Abstract Quantum computing has been developed for many physical systems, and superconducting qubits are now in the integration phase. To efficiently design a many qubit system, an appropriate circuit simulator is necessary. Despite the existence of simulators for circuits including Josephson junctions, simpler circuit simulators are desirable when considering integrated qubits controlled by millions of transistors. This study examines the application of conventional Simulation Program with Integrated Circuit Emphasis simulators to analyze transmission signals of the system composed of transmons in the dispersive regime. Further, the influences of device parameter variations caused by the fabrication process can be taken into the model.
Abstract Quantum computing has been developed for many physical systems, and superconducting qubits are now in the integration phase. To efficiently design a many qubit system, an appropriate circuit simulator is necessary. Despite the existence of simulators for circuits including Josephson junctions, simpler circuit simulators are desirable when considering integrated qubits controlled by millions of transistors. This study examines the application of conventional Simulation Program with Integrated Circuit Emphasis simulators to analyze transmission signals of the system composed of transmons in the dispersive regime. Further, the influences of device parameter variations caused by the fabrication process can be taken into the model.
•Classical superconducting circuit simulators are powerful and available. •Include Josephson junction as basic element. •Provide efficient time-domain simulations of complex circuits. •May show effects otherwise attributed to quantum circuits.
•Circuits of coupled superconducting qubits are being developed for quantum computing (QC). •Entangled quantum theory incompatible with classical simulators. •Quantum model difficult to simulate on conventional computers for complex circuits already being tested. •Classical circuit simulations should provide the baseline to compare with quantum effects, but this is seldom done. •Coupled oscillators are delocalized even in classical limit.
Superconducting quantum circuits (SQCs), composed of superconducting capacitors, inductances, Josephson junctions, and transmission lines, exhibit macroscopic quantum effects at ultra-low temperatures. Due to the extremely low dissipation of superconductors, an important application of SQCs is superconducting qubits with long coherence time. Quantum computing based on superconducting qubits is a leading physical realization method of quantum computing, which is theoretically capable of accelerating many computational problems including quantum simulation, database searching, and optimization. In the long run, to use the power of quantum computing to its full extent, universal quantum computers should be constructed with quantum error correction. In the short term, one of the most pressing targets of the superconducting quantum computing community is to demonstrate quantum advantage using noisy intermediate-scale quantum chips. Both goals rely on the increasing of the number of coupled qubits in a quantum circuit and the quality of these qubits, which dictate the breadth and the depth of a problem it can solve, respectively. The fabrication of SQCs has adopted a few manufacturing processes from conventional integrated circuits. Quantum chips containing multiple superconducting qubits can be made and packaged on a large scale. “Quantum supremacy” has been demonstrated on a quantum chip with fifty-three qubits fabricated using the flip-chip bonding technology. However, to demonstrate quantum advantage, the quality and quantity of qubits need to increase simultaneously. Dissipative channels emerge in circuit design, material preparation, chip fabrication, and working environment, limiting the lifetime of superconducting qubits. For quantum chips with tens to hundreds of qubits, the integration will also introduce extra processing steps which may degrade the qubits, and unwanted coupling to loss channels. Most of these channels are microscopically related to materials constructing the quantum chips, chip surfaces, and material interfaces. Thus, it is important to investigate the material growth and device fabrication of SQCs, and to understand the material related loss mechanisms. This review paper investigates the material related topics in superconducting quantum circuits pertinent to the quantum computing application from a comprehensive perspective. The history of SQCs is briefly mentioned, followed by the peculiar characteristics as an engineerable quantum system, and a roadmap to quantum advantage and universal quantum computing in the next a few years. Technically, the superconducting quantum computer is compared to a Schrodinger’s cat, and can be boiled down into three parts, i.e., quantum chips, the environment, and the operating system, corresponding to the cat, the box, and the observer, respectively. The material related decoherence channels of the SQCs can be sorted into four categories; each will be discussed in details. To fabricate SQCs with minimal loss, the processing technologies are elaborated, including qubit design, material selection, surface treatments, film growth, and Josephson junction, etc. Though there are general guidelines that amorphous materials should be avoided and processing induced damage should be minimized, more is to be investigated due to the emerging of new materials and new fabrication methods. The last part presents the potential application of the superconducting quantum computer and its current state of play. SQC for quantum computing is a multi-discipline research topic, demanding joint efforts from different scientific and technical areas. Materials science and device processing will play important roles along the way to quantum practicality.
