This thesis demonstrates the experimental generation of two-dimensional Continuous Variable (CV) cluster states in a superconducting microwave frequency comb using parametric pumping. We develop the Pump Projection Method (PPM) to solve the inverse parametric problem: given a target multimode correlation structure, we determine the required pump configuration by exploiting the orthogonality of elementary coupling matrices in Hilbert-Schmidt space. We experimentally generate square-lattice and honeycomb-lattice cluster states with up to several tens of modes, verified through nullifier measurements showing squeezing below the vacuum level. The states exhibit scalability with respect to mode number and robustness against frequency spacing variations. A dissipative model explains the optimal pumping regime, while hidden entanglement analysis confirms negligible unwanted correlations. These results establish a systematic framework for engineering programmable multimode entanglement in superconducting circuits, providing a versatile platform for Measurement-Based Quantum Computation (MBQC) in the microwave domain.
This thesis demonstrates the experimental generation of two-dimensional Continuous Variable (CV) cluster states in a superconducting microwave frequency comb using parametric pumping. We develop the Pump Projection Method (PPM) to solve the inverse parametric problem: given a target multimode correlation structure, we determine the required pump configuration by exploiting the orthogonality of elementary coupling matrices in Hilbert-Schmidt space. We experimentally generate square-lattice and honeycomb-lattice cluster states with up to several tens of modes, verified through nullifier measurements showing squeezing below the vacuum level. The states exhibit scalability with respect to mode number and robustness against frequency spacing variations. A dissipative model explains the optimal pumping regime, while hidden entanglement analysis confirms negligible unwanted correlations. These results establish a systematic framework for engineering programmable multimode entanglement in superconducting circuits, providing a versatile platform for Measurement-Based Quantum Computation (MBQC) in the microwave domain.
We demonstrate the experimental realization of two-dimensional, continuous variable (CV) cluster states between 191 microwave frequency modes. This result is obtained by exposing vacuum fluctuations to the input of a Josephson Parametric Amplifier, parametrically pumped by a sum of coherent tones around twice its resonant frequency. By carefully tuning pump frequencies, amplitudes, and phases we engineer the interference between mixing products and realize honeycomb and square lattice CV cluster states with three and four pump tones respectively. We prove the presence of the cluster states with a suitable nullifier test, reaching up to −1.2 dB of squeezing of the cluster state's nullifiers. We study hidden entanglement (HE) and show no hidden entanglement up to ∼−1 dB of squeezing and negligible HE at optimal squeezing.
We describe an experiment demonstrating the generation of three independent square-ladder continuous-variable cluster states with up to 94 qumodes of a microwave frequency comb. This entanglement structure at a large scale is realized by injecting vacuum fluctuations into a Josephson Parametric Amplifier pumped by three coherent signals around twice its resonance frequency, each having a particular well-defined phase relation. We reach up to 1.4 dB of squeezing of the nullifier that verifies the cluster state on the square ladder graph. Our results are consistent with a more familiar measure of two-mode squeezing, where we find up to 5.42 dB for one pump, and up to 1 dB for three pumps.
Cluster states are a fundamental resource for continuous-variable quantum computing, enabling measurement-based protocols that can scale beyond the limitations of qubit-based architectures. Here, we demonstrate on-demand generation of multimode entangled microwave cluster states using a programmable Josephson Traveling-Wave Parametric Amplifier (JTWPA) operated in the three-wave mixing regime. By injecting a tailored, non-equidistant set of pump tones via an arbitrary waveform generator, we engineer frequency-specific nonlinear couplings between multiple frequency modes. The entanglement structure is verified via frequency-resolved heterodyne detection of quadrature nullifiers, confirming the target graph topology of the cluster state. Our approach allows reconfigurability through the pumps spectrum and supports scalability by leveraging the wide bandwidth and spatial homogeneity of the JTWPA. This platform opens new avenues for scalable measurement-based quantum information processing in the microwave domain, compatible with superconducting circuit architectures.
