The simplest form of dipole interaction between an atom and a single photon field mode, is described by the vacuum Rabi model. Strong atom-photon coupling, which is described by the simpler Jaynes...Show moreThe simplest form of dipole interaction between an atom and a single photon field mode, is described by the vacuum Rabi model. Strong atom-photon coupling, which is described by the simpler Jaynes-Cummings model, has been achieved in many platforms, such as cavity and circuit quantum electrodynamics (QED) and has brought a lot of success towards experimental quantum information processing over the past years. The full Rabi model dynamics can only be obtained in the so-called ultra-strong and deep-strong coupling regimes where the interaction coupling strength is comparable or higher than the natural system frequencies. However, due to our inability to achieve such high coupling strengths, these regimes remain largely unexplored in the lab. In this thesis, we investigate the possibility of reaching these regimes in a circuit QED setup, by means of a recently proposed analog-digital quantum simulation. Following a detailed numerical model of the proposed scheme, where we include the most important experimental limitations, we demonstrate the feasibility of the proposal using a transmon coupled to a 2D superconducting resonator, for a certain range of design parameters. Moreover, we show that the Wigner function representation of the resonator state in phase space is instrumental in order to probe the signature of deep-strong coupling in the system. Following these results, we design a device that will enable us to carry out the experiment with high fidelity measurements and perform direct Wigner tomography inside the resonator.Show less
Quantum computing promises to deliver exponential speed-up over classical machines in solving specific problems. However, quantum information is susceptible to decoherence and errors, and fault...Show moreQuantum computing promises to deliver exponential speed-up over classical machines in solving specific problems. However, quantum information is susceptible to decoherence and errors, and fault-tolerant quantum computing (FTQC) is the only realistic approach. In FTQC, operations are performed on logical qubits which are encoded in physical qubits such that errors are correctable or trackable. Specifically, in the repetition code for quantum error correction (QEC), qubits are encoded in Greenberger-Horne-Zeilinger (GHZ)-type states to be protected from bit-flip or phase-flip errors. It is important not to leave the protected subspace at any time to meet the basic requirement for FTQC. Previous demonstrations of the repetition code in various physical systems have circumvented this requirement, detecting errors at the cost of decoding the logical qubit. Using five superconducting qubits in circuit quantum electrodynamics, we demonstrate quantum bit-flip error detection at the logical-qubit level by stabiliser measurements for the first time. These stabilisers are assessed by their ability to generate GHZ-type entanglement: projecting a maximal superposition state into the subspaces being stabilised, while maintaining the coherence within each. To further characterise the error detection, we intentionally apply errors on all qubits and assess the fidelities both in the encoded subspace and at the logical-qubit level. Although current fidelities of the stabiliser measurements preclude improvements by error detection over idling, this demonstration is a critical step towards larger codes based on stabiliser measurements in the paradigm of FTQC.Show less
