42 concepts.
Search superconducting quantum circuits, from Cooper pairs to quantum error correction.
01 · Chapter 1BCS superconductivityElectrons form correlated Cooper pairs below a critical temperature.02 · Chapter 1Cooper pairs and condensate phaseCooper pairs carry charge two electron charges and support a coherent order-parameter phase.03 · Chapter 1London equations and penetration depthSuperconducting screening confines magnetic fields to a penetration layer.04 · Chapter 1Flux quantizationThe superconducting phase winds by integer multiples of two pi around a closed loop.05 · Chapter 1Josephson effectCoherent Cooper-pair tunneling through a weak link produces nonlinear supercurrent.06 · Chapter 1Josephson voltage-phase relationA voltage drives time evolution of the gauge-invariant phase difference.07 · Chapter 1Josephson energy and inductanceA junction stores nonlinear potential energy and acts as a tunable inductive element.08 · Chapter 1SQUIDs and flux tunabilityTwo junctions in a loop create a flux-dependent effective Josephson energy.09 · Chapter 2Circuit nodes and flux variablesNode fluxes provide generalized coordinates for lumped superconducting circuits.10 · Chapter 2Lagrangian and Hamiltonian formulationClassical circuit energies lead to a Hamiltonian suitable for quantization.11 · Chapter 2Canonical quantization of LC circuitsCircuit flux and charge become noncommuting observables.12 · Chapter 2Zero-point voltage and currentEven the circuit ground state contains quantum electrical fluctuations.13 · Chapter 2Cooper-pair boxCharging energy and Josephson tunneling compete to create an artificial atom.14 · Chapter 2Transmon qubitA large Josephson-to-charging energy ratio suppresses charge dispersion while retaining anharmonicity.15 · Chapter 2Flux qubitA superconducting loop can encode states with different persistent-current orientations.16 · Chapter 2FluxoniumA small junction shunted by a superinductance produces rich flux-dependent spectra.17 · Chapter 2Phase qubits and potential wellsMetastable Josephson potential wells can encode a few low-lying quantum levels.18 · Chapter 2Anharmonicity and leakageNonuniform energy-level spacing enables selective qubit operations.19 · Chapter 3Microwave resonatorsSuperconducting transmission lines form high-Q standing-wave microwave modes.20 · Chapter 3Circuit quantum electrodynamicsArtificial atoms interact with quantized microwave cavity fields.21 · Chapter 3Dispersive regimeOff-resonant coupling produces qubit-state-dependent cavity frequencies.22 · Chapter 3Qubit relaxation T1Energy decay transfers qubit excitation into environmental degrees of freedom.23 · Chapter 3Dephasing T2 and Ramsey fringesPhase coherence decays from relaxation and frequency fluctuations.24 · Chapter 3Echo and dynamical decouplingRefocusing pulses suppress certain slow fluctuations.25 · Chapter 3Quasiparticles and dielectric lossMicroscopic defects and nonequilibrium excitations limit superconducting coherence.26 · Chapter 3Thermalization and dilution refrigerationMicrowave qubits require strong thermal isolation and low effective excitation temperature.27 · Chapter 4Single-qubit microwave controlResonant drives rotate a qubit on its Bloch sphere.28 · Chapter 4DRAG pulse shapingQuadrature shaping suppresses leakage from weakly anharmonic qubits.29 · Chapter 4Controlled-Z gatesConditional energy shifts generate a two-qubit phase gate.30 · Chapter 4Cross-resonance gatesDriving one coupled qubit near another qubit frequency produces an effective conditional rotation.31 · Chapter 4Parametric iSWAP interactionsModulating circuit parameters can resonantly exchange qubit excitations.32 · Chapter 5Readout resonator and measurement chainDispersive readout maps qubit states to microwave field responses.33 · Chapter 5Josephson parametric amplifiersJosephson nonlinearity amplifies weak microwave signals near the quantum noise limit.34 · Chapter 5Two-mode squeezing circuitsThree- or four-wave mixing can generate correlated microwave photon pairs.35 · Chapter 5Quantum-limited measurementInformation gain and disturbance are linked by quantum mechanics.36 · Chapter 5Lindblad master equationsOpen-system models describe relaxation, dephasing and driven gates.37 · Chapter 5Spectroscopy and calibrationMicrowave spectroscopy reconstructs transition frequencies and couplings.38 · Chapter 6Surface-code stabilizersRepeated parity measurements detect errors without directly measuring logical information.39 · Chapter 6Leakage and correlated errorsErrors outside the computational subspace challenge standard qubit noise models.40 · Chapter 6Circuit simulation with black-box quantizationDistributed electromagnetic modes can be converted into effective quantum circuit Hamiltonians.41 · Chapter 6Noise spectroscopy and filter functionsControl sequences select which environmental noise frequencies affect coherence.42 · Chapter 6Scalable processors and packagingLarge systems require simultaneous control of coherence, wiring, crosstalk and calibration.