Multimode superconducting parametric cavity is a flexible platform that has been used to study a variety of topics in microwave quantum optics ranging from parametric amplification, entanglement generation to higher order spontaneous parametric downconversion (SPDC). \nLeveraging the extensive toolbox of interactions available in this system, we can look to explore exciting applications in quantum computation and simulation. \nIn this thesis, we study the use of the parametric cavity to realize continuous variable (CV) quantum computation. \nWe propose and examine in detail the scheme to compute with the microwave photons in the orthogonal frequency modes of the cavity via successive application of parametric pump pulses or cavity drives. \nThe family of all Gaussian transformations can be accomplished easily with interactions already demonstrated in this system. \nFrom recent results and proposals involving higher order SPDC, there are also clear pathways towards realizing the non-Gaussian resources necessary for universal computation. \nCommon measurements on the system are accomplished with standard measurement techniques on the output state of the cavity and additional useful measurements may be implemented using available parametric interactions or new device designs involving a qubit as a nonlinear probe. \nUsing the parametric cavity, we experimentally implemented a hybrid quantum-classical machine learning algorithm called the Quantum Kitchen Sinks (QKS) as the first step towards developing this platform for quantum computation. \nThe algorithm is studied over two sets of experiments starting from partial experimental implementation of the quantum variational circuits to fully experimental implementation using multiple simultaneous continuous wave (CW) pumps. \nIn both cases, we find that the quantum part of the algorithm implemented in the parametric cavity improved the classification accuracy on a difficult synthetic data set up to 90.1% and 99.5% respectively when compared to a classical linear machine learning algorithm.
Multimode superconducting parametric cavity is a flexible platform that has been used to study a variety of topics in microwave quantum optics ranging from parametric amplification, entanglement generation to higher order spontaneous parametric downconversion (SPDC). \nLeveraging the extensive toolbox of interactions available in this system, we can look to explore exciting applications in quantum computation and simulation. \nIn this thesis, we study the use of the parametric cavity to realize continuous variable (CV) quantum computation. \nWe propose and examine in detail the scheme to compute with the microwave photons in the orthogonal frequency modes of the cavity via successive application of parametric pump pulses or cavity drives. \nThe family of all Gaussian transformations can be accomplished easily with interactions already demonstrated in this system. \nFrom recent results and proposals involving higher order SPDC, there are also clear pathways towards realizing the non-Gaussian resources necessary for universal computation. \nCommon measurements on the system are accomplished with standard measurement techniques on the output state of the cavity and additional useful measurements may be implemented using available parametric interactions or new device designs involving a qubit as a nonlinear probe. \nUsing the parametric cavity, we experimentally implemented a hybrid quantum-classical machine learning algorithm called the Quantum Kitchen Sinks (QKS) as the first step towards developing this platform for quantum computation. \nThe algorithm is studied over two sets of experiments starting from partial experimental implementation of the quantum variational circuits to fully experimental implementation using multiple simultaneous continuous wave (CW) pumps. \nIn both cases, we find that the quantum part of the algorithm implemented in the parametric cavity improved the classification accuracy on a difficult synthetic data set up to 90.1% and 99.5% respectively when compared to a classical linear machine learning algorithm.
