Quantum system based on superconducting circuit is considered as one of the most promising schemes to realize quantum computers due to its controllability, low dissipation and scalability. To implement large scale quantum computation, coherent coupling between qubits is crucial for controlling and transferring quantum states. In this review paper, we summarize the progress of coupled superconducting qubits, including local coupling via capacitance or inductance, multiple qubits coherent interaction through one-dimensional resonator as circuit quantum electrodynamics, and superconducting qubits in a three-dimensional waveguide cavity. Hamiltonians of various coupling schemes are analyzed and classification of these coupling structures is summarized based on the coupling range and tunability.
Quantum system based on superconducting circuit is considered as one of the most promising schemes to realize quantum computers due to its controllability, low dissipation and scalability. To implement large scale quantum computation, coherent coupling between qubits is crucial for controlling and transferring quantum states. In this review paper, we summarize the progress of coupled superconducting qubits, including local coupling via capacitance or inductance, multiple qubits coherent interaction through one-dimensional resonator as circuit quantum electrodynamics, and superconducting qubits in a three-dimensional waveguide cavity. Hamiltonians of various coupling schemes are analyzed and classification of these coupling structures is summarized based on the coupling range and tunability.
Quantum information processing using superconducting qubit based on Josephson junction has become one of the most promising candidates for possible realization of a quantum computer. In the heart of the qubit circuits, the superconducting microwave resonator plays a key role in quantum operations and measurements, which enables single-photon level microwave quantum optics. During last decade, the coherence time, or the lifetime of the quantum state, of the superconducting qubit has been dramatically improved. Among several technological innovations, the improvement of superconducting microwave resonator's quality has been the main driving force in getting the qubit performance almost ready for elementary quantum computing architecture. In this paper, I will briefly review very recent progresses of the superconducting microwave resonators especially aimed for quantum device applications during the last decade. The progresses have been driven by ingenious circuit design, material improvement, and new measurement techniques. Even a rather radical idea of three-dimensional large resonators have been successfully implemented in a qubit circuit. All those efforts contributed to our understanding of the qubit decoherence mechanism and as a result to the improvement of qubit performance.
Superconducting circuits based on Josephson junctions are regarded as one of the most promising technologies for the implementation of scalable quantum computers. This review presents the basic principles of superconducting qubits and shows the progress of quantum computing and quantum simulation based on superconducting qubits in recent years. The experimental realization of gate operations, readout, error correction codes, as well as some quantum algorithms are summarized, followed by an introduction of quantum simulation. And then some important applications in fields including condensed matter physics, quantum annealing, and quantum chemistry are discussed.
Superconducting qubits, realized by incorporating Josephson junctions into superconducting circuits, behave as artificial atoms with anharmonic energy spectra and can be precisely controlled and measured using microwave cavities within the framework of circuit quantum electrodynamics (cQED). Since its emergence in the early 2000s, cQED has established superconducting qubits as leading candidates for scalable quantum devices and has enabled the exploration of hybrid quantum systems that integrate disparate physical platformsThis review surveys superconducting hybrid quantum electromechanical systems in which mechanical resonators are coupled to superconducting qubits, with a focus on two widely used qubit platforms: the transmon and the fluxonium. We provide an overview of the underlying coupling mechanisms arising from interactions through the phase and charge degrees of freedom of the qubit, and discuss how these mechanisms give rise to both longitudinal and transverse qubit-mechanical interactions. We further review extensions of electromechanical platforms to electro-optomechanical architectures, in which optical cavities are integrated to enable coherent interfacing between superconducting circuits and optical photons. This review aims to present a unified framework and perspective on qubit-mechanical and qubit-mechanical-optical hybrid systems in superconducting quantum technologies and applications related to sensors.
