Over the past decade, quantum coherent behavior has been observed in electrical circuits engineered to have discrete, individually addressable energy levels. These devices operate at cryogenic temperatures and microwave frequencies-conditions which permit the utilization of superconducting passive and active resonant circuits for measurement. The basic architecture of a quantum dispersive measurement consisting of a two level quantum bit coupled to a LC tank circuit is reviewed. Recent progress with this type of readout has led to the real time monitoring of a superconducting qubit with the observation of quantum jumps between energy levels.
Over the past decade, quantum coherent behavior has been observed in electrical circuits engineered to have discrete, individually addressable energy levels. These devices operate at cryogenic temperatures and microwave frequencies-conditions which permit the utilization of superconducting passive and active resonant circuits for measurement. The basic architecture of a quantum dispersive measurement consisting of a two level quantum bit coupled to a LC tank circuit is reviewed. Recent progress with this type of readout has led to the real time monitoring of a superconducting qubit with the observation of quantum jumps between energy levels.
Superconducting qubits are Josephson junction-based circuits that exhibit macroscopic quantum behavior and can be manipulated as artificial atoms. Benefiting from the well-developed technology of microfabrication and microwave engineering, superconducting qubits have great advantages in design flexibility, controllability, and scalability. Over the past decade, there has been rapid progress in the field, which greatly improved our understanding of qubit decoherence and circuit optimization. The single-qubit coherence time has been steadily raised to the order of 10 to 100 μs, allowing for the demonstration of high-fidelity gate operations and measurement-based feedback control. Here we review recent progress in the coherence and readout of superconducting qubits.
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.
Coherent circuits based on superconducting elements hold tremendous promise for the practical implementation of quantum information technology: advanced computation, cryptography, and hardware simulation of complex materials systems are envisioned applications. Such circuits are essentially engineered atoms with level transitions in the 4-8 GHz regime; as such “read” and “write” operations are performed with the aid of fast microwave pulses and low-noise amplifiers, respectively. Recent advances in cavity-based superconducting parametric amplifiers have enabled real-time measurement and feedback in one and two qubits. We demonstrate a novel Josephson junction transmission-line based traveling-wave amplifier which employs sub-wavelength phase matching resonators to achieve high gain, several GHz of bandwidth, and near quantum-noise limited performance. Such devices will enable multiplexed qubit readout in integrated architectures comprised of a variety of microwave frequency analog and digital superconducting technologies: signal sources, multiplexers, ADCs, DACs, mixers, and amplifiers.
A superconducting flux qubit is inductively coupled to a superconducting quantum interference device (SQUID) magnetometer, capacitively shunted to form a 1.294-GHz resonator. The qubit-state-dependent resonator frequency is weakly probed with a microwave signal and detected with a microstrip SQUID amplifier. At a mean resonator occupation n=1.5 photons, the readout visibility is increased by a factor of 4.5 over that using a cryogenic semiconductor amplifier. As n is increased from 0.008 to 0.1, no reduction in T1 is observed, potentially enabling continuous monitoring of the qubit state.
Spectral properties of a quantum circuit are efficiently read out by monitoring the resonance frequency shift it induces in a microwave resonator coupled to it. When the two systems are strongly detuned, theory attributes the shift to an effective resonator capacitance or inductance that depends on the quantum circuit state. At small detuning, the shift arises from the exchange of virtual photons, as described by the Jaynes-Cummings model. Here we present a theory bridging these two limits and illustrate, with several examples, its necessity for a general description of quantum circuits readout. Circuit Quantum Electrodynamics (cQED) is at the heart of most advanced superconducting quantum technologies. Different types of superconducting qubits can be strongly coupled to microwave resonators thus achieving regimes and phenomenena which cannot be reached within the realm of quantum optics [1]. More recently, strong coupling between microwave resonators and a variety of other quantum systems not necessarily involving superconductors has been achieved [2], extending further the realm of cQED. In all these applications the measurement of the qubit or the hybrid device state is achieved by monitoring the resonator properties. Theoretically , two regimes have been approached using disconnected descriptions [3]: the dispersive regime, where the qubit-resonator detuning is larger than the coupling strength yet small enough to allow the exchange of virtual photons, and the adiabatic regime, where the de-tuning is sufficiently large for virtual processes to be strongly suppressed. The