The flexible engineering of superconducting circuits, together with the nonlinearity available from Josephson junctions, have made microwave quantum optics a blooming research field in the past decade. Key experiments originally performed in the optical domain have become very accessible on this microwave-frequency, such that strong atom-field interactions and optical parametric interactions in microwave. From the latter, one example is the implementation of spontaneous parametric downconversion (SPDC). This process is particularly interesting as it can act as a nonclassical radiation source which give a number of potential applications in quantum information processing. We will focus on studying SPDC in microwave throughout this thesis. \n \nIn the first half of this thesis, from designs to measurements, we will explore the well-known two-photon parametric processes, SPDC and coherent coupling, which are generated by quadratic Hamiltonians. Using three resonant modes of a SQUID-terminated parametric cavity, we proceeded to combine different two-photon processes in an effort to demonstrate a multipartite nonclassical radiation source. With detailed system gain and noise calibration of our cryogenic microwave network, we confirmed our implementation by experimentally verifying that the generated states contain genuine tripartite entanglement. This multimode entangled radiation source can be an important resource for future experiments on quantum networking. \n \nWhile two-photon parametric processes have found numerous important applications, they have also been the limit of experiments for over three decades, with higher-order parametric processes seemingly out of reach. In the second half of this thesis, we explore the potential of parametric resonators for achieving such higher-order processes. To do this, we first studied the necessary conditions for accessing cubic Hamiltonians through our SQUID-based interactions. We then fabricated a device dedicated to performing three-photon processes through these cubic Hamiltonians. For the first time, we observed a direct generation of photon triplets by a single SPDC process in microwave . The generation rate can exceed a photon flux density of 60 photon per second per Hertz at the device output, far surpassing any record to date for photon triplets. We studied various pump configurations corresponding to different three-photon SPDC processes starting from a cold vacuum state. Pumping at triple the frequency of a single mode, we observed a phase-space distribution with a non-Gaussian profile which shows strong skewness (third moment) in the quadrature amplitude distribution. We reconstruct the Wigner function of the propagating states from the directly measured moment matrix, demonstrating Wigner negativity. Pumping at the sum frequency of three modes, we observed non-zero coskewness between the quadrature amplitudes of the modes. By analysing the output signals and comparing their characteristics to the predicted theoretical signatures, we confirm our implementation of three-photon SPDC processes generated by specific cubic Hamiltonians. These types of non-Gaussian states have been suggested as a resource enabling universal quantum computation with continuous variables. Our results thus open up the realm of three-photon quantum optics, enabling a wealth of novel experimental and theoretical studies.
Multimode cavity quantum electrodynamics-where a two-level system interacts simultaneously with many cavity modes-provides a versatile framework for quantum information processing and quantum optics. Because of the combination of long coherence times and large interaction strengths, one of the leading experimental platforms for cavity QED involves coupling a superconducting circuit to a 3D microwave cavity. In this work, we realize a 3D multimode circuit QED system with single photon lifetimes of 2 ms across 9 modes of a novel seamless cavity. We demonstrate a variety of protocols for universal single-mode quantum control applicable across all cavity modes, using only a single drive line. We achieve this by developing a straightforward flute method for creating monolithic superconducting microwave cavities that reduces loss while simultaneously allowing control of the mode spectrum and mode-qubit interaction. We highlight the flexibility and ease of implementation of this technique by using it to fabricate a variety of 3D cavity geometries, providing a template for engineering multimode quantum systems with exceptionally low dissipation. This work is an important step towards realizing hardware efficient random access quantum memories and processors, and for exploring quantum many-body physics with photons.
One of the primary requirements for superconducting quantum information processors is high-fidelity, quantum non-demolition qubit readout. In superconducting circuits, we perform measurements with quantum-limited microwave amplifiers. These amplifiers are based on microwave cavities and powered by Josephson-junction based nonlinearities, which we drive to parametrically modulate the circuit and generate gain. However, cavity-based amplifiers generally suffer from a fixed gain-bandwidth product, a limited dynamic range, and the absence of directionality, and so they must be operated with external lossy microwave commercial components such as circulators. Many of these limitations can be circumvented by combining multiple parametric processes in a few-mode device, in particular by combining parametric drives which produce gain and those which produce gainless photon conversion. By combining balanced gain and conversion processes between a pair of modes, we have demonstrated transmission-only, phase-sensitive, gain-bandwidth-free amplification. We have also used measurements of transmon qubits with this mode of amplification to demonstrate its practical utility. More, by combining multiple instances of imbalanced gain and conversion processes among three modes, we have realized devices with non-reciprocal, transmission-only amplification, matched ports, and a large, gain-independent bandwidth. One of the biggest challenges in tuning multiple parametric processes is both inherent and dynamically-generated higher order nonlinearities in the device, which shift mode frequencies and parametric coupling strengths with pump power, preventing accurate balancing of the parametric processes. These can be controlled through engineering the Hamiltonian of the nonlinear element, in this thesis either a linearly-shunted Josephson Ring Modulator or SNAIL (Superconducting Nonlinear Asymmetric Inductive eLements), which for certain applied flux values can minimize or even change the sign of higher-order even nonlinearities. Additionally, we have explored a range of circuit parameters, allowing us to also control the relative size of odd-order nonlinearities. We have developed a series of prototypes which implement these concepts, and have achieved both high-dynamic range singly pumped amplifiers, and a promising platform for multi-parametric devices. We conclude by presenting recent progress towards implementing multiple parametric schemes that generates a practical directional amplifier, and discuss the remaining obstacles to a truly ideal parametric amplifiers.
