and Cavity System6.1.1.1 Calculation of p m in the Classical Picture (Using FEM Simulation)6.1.1.2 Calculation of Quantum Zero-Point Fluctuations6.1.2 Quantization of the General Josephson System6.1.2.1 Quantum Hamiltonian of General Josephson System6.2 EPR Analysis of Quantum Circuit in Qiskit Metal6.2.1 Step 1: Design the Circuit Layout in Qiskit Metal6.2.2 Step 2: Perform Eigenmode Analysis in Ansys HFSS6.2.3 Step 3: Run EPR Analysis and Construct the Quantum Hamiltonian6.3 EPR Examples in Qiskit Metal6.3.1 Example of Single Transmon Qubit6.3.1.1 Import Required Libraries6.3.1.2 Create a Qubit Design in Qiskit Metal GUI6.3.1.3 Finite Element Eigenmode Analysis6.3.1.4 Execute Simulation and Verify Convergence and Electromagnetic Fields6.3.1.5 EPR Analysis Setup6.3.2 Example of CPW Resonator6.3.2.1 Create a Design in Qiskit Metal GUI6.3.2.2 Finite Element Eigenmode Analysis6.3.2.3 Refining Convergence and EM Field Analysis6.3.2.4 EPR Analysis of the Resonator6.3.3 Example of the Combined System of Transmon Qubit and CPW Resonator6.3.3.1 Setting Convergence Parameters and Junction Properties6.3.3.2 Visualizing the Electric Field Distribution6.3.3.3 Electric Field Distribution for Combined System6.3.3.4 EPR Analysis of the Combined System6.3.3.5 Microwave Analysis and Energy Results6.3.3.6 Kerr Nonlinear Results6.3.4 Example of a Combined System of Two Transmon Qubits6.3.4.1 Defining Junction Inductance and Capacitance6.3.4.2 Eigenmode Analysis Setup6.3.4.3 Eigenmode Analysis Setup with Buffer Adjustment6.3.5 Double-Hanger Resonator (S Param)6.3.5.1 Setup6.3.5.2 Execute Simulation and Verify Convergence6.3.5.3 Execute Simulation and Observe the Impedance6.4 Conclusion
7. Modelling the Hamiltonian Transmon Qubit Cooper Pair Box in the Charge Basis
7.1 Cooper Pair Box to Transmon Qubit7.2 Hamiltonian Model Cooper Pair Box (Hcpb) Class7.3 Modeling of a Transmon Qubit7.3.1 Energy Level Computation7.3.2 Comparison with the Analytic Expressions for Energy7.3.3 Wave function Plotting7.3.3.1 Verification of Orthonormality of the Wave functions7.4 Additional Analysis7.4.1 Charge Dispersion7.4.2 Energy Level Differences7.4.3 Anharmonicity7.4.4 Dephasing Time (T2)7.5 Qutip Simulation7.6 Back-Calculation of E J and E c 7.7 Conclusion
8. Manufacturing: Fabrication and Packaging of Qubits
8.1 Sputtering8.1.1 Ion Beam Sputtering8.1.2 Gas Flow Sputtering8.2 Evaporation8.2.1 Shadow Evaporation8.3 Creation of Unwanted Josephson Junctions and Generation of Supercurrents8.3.1 Phonons8.3.2 Supercurrents and Magnetism8.4 Flip Chip8.5 Chip Fabrication Parameters8.5.1 Inter-Chip Spacing8.5.2 Chip Tilt8.5.3 Transition Temperatures8.6 Conclusion
References
Index

Overview

Understand and implement superconducting Qubit Design using Qiskit Metal in the Quantum Computing environment. This book provides practical knowledge and step-by-step guidance on designing, analyzing, and fabricating quantum chips.

The book begins with an introduction to the fundamentals of quantum computing, covering essential terms, concepts, and the history of quantum computers. It explores the differences between quantum and classical computers and provides an overview of superconducting qubits. Next, you will learn the theory and practical aspects of superconducting qubits. Detailed mathematical and computational analyses of different qubit types and circuits are provided, along with a comprehensive guide to creating quantum circuits using Qiskit and Qiskit Metal. You will learn to design quantum chips and analyze components such as Josephson junctions and qubit couplers, using advanced methods such as the Lumped Oscillator Model, Quasi-Lumped Oscillator Model, and Energy Participation Ratio Method. Finally, the book covers the fabrication of superconducting qubits, detailing the manufacturing process, requirements, and methods to address fabrication issues.

After reading this book, you will be able to advance your understanding and skills in this cutting-edge field, making complex concepts accessible and providing a roadmap for practical application.

What You Will Learn

Install the Qiskit framework for creating basic quantum computing circuits
Create your first superconducting qubit chip from scratch
Formulate the back-end mathematical and computational model for the generated superconducting chips
Understand the Quasi-LOM (lumped oscillator model) and how it differs from the LOM

Who This Book Is For

Quantum computing professionals working with superconducting qubits

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