The present review attempts to sum up the advancements in circuit quantum electrodynamics (CQED) that has raised our hope for realizing scalable quantum information processing (QIP). Research reveals the advantages of (QIP) over classical information processing in terms of information storage capacity and speed of processing. In this context, the mathematical framework for QIP, like Quantum Fisher Information and computations based on Hilbert space is reviewed. CQED architectures of ever improving configuration are being reported in technical literature. Further, improvements are noticed in coupling strengths between the qubit and the resonator by application of robust protocols. The review highlights the Research efforts and the advancements achieved through faithful quantum state transfer between spatially separated qubits. The important phenomenon of entanglement, deterministic and multipartite, as the cornerstone for scalable QIP is discussed to bring forth the advancements achieved in reducing decoherence and decay. The author sums up the review with a discussion of selected patents and commercial endeavours in the field.
The present review attempts to sum up the advancements in circuit quantum electrodynamics (CQED) that has raised our hope for realizing scalable quantum information processing (QIP). Research reveals the advantages of (QIP) over classical information processing in terms of information storage capacity and speed of processing. In this context, the mathematical framework for QIP, like Quantum Fisher Information and computations based on Hilbert space is reviewed. CQED architectures of ever improving configuration are being reported in technical literature. Further, improvements are noticed in coupling strengths between the qubit and the resonator by application of robust protocols. The review highlights the Research efforts and the advancements achieved through faithful quantum state transfer between spatially separated qubits. The important phenomenon of entanglement, deterministic and multipartite, as the cornerstone for scalable QIP is discussed to bring forth the advancements achieved in reducing decoherence and decay. The author sums up the review with a discussion of selected patents and commercial endeavours in the field.
Abstract The unique features of quantum theory offer a powerful new paradigm for information processing. Translating these mathematical abstractions into useful algorithms and applications requires quantum systems with significant complexity and sufficiently low error rates. Such quantum systems must be made from robust hardware that can coherently store, process, and extract the encoded information, as well as possess effective quantum error correction (QEC) protocols to detect and correct errors. Circuit quantum electrodynamics (cQED) provides a promising hardware platform for implementing robust quantum devices. In particular, bosonic encodings in cQED that use multi-photon states of superconducting cavities to encode information have shown success in realizing hardware-efficient QEC. Here, we review recent developments in the theory and implementation of QEC with bosonic codes and report the progress made toward realizing fault-tolerant quantum information processing with cQED devices.
During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.
In this thesis, experimentally relevant aspects and open questions of quantum information processing and measurement in circuit quantum electrodynamics have been investigated theoretically. Circuit quantum electrodynamics is a relatively young field combining superconducting transmission line resonators on-chip with superconducting quantum bits which serve as artificial atoms. Remarkable experiments have underlined the prospects of circuit QED as a possible architecture for quantum information processing as well as a framework within which quantum optics experiments can be performed. In contrast to their optical counterparts, these experiments reach the ultra-strong coupling limit and allow e.g. the generation of Fock states, the study of decoherence and the observation of quantum jumps. We present the physics of superconducting circuits based on the Josephson junction as a non-linear circuit element. We discuss the various types of quantum bits (qubits) before turning to an introduction on cavity QED and conclude the introduction with a brief presentation of the most relevant experiments and a short introduction to the principles and prospects of quantum information processing. Building on the pioneering theoretical and experimental work in which up to three qubits have been integrated on a chip and successfully coupled via a cavity mode, we propose a scheme to overcome the natural limits concerning scalability in these systems. Usually, scalability is severely limited by the resonance width of the qubit transitions and the attainable frequency range for both qubit transition and cavity resonance frequencies. This limits the present setups to at most ten qubits. As a possible solution, we propose and investigate a cross-bar grid layout of cavities with qubits at the intersections. It turns out that this setup, allowing for up to about 1000 qubits, offers significant advantages over e.g. nearest-neighbor coupling schemes. In addition, it can serve as a building block for a truly scalable scheme for fault-tolerant quantum information processing with superconducting