Quantum computers have huge potential applications, but do not currently exist. It has already been proven that a quantum computer would outperform the best classical supercomputers in certain problems, some of which have vital connections with our daily lives. For example, quantum computers efficiently solve the prime number factoring problem, which in turn is the foundation of the RSA algorithm behind most online transactions. There is a great deal of current effort to implement quantum computers, and we have seen good progress in platforms including superconducting circuits, ion traps, and photons in cavity QED systems and spins in semiconductors. These machines include up to roughly 50 quantum bits at present, but they are not very useful as quantum errors quickly decohere the computer's state and prevent computation. These errors can be mitigated via quantum error correction at the cost of additional size and complexity. Progress in the field towards error corrected, large-scale quantum machines requires us to require new tools for controlling, coupling, and reading out qubits. In this thesis, I will focus on such explorations in superconducting circuits. In this thesis, we seek to expand the already flexible toolkit of quantum circuits by exploring the uses of parametric couplings based on third-order nonlinearities. This type of nonlinearities has only been used in quantum-limited amplifiers before, here we try to further explore their applications by creating new methods for controlling and measuring qubits that based on it. In the first experiment, we address the problem of implementing a highly efficient quantum non-demolition qubit readout. With the use of two-mode squeezed (TMS) light and combined with phase-preserving parametric amplifiers into an interferometer for dispersive qubit readout, we demonstrate a measurement scheme with a 44% improvement in power signal-to-noise ratio. We also investigate the back-action of the measurement scheme. In the second experiment, we create an effective chemical potential for photons with parametric system-bath coupling. In particular, we use a lossy Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) as both the bath and coupler. The bath engineering is realized by combining the multiple parametric drives and the dissipation together.
The research reported here details experimental progress toward future superconductor-based quantum computing technologies. Specifically, we present techniques for moving quantum information between various cavity resonators -- spatially as well as between frequencies. Rather than using traditional resonant coupling though, we induce non-resonant coupling through parametric frequency conversion. This technology is mediated by chip-based, micro-fabricated, Josephson Junction circuits.\nParametric processes have the advantage over traditional coupling by allowing the constituents of the system -- for example: cavity modes or qubits -- to remain fixed in frequency, tuned to their optimal operation frequency, thereby avoiding unwanted resonant interactions. As the number of constituents grows -- as quantum computing architectures expand to more and more bits -- these techniques will become necessary to optimize performance.\nOutside of the focus on quantum computation, these techniques have wide application for materials research, quantum optics, and extending traditionally optical-frequency experiments to microwave-frequencies. To that end, we demonstrate a hybrid quantum technology which expands the toolbox of superconducting quantum information to a new system, namely sapphire whispering gallery mode resonators. These resonators have been studied in the optical frequency domain, but here we demonstrate their usefulness at microwave frequencies.\nAll of the experiments in this dissertation should be considered proof-of-principle demonstrations of a future technology. Thus, we note when and where improvements for future devices will be necessary.
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.