Detecting weak radio-frequency electromagnetic fields plays a crucial role in a wide range of fields, from radio astronomy to nuclear magnetic resonance imaging. In quantum optics, the ultimate limit of a weak field is a single photon. Detecting and manipulating single photons at megahertz frequencies presents a challenge because, even at cryogenic temperatures, thermal fluctuations are appreciable. Using a gigahertz superconducting qubit, we observed the quantization of a megahertz radio-frequency resonator, cooled it to the ground state, and stabilized Fock states. Releasing the resonator from our control, we observed its rethermalization with nanosecond resolution. Extending circuit quantum electrodynamics to the megahertz regime, we have enabled the exploration of thermodynamics at the quantum scale and allowed interfacing quantum circuits with megahertz systems such as spin systems or macroscopic mechanical oscillators.

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This thesis mainly summarizes two experiments that relate to building a quantum computer out of superconducting transmon qubits. Transmon qubits have emerged as one of the foremost solid state qubits, realizing processors with more than ten qubits and demonstrating small scale quantum algorithms as well as quantum error correction schemes. Right now, there is a race between different academic and industry research groups to scale up transmon qubit processors. The first experiment was a demonstration of qubit control by selective broadcasting in order to reduce the scaling of expensive electronics with the number of qubits for individual single-qubit control. We demonstrated that we can bring two transmon qubits to the same frequency (combining fabrication accuracy and in-situ fine tuning) and use the same hardware to control both, routing the pulses with a nanosecond-timescale vector switch matrix. Despite the compromises required by this technique, we show a scalable path to single qubit control beyond the threshold required for quantum error correction. In benchmarking, we take into account gate leakage due to the fact that transmons are fundamentally multi-level systems. In the second experiment we establish entanglement between two transmon qubits on different chips. We use an entanglement by measurement scheme and demonstrate that we can overcome minor fabrication imperfections by shaping our measurement pulses. Ultimately, performance is mainly limited by photon loss between the chips and up to the amplification chain. This entanglement mediated by traveling photons could be used to make a distributed transmon processor where computations are spread across several chip modules. This modularity could enable connectivities that cannot be realized on chip and ease fabrication requirements, as modules could be individually fabricated and selected. Thus, both of these experiments fit into the larger effort to converge on the hardware, control equipment and architecture of a future large-scale transmon quantum computer. Other experiments I contributed to are summarized in the conclusion chapter to show the diverse physics that can be studied in cQED experiments. @en

While the on-chip processing power in circuit QED devices is growing rapidly, an open challenge is to establish high-fidelity quantum links between qubits on different chips. Here, we show entanglement between transmon qubits on different cQED chips with 49% concurrence and 73% Bell-state fidelity. We engineer a half-parity measurement by successively reflecting a coherent microwave field off two nearly identical transmon-resonator systems. By ensuring the measured output field does not distinguish |01) from |10), unentangled superposition states are probabilistically projected onto entangled states in the odd-parity subspace. We use in situ tunability and an additional weakly coupled driving field on the second resonator to overcome imperfect matching due to fabrication variations. To demonstrate the flexibility of this approach, we also produce an even-parity entangled state of similar quality, by engineering the matching of outputs for the |00) and |11) states. The protocol is characterized over a range of measurement strengths using quantum state tomography showing good agreement with a comprehensive theoretical model.

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Analog quantum simulations offer rich opportunities for exploring complex quantum systems and phenomena through the use of specially engineered, well-controlled quantum systems. A critical element, increasing the scope and flexibility of such experimental platforms, is the ability to access and tune in situ different interaction regimes. Here, we present a superconducting circuit building block of two highly coherent transmons featuring in situ tuneable photon hopping and nonlinear cross-Kerr couplings. The interactions are mediated via a nonlinear coupler, consisting of a large capacitor in parallel with a tuneable superconducting quantum interference device (SQUID). We demonstrate the working principle by experimentally characterising the system in the single-excitation and two-excitation manifolds, and derive a full theoretical model that accurately describes our measurements. Both qubits have high coherence properties, with typical relaxation times in the range of 15 to 40 μs at all bias points of the coupler. Our device could be used as a scalable building block in analog quantum simulators of extended Bose-Hubbard and Heisenberg XXZ models, and may also have applications in quantum computing such as realising fast two-qubit gates and perfect state transfer protocols.@en

We present an experimental study of flux- and gate-tunable nanowire transmons with state-of-the-art relaxation time allowing quantitative extraction of flux and charge noise coupling to the Josephson energy. We evidence coherence sweet spots for charge, tuned by voltage on a proximal side gate, where first order sensitivity to switching two-level systems and background 1/f noise is minimized. Next, we investigate the evolution of a nanowire transmon in a parallel magnetic field up to 70 mT, the upper bound set by the closing of the induced gap. Several features observed in the field dependence of qubit energy relaxation and dephasing times are not fully understood. Using nanowires with a thinner, partially covering Al shell will enable operation of these circuits up to 0.5 T, a regime relevant for topological quantum computation and other applications.

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The quantum Rabi model describing the fundamental interaction between light and matter is a cornerstone of quantum physics. It predicts exotic phenomena like quantum phase transitions and ground-state entanglement in ultrastrong and deep-strong coupling regimes, where coupling strengths are comparable to or larger than subsystem energies. Demonstrating dynamics remains an outstanding challenge, the few experiments reaching these regimes being limited to spectroscopy. Here, we employ a circuit quantum electrodynamics chip with moderate coupling between a resonator and transmon qubit to realise accurate digital quantum simulation of deep-strong coupling dynamics. We advance the state of the art in solid-state digital quantum simulation by using up to 90 second-order Trotter steps and probing both subsystems in a combined Hilbert space dimension of 80, demonstrating characteristic Schrödinger-cat-like entanglement and large photon build-up. Our approach will enable exploration of extreme coupling regimes and quantum phase transitions, and demonstrates a clear first step towards larger complexities such as in the Dicke model.

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We present two pulse schemes to actively deplete measurement photons from a readout resonator in the nonlinear dispersive regime of circuit QED. One method uses digital feedback conditioned on the measurement outcome, while the other is unconditional. In the absence of analytic forms and symmetries to exploit in this nonlinear regime, the depletion pulses are numerically optimized using the Powell method. We speed up photon depletion by more than six inverse resonator linewidths, saving approximately 1650 ns compared to depletion by waiting. We quantify the benefit by emulating an ancilla qubit performing repeated quantum-parity checks in a repetition code. Fast depletion increases the mean number of cycles to a spurious error detection event from order 1 to 75 at a 1-μs cycle time.

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