circuits by combining 7x7 arrays in a staircase manner. Furthermore, we discuss and simulate different possibilities to improve upon the suggested scheme by e.g. using resonant gates and optimal control theory. Another focus of the present thesis is measurement physics. In order to investigate e.g. the possibilities of using a circuit QED system to dispersively detect single microwave photons or to generate multi-qubit entangled states, we introduce in a pedagogical manner the basics of stochastic master equations which generate quantum trajectories before turning to concrete applications. Quantum trajectories have proven to be a state-of-the-art tool to analyze measurement situations in a very realistic manner by giving access to both the measurement record as well as the internal quantum dynamics conditioned on this record. Using the method of quantum trajectories as generated by stochastic master equations, we discuss a scheme to efficiently generate multi-qubit entangled states in a very flexible way. The method is based on a collective, dispersive qubit readout. By this measurement, a suitable product state of N qubits can be reliably converted into e.g. an N-qubit Greenberger-Horne-Zeilinger or W state. We propose and discuss the scheme and investigate the effects of decoherence and parameter spread as they would be encountered in experiment. Last but not least, we propose and fully analyze a scheme to dispersively detect single itinerant microwave photons. While experiments to generate single microwave photons have already been successfully performed, their single-shot quantum non-demolition detection has not been possible so far. The scheme presented in this thesis closes this gap in the circuit QED toolbox and reaches detection efficiencies of 30% only limited by fundamental quantum mechanics in this case the Quantum Zeno effect. This detection scheme could be used in quantum communication or quantum cryptography applications.
"Along with these developments, personal microwave technology has enabled strong non-linear effects at the photon level, leading to readily observable novel parameter regimes in quantum optics. Circuit QED has opened up new opportunities to explore the rich physics of quantum information processing (QIP) and quantum optics (QO), making them scalable on the road to quantum computing. However, we must also discuss some of the challenges involved. Quantum Technologies (QT) is a cross-disciplinary field that has made great progress in recent years. Technologies that can explicitly represent individual quantum states, as well as superposition and entanglement, are now being developed to exploit the 'strange' properties of quantum mechanics. In quantum communication, individual or entangled photons are used to securely send data, while quantum simulation utilizes well-controlled quantum systems that are less accessible. Interest is growing in higher dimensional quantum states and quantum communication, as the extended availability of Hilbert space and greater information capacity, along with increased noise elasticity, offer many advantages and new research possibilities. Let's focus our attention on the benefits of higher dimensional quantum states for quantum communication, as shown by Kuditz and others. Nevertheless, it has been demonstrated that higher dimensional quantum states can also provide improvements in many other areas."
We discuss different ways of generating entanglement in the original picture of circuit QED (XcQED) and several restrictions that arise in the context of a large-scale quantum architecture. To alleviate some of the issues posed by the presence of the nonlinearities inherent to these systems, we introduce a layout for circuit QED, wherein an artificial atom is coupled to a quantized radiation field via its longitudinal degree of freedom (ZcQED). This system is akin to ion traps used in atomic physics, but it relies on fixed coupling between the atom and the resonator. We describe a scalable architecture for processing quantum information with superconducting qubits, which is free from any type of residual interaction between the atomic and photonic degrees of freedom. Tunable interactions can be realized based on sideband transitions, and the system can be operated out of the Lamb-Dicke regime, allowing it to benefit from the possibility of achieving large coupling strengths between atoms and resonators. We also discuss a readout scheme that does not require any extra circuits and allows a qubit-specific measurement of the state of the quantum register inspired by the electron shelving technique. This scheme is quantum nondemolition (QND)-like, and allows for single-shot determination of the qubit states.
Circuit Quantum Electrodynamics (cQED), the study of the interaction between superconducting circuits behaving as artificial atoms and 1-dimensional transmission-line resonators, has shown much promise for quantum information processing tasks. For the purposes of quantum computing it is usual to approximate the artificial atoms as 2-level qubits, and much effort has been expended on attempts to isolate these qubits from the environment and to invent ever more sophisticated control and measurement schemes. Rather than focussing on these technological aspects of the field, this thesis investigates the opportunities for using these carefully engineered systems for answering questions of fundamental physics.