The precise control, entanglement, and measurement of quantum systems are central challenges in realizing scalable quantum information processing. This dissertation investigates how parametric modulation and engineered nonlinearity can be harnessed to both manipulate and measure superconducting qubits with high fidelity. In one part, controlled parametric drives are used to generate entanglement between qubit pairs and employ their joint states as probes of environmental dynamics. This approach enables the exploration of the non-Markovian nature of quantum environments, revealing how memory effects influence qubit coherence and energy relaxation. In a separate but conceptually related study, the same principle of parametric driving is utilized to design and analyze quantum-limited amplifiers based on three-wave mixing in weakly nonlinear Josephson circuits. An amplifier with a higher coupling quality factor than conventional JPAs is employed, allowing the two modes of a parity-time (PT) symmetric dimer to be mapped onto the in-phase (I) and quadrature (Q) components of the Josephson parametric amplifier. This mapping enables controlled exploration of non-Hermitian dynamics and mode coalescence within the amplifier’s quadrature space, offering new insights into PT-symmetric behavior and quantum-limited detection. Collectively, these investigations unify the themes of parametric control, entanglement, and amplification, advancing the broader understanding of quantum measurement and open-system dynamics.
The precise control, entanglement, and measurement of quantum systems are central challenges in realizing scalable quantum information processing. This dissertation investigates how parametric modulation and engineered nonlinearity can be harnessed to both manipulate and measure superconducting qubits with high fidelity. In one part, controlled parametric drives are used to generate entanglement between qubit pairs and employ their joint states as probes of environmental dynamics. This approach enables the exploration of the non-Markovian nature of quantum environments, revealing how memory effects influence qubit coherence and energy relaxation. In a separate but conceptually related study, the same principle of parametric driving is utilized to design and analyze quantum-limited amplifiers based on three-wave mixing in weakly nonlinear Josephson circuits. An amplifier with a higher coupling quality factor than conventional JPAs is employed, allowing the two modes of a parity-time (PT) symmetric dimer to be mapped onto the in-phase (I) and quadrature (Q) components of the Josephson parametric amplifier. This mapping enables controlled exploration of non-Hermitian dynamics and mode coalescence within the amplifier’s quadrature space, offering new insights into PT-symmetric behavior and quantum-limited detection. Collectively, these investigations unify the themes of parametric control, entanglement, and amplification, advancing the broader understanding of quantum measurement and open-system dynamics.
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.
Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.
Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.
One-dimensional Josephson waveguides have generated significant interest in the fields of quantum technology and superconducting quantum information because they allow complete control over wave dispersion and nonlinear interactions.A variety of Josephson waveguides have been proposed and realized in the recent years, with applications ranging from near quantum-limited broadband amplification to multi-mode entanglement generation and non-reciprocal signals transmission.This thesis explores parametric interactions and entanglement generation in a novel architecture of Josephson waveguide. The latter consists of a high-pass microwave network and realizes an artificial material showing left-handed wave dispersion (or equivalently negative refractive index). The left-handed dispersion, combined with the Josephson nonlinearity, enables for various parametric processes, ranging from self-phase-matched broadband amplification of co-propagating modes to amplification and mixing of waves propagating in opposite directions. The realization of such Josephson waveguide opens new avenues within the framework of Josephson traveling wave parametric amplifiers and converters.Beyond these classical nonlinear optical processes, negative index Josephson waveguide are also powerful tools to generate nonclassical states of light such as broadband two-mode vacuum squeezed states and spatially separated entangled photon pairs. Here, we report about the measurements of such quantum states with this novel Josephson waveguide architecture, opening new perspectives for quantum sensing and quantum radar and illumination protocols, and more generally for microwave applications requiring the routing of entangled photons in different directions.
Quantum computing and quantum information processing are fast developing fields. As more and more qubits are integrated into the quantum computing systems, a deeper understanding and more careful modeling of the dynamics of these quantum systems in presence of driving and/or loss are necessary, not only for optimizing existing quantum devices, but also for designing and achieving novel method for more precise manipulation of these quantum systems. Our work investigating these quantum systems is inspired by quantum optics, a field focused on the quantum description of light and light-matter interactions. In this thesis, we use the theoretical toolboxes provided by quantum optics as well as condensed matter theory to investigate and model realistic quantum systems. Specifically, we focus on the Nitrogen-vacancy centers in diamond crystal, a Josephson parametric amplifier (that uses Josephson junctions as its non-linear elements), and plasmonic nanowire system. With the knowledge of the dynamics of these systems, we proposed single-photon heralded two-NV center quantum gates; designed and optimized the superconducting circuit for a Josephson parametric amplifier to improve the amplifier's saturation power; and designed new methods for robust light manipulation using topologically protected plasmonic modes. All the devices that we study are either ready to be implemented in experiments or have already been built. Further, as discussed in this thesis, our theoretical analysis of NV-centers can be extended to similar device types like solid-state defect centers, while our analysis of Josephson parametric amplifiers can be extended to other types of superconducting circuit systems.
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.