Digital measurement and control of microwave quantum circuits

Abstract: Superconducting circuits are well established tools for quantum sensing anda promising new platform for quantum computing. Typically these quantumcircuits operate at microwave frequencies where the thermal noise at 10mK in a dilution refrigerator is small compared to the ground-state energy.Controlling the quantum state of these circuits requires well-timed, phase-coherent microwave pulses. This thesis describes an instrument based onsynchronous direct digital synthesis and sampling at microwave frequenciesto control and measure the response of superconducting quantum circuits.This all-digital approach allows for up and down conversion to microwavebands without analog IQ mixers, reducing the complexity of the controlsystem and enabling advanced signal processing via software. The thesisalso describes how the instrument is used to explore the quantum propertiesof a variety of different superconducting circuits.We characterise and benchmark a sample containing two transmon qubitsconnected by a parametric coupler. Randomized benchmarking showscoherence-limited fidelity of single-qubit gates. We successfully operate atwo-qubit iSWAP gate where controlling the relative phase of microwavepulses is necessary. Using a 3D cavity coupled to a transmon qubit we createarbitrary bosonic states using interleaved sequences of pulses which displacethe cavity oscillation and perform selective number-dependent arbitrary-phase (SNAP) gates. In the area of measurement-based quantum computingwe explore the generation of entangled states of travelling waves generatedby scattering vacuum noise off a Josephson parametric amplifier. The en-tanglement is generated and detected using a phase-coherent pumping anddetection scheme at multiple frequencies. We apply this same scheme to alsostudy frequency-domain entanglement between multiple standing waves ofa nonlinear surface-acoustic-wave resonator. The multifrequency capabili-ties of the instrument are also used to study single-photon detection in thefar infrared by multiplexed readout of arrays of quantum-capacitance sen-sors. The capabilities of the instrument are further showcased through theimplementation of a coherent real-time noise-radar system, highlighting itspractical utility beyond quantum exploration.