In a quantum computer, the information carriers, which are bits in ordinary computers, are implemented as devices that exhibit coherent superpositions of physical states and entanglement. Such components, known as quantum bits or qubits, can be realized with various different types of two-state quantum systems. Quantum computers will be built for computational speed, with hoped for applications especially in cryptography and in other tasks where classical computers remain inefficient. Circuit quantum electrodynamics (cQED) is a quantum-computer architecture which employs superconducting electronic components and microwave photon fields as building blocks. Compared to cavity quantum electrodynamics (CQED), where atoms are trapped in physical cavities, cQED is more attractive in that its qubits are tunable and conveniently integrable with the electronics already in use. This architecture has shown some of the most promising qubit designs, despite their coherence times reaching tens of microseconds, are still below the state of the art with spin qubits, which reach milliseconds. Coherence times are historically the most relevant parameters describing the fitness of a qubit, although these days not necessarily the limiting factor. This thesis presents a comprehensive set of theoretical and experimental methods for measuring the characteristic parameters of superconducting qubits. We especially study transmission-line-shunted plasma oscillation qubits, or transmons, and presents experimental results for a single sample. Transmon capacitively couples a superconducting quantum interference device (SQUID) with a coplanar waveguide (CPW) resonator, often with added frequency tunability utilizing an external magnet. The number of superconducting charge carriers tunnelled through a junction in the SQUID are used as qubit degrees of freedom. Readout of the qubit state is carried out by measuring transmission through the CPW. A cryogenic setup is employed with measurement and driving pulses delivered from microwave sources. Steady-state spectroscopy is employed to determine the resonance frequencies of the qubit and the resonator, qubit-resonator coupling constants, and the energy parameters of the qubit. Pulse-modulated measurements are employed to determine the coherence times of the qubit. The related analysis- and simulation programs and scripts are collected togithub.com/patomaki.
In the last two decades, the field of circuit quantum electrodynamics, that studies the interaction between superconducting qubits and 1-dimensional waveguides, has been of great interest. It provides a great potential to build quantum devices, which are important for quantum computing, quantum communication and quantum information. The restriction to one dimension decreases losses and information can be transferred efficiently. Superconducting qubits are artificial atoms that consist of a non-linear Josephson element and work in the microwave regime. These superconducting qubits make on-chip tunable quantum experiments possible.In the appended paper, we investigate the spontaneous emission of an initially excited artificial atom (superconducting transmon qubit) which is capacitively coupled to a semi-infinite transmission line (atom in front of a mirror). We can choose the distance to the mirror arbitrarily so the interaction with the reflected field is delayed if the qubit is far away from the mirror and we have to take time-delay effects into account. We derive equations of motion for the transmon by circuit quantization and solve them semi-classically. In this thesis we give an introduction to circuit quantization, transmission lines and superconducting qubits. Then we discuss the methods and results of the appended paper which are based on the topics introduced.
The concept of a quantum computer was invented in the beginning of the 1980s as a quantum generalization of the reversible classical computer. After discoveries in the middle of the 1990s of quantum algorithms, which wouldsolve some problems considered intractable for classical computers, the field of quantum computing has developed rapidly. A wide range of quantum systems are investigated for their possible ability to implement quantum algorithms in practice. The most promising solid state implementations are superconducting electrical circuits based on the Josephson effect, and the Coulomb blockade effect. Superconducting circuits are macroscopic quantum systems which can be fabricated using standard lithography technologies. Superconducting qubits - basic building blocks of a quantum computer - have been developed at several research laboratories, among others the MC2 here at Chalmers. This thesis presents a theoretical investigation of controllable coupling of superconducting qubits based on the single Cooper-pair box. Two coupling schemes are investigated in detail: current-controlled coupling via large Josephson junctions, and coupling via a superconducting stripline cavity. Both coupling designs are scalable and suitable for the charge regime of the single Cooper-pair box, as well as for the charge-phase regime where the qubit is better protected from environmental noise. Quantum gate protocols which are relevant for these physical couplings are discussed. The investigations show that, for both considered designs, the simplest two-qubit gate is the conditional phase-shift gate. This gate is universal for quantum computing, and it can create maximallyentangled qubit pairs in only one run. The investigation combines methods from electrical engineering, quantum mechanics and quantum computer science.