Principles of Superconducting Quantum Computers
Daniel D. Stancil
North Carolina State University
Raleigh, North Carolina
Gregory T. Byrd
North Carolina State University
Raleigh, North Carolina
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Dedicated to the pioneers of the first Quantum Revolution, who paved the way.
Contents 1
Cover
5
Preface
8 1 Qubits, Gates, and Circuits1.1 Bits and Qubits1.1.1 Circuits in Space vs. Circuits in Time1.1.2 Superposition1.1.3 No Cloning1.1.4 Reversibility1.1.5 Entanglement1.2 Single-Qubit States1.3 Measurement and the Born Rule1.4 Unitary Operations and Single-Qubit Gates1.5 Two-Qubit Gates1.5.1 Two-Qubit States1.5.2 Matrix Representation of Two-Qubit Gates1.5.3 Controlled-NOT1.6 Bell State1.7 No Cloning, Revisited1.8 Example: Deutsch’s Problem1.9 Key Characteristics of Quantum Computing1.10 Quantum Computing Systems1.11 Exercises 9 2 Physics of Single Qubit Gates2.1 Requirements for a Quantum Computer2.2 Single Qubit Gates2.2.1 Rotations2.2.2 Two State Systems2.2.3 Creating Rotations: Rabi Oscillations2.3 Quantum State Tomography2.4 Expectation Values and the Pauli Operators2.5 Density Matrix2.6 Exercises 10 3 Physics of Two Qubit Gates3.1 √ iSWAP Gate3.2 Coupled Tunable Qubits3.3 Cross Resonance Scheme3.4 Other Controlled Gates3.5 Two-Qubit States and the Density Matrix3.6 Exercises 11 4 Superconducting Quantum Computer Systems4.1 Transmission Lines4.1.1 General Transmission Line Equations4.1.2 Lossless Transmission Lines4.1.3 Transmission Lines with Loss4.2 Terminated Lossless Line4.2.1 Reflection Coefficient4.2.2 Power (Flow of Energy) and Return Loss4.2.3 Standing Wave Ratio (SWR)4.2.4 Impedance as a Function of Position4.2.5 Quarter Wave Transformer4.2.6 Coaxial, Microstrip, and Coplanar Lines4.3 S Parameters4.3.1 Lossless Condition4.3.2 Reciprocity4.4 Transmission (ABCD) Matrices4.5 Attenuators4.6 Circulators and Isolators4.7 Power Dividers/Combiners4.8 Mixers4.9 Low-Pass Filters4.10 Noise4.10.1 Thermal Noise4.10.2 Equivalent Noise Temperature4.10.3 Noise Factor and Noise Figure4.10.4 Attenuators and Noise4.10.5 Noise in Cascaded Systems4.11 Low Noise Amplifiers4.12 Exercises