The creation of high-quality cluster states in superconducting microwave circuits is a relevant ingredient in continuous-variable quantum computing. Although large-scale cluster states have been established in optical systems, dissipation prevents their direct applicability to the microwave realm. Recent improvements in superconducting parametric circuits, in particular Josephson parametric amplifiers (JPA) and traveling wave parametric amplifiers (TWPA), have permitted substantial progress in producing entangled states using microwave photons. In this paper, we examine experimentally and theoretically the effects of numerous parametric pump tones on the degree of two-mode squeezing in a quantum circuit and apply it to the JPA. We find that additional pumps diminish the initial two-mode correlations achieved with a single pump by redistributing it among a larger network of modes and by introducing entanglement with additional idler frequencies. Taking into account the actual heterodyne measurement conditions, the experimental results are consistent with theoretical expectations.
This thesis investigates quantum correlations in microwave fields generated by superconducting parametric amplifier circuits with the ultimate goal of realizing measurement-based continuous variable quantum computing. We model the Josephson Parametric Amplifier (JPA) and kinetic inductance parametric amplifier (KIPA) within a Hamiltonian framework in which inductance modulation generates the universal squeezing Hamiltonian. We derive closed-form expressions for the two-mode covariance matrix of the output field and characterize squeezing as a function of pump strength, external coupling, and internal loss. We obtain a maximum squeezing condition, showing that it is achieved when the parametric drive strength equals half the external dissipation rate, and that it is significantly degraded by internal loss. We then elucidate the connection between the frequency-domain covariance matrix and the time-domain autocorrelation functions via an inverse Fourier transform, and we identify a divergence of the correlation time as the parametric drive approaches the instability threshold. This divergence or critical slowing-down is demonstrated theoretically through simulations and verified experimentally using a KIPA.
Quantum optics has been, from its beginning, a driving force both for the exploration of fundamental limits of the quantum world and for conceiving seminal ideas and applications of the so-called quantum technologies. The last 20 years have seen a rapid development of ideas and proof-of-principle experiments involving the fields of quantum communication, quantum computation, quantum metrology and quantum simulation. The so called continuous variable (CV) approach to quantum optics, which uses many photon in collective states, and continuous observables like the quadratures of the electric field to encode information, has many interesting properties, especially from a communications perspective. It is inherently broadband and compatible with standard telecom infrastructures. Moreover, in CV, entanglement, one of the fundamental resource of quantum optics, can be generated deterministically. One of the main challenges for all quantum information technologies is scalability, being able to generate and manipulate a large number of quantum resources to achieve practical tasks efficiently. One approach to solve the issue of scalability is to use highly multimode quantum states. The quantum description of the electromagnetic field associate each photon (particle of light) with a mode (way for light to propagate). In a mutlimodal approach, we look at the quantum state bases and optical modes bases conjointly and tailor quantum fields not only in given modes, but also optimize the spatio-temporal shapes of the modes in which the state is defined. This opens wide perspectives for treating complex quantum states. In particular, using ultra-fast pulses of light which contain many temporal/spectral modes, we are able to generate large and complex entangled states of light using simple resources. In this thesis, we used an optical parametric oscillator pumped synchronously (SPOPO) with a frequency comb to generate multimode squeezed vacuum states which can be used to form cluster states: a large collection of modes (the nodes) entangled to each other in a certain way. These state are the basic resource for Measurement Based Quantum Computation (MBQC). This set-up has the advantage to generate entanglement in many mode with a single device. It is also highly tunable. Indeed, by tuning the spectrum of the OPO pump with a pulse shaper, one can tailor the properties of the generated quantum state. In this work, we focus on the optimization of the pump spectral shape to generate specific states. Using simulations based on Machine Learning Algorithms (MLA), we find optimal pump profile for typical target states. We then implement those shapes on the experimental set-up and measure the resulting states using multipixel homodyne detection. We also study intra-cavity dispersion effects. Dispersion inside the SPOPO cavity is indeed one of the main factor that limits the number of entangled modes in the generated quantum states. A systematic study of dispersion effects is therefore necessary to model the SPOPO output accurately. This works paves the way toward a fully tunable device that can be optimized in real time to generate specific quantum resources tailored for specific tasks.