dispersive regime, which describes level repulsion between those of the quantum circuit and of the resonator, is typically dealt with using a Jaynes-Cummings Hamiltonian within different levels of approximation [3-10]. In contrast, the adiabatic regime accounts for the renormalization of the resonator capaci-tance/inductance by the effective capacitance of the circuit , including its "quantum capacitance" [11, 12], or its effective inductance [13, 14], which modifies the resonator frequency [15, 16]. However, there is no actual border between these two regimes which could justify a separate treatment, as illustrated by recent experiments on hybrid cQED setups [17] that reveal features of both regimes for the same device. This situation claims for a unified description of quantum circuits readout, going beyond the standard Jaynes-Cummings model, which could be applied to different types of devices over a large range of parameters. * Corresponding author : a.l.yeyati@uam.es In the present Letter we derive a general expression for the resonator frequency shift when coupled to a generic quantum circuit. This expression naturally interpolates between the adiabatic and the dispersive regimes, thus allowing to clarify their origin from the same coupling Hamiltonian. In addition our formalism is not restricted to the usual two-level approximations but any multilevel situation can be described on the same footing. We illustrate the importance of the different terms in our expression by analyzing well-known models like a short single channel superconducting weak link hosting Andreev states, the RF-SQUID and the Cooper pair box. Resonator-quantum circuit coupling.-The system we consider comprises a resonant circuit and a quantum circuit coupled through phase or charge fluctuations as depicted in Figs. 1(a), 2(a) and in the inset of Fig. 3. The resonant circuit is represented as a lumped-element LC resonator with bare resonance frequency f r = ω r /2π, with ω r = 1/ √ L r C r. Introducing the photon annihilation (creation) operators a (a †), it can be described by the Hamiltonian H r = ω r a † a. On the other hand, the quantum circuit Hamiltonian,Ĥ qc (x), depends on a dimensionless control parameter x, corresponding to an excess charge on a capacitor or a flux through a loop. We denote by |Φ i (x) the eigenstates of the uncoupled quantum circuit,Ĥ qc (x)|Φ i (x) = E i (x)|Φ i (x). Flux (charge) fluctuations in the resonator lead to x → x 0 +x r , wherex r = λ(s a + s * a †) with a coupling constant λ, depending on a coupling scheme [19], and s = 1 (−i). We assume λ 1 in accordance with experiments. The resonator-quantum circuit coupling HamiltonianĤ c is obtained by expandingĤ qc (x 0 +x r) up to second order inx rĤ c (x 0) =x rĤ qc (x 0) +x 2 r 2Ĥ qc (x 0), (1) where the prime stands for the derivative with respect to x. The Hamiltonian describing resonator, quantum
Superconducting qubits are a promising technology for building a scalable quantum computer. An important architecture employed in the field is called Circuit Quantum Electrodynamics (circuit QED), where such qubits are combined with high quality microwave cavities to study the interaction between artificial atoms and single microwave photons. The ultra-strong coupling achieved in these systems allows for control and readout of the quantum state of qubits to perform quantum information processing. The work on circuit QED performed in this thesis consisted of realizing an experimental setup for qubit experiments in a new laboratory, investigating the coherence and decay of higher energy levels of superconducting transmon qubits and finally demonstrating a novel coaxial form of circuit QED. Designing and building a 3D circuit QED setup involved the following main accomplishments: producing high quality 3D cavities; designing and installing the cryogenic microwave setup as well as the room temperature amplification and data acquisition circuitry; successfully developing a recipe for the fabrication of Josephson junctions; controlling and measuring superconducting 3D transmon qubits at 10mK. Several qubits were fully characterised and have shown coherence times of several microseconds and relaxation times up to 25μs. Superconducting qubits in fact possess higher energy levels that can provide significant computational advantages in quantum information applications. In experiments performed at MIT, preparation and control of the five lowest states of a transmon qubit was demonstrated, followed by an investigation of the phase coherence and decay dynamics of these higher energy levels. The decay was found to proceed mainly sequentially with relaxation times in excess of 20μs for all transitions. A direct measurement of the charge dispersion of these levels was performed to explore their characteristics of dephasing. This experiment was also reproduced on a 3D transmon fabricated and measured in Oxford, where due to a higher effective qubit temperature a multi-level decay model including thermal excitations was developed to explain the observed relaxation dynamics. Finally, a coaxial transmon, which we name the coaxmon, is presented and measured with a coaxial LC readout resonator and input/output coupling ports placed inline along the third dimension. This novel coaxial circuit QED architecture holds great promise for developing a scalable planar grid of qubits to build a quantum computer.