The leading approach to attempt quantum computing is based on superconductors. In particular, Circuit Quantum Electrodynamic systems (circuit QED) are used to couple photons stored in a microwave resonator to a quantum bit (qubit), allowing the qubit to be controlled and measured. A lumped element parallel RLC circuit will be used to model a superconducting coplanar microwave resonator, in order to gain an intuitive understanding of how various parameters affect its electromagnetic properties, and how they can be optimised to provide desired specifications. Resonator quality factors will also be realised, which describe the effects of coupling the microwave resonator to external input/output transmission lines. The qubit is generated by a superconducting capacitively shunted Josephson Junction; the transmon, and its operation and non-linear behaviour will be discussed in this report. The transmon is integrated with a microwave resonator to generate the circuit QED system, and the derivation of the systems Hamiltonian will allow us to determine the equations describing the behaviour of the system, and therefore how it may be controlled and measured. The Bloch sphere will be introduced, which provides a useful geometric representation of the state space of a two-level quantum system. Mapping the derived Hamiltonian to the time-dependent Schrodinger equation facilitates realisation of control mechanisms of the qubit based on rotations about the Bloch sphere.
The superconducting qubit quantum computer is one of the most promising quantum computing architectures for large-scale integration due to its maturity and close proximity to the well-established semiconductor manufacturing infrastructure. From an education perspective, it also bridges classical microwave electronics and quantum electrodynamics. In this paper, we will review the basics of quantum computers, superconductivity, and Josephson junctions. We then introduce important technologies and concepts related to DiVincenzo's criteria, which are the necessary conditions for the superconducting qubits to work as a useful quantum computer. Firstly, we will discuss various types of superconducting qubits formed with Josephson junctions, from which we will understand the trade-off across multiple design parameters, including their noise immunity. Secondly, we will discuss different schemes to achieve entanglement gate operations, which are a major bottleneck in achieving more efficient fault-tolerant quantum computing. Thirdly, we will review readout engineering, including the implementations of the Purcell filters and quantum-limited amplifiers. Finally, we will discuss the nature and review the studies of two-level system defects, which are currently the limiting factor of qubit coherence time. DiVincenzo's criteria are only the necessary conditions for a technology to be eligible for quantum computing. To have a useful quantum computer, large-scale integration is required. We will review proposals and developments for the large-scale integration of superconducting qubit devices. By comparing with the application of electronic design automation (EDA) in semiconductors, we will also review the use of EDA in superconducting qubit quantum computer design, which is necessary for its large-scale integration.
The field of superconducting quantum computing, based on Josephson junctions, has recently seen remarkable strides in scaling the number of logical qubits. In particular, the fidelities of one- and two-qubit gates have reached the breakeven point with the novel error mitigation and correction methods. Parallel to these advances is the effort to expand the Hilbert space within a single junction or device by employing high-dimensional qubits, otherwise known as qudits. Research has demonstrated the possibility of driving higher-order transitions in a transmon or designing innovative multimode superconducting circuits, termed multimons. These advances can significantly expand the computational basis while simplifying the interconnects in a large-scale quantum processor. In this work we extend the measurement theory of a conventional superconducting qubit to that of a qudit, focusing on modeling the dispersive quadrature measurement in an open quantum system. Under the Markov assumption, the qudit Lindblad and stochastic master equations are formulated and analyzed; in addition, both the ensemble-averaged and the quantum-jump approach of decoherence analysis are detailed with analytical and numerical comparisons. We verify our stochastic model with a series of experimental results on a transmon-type qutrit, verifying the validity of our high-dimensional formalism.
Abstract We apply polymer quantization, a quantization technique sometimes used in high energy physics, to several superconducting circuits including: transmons, transmission line resonators, and LC circuits. In the case of transmon qubits and transmission line resonators, experimental predictions are very close to what is found with canonical quantization, though in this approach constant charge offsets can be interpreted as quantization ambiguities. In the case of LC circuits, polymer quantization predicts nonlinearities which are not present in the canonical approach. Based on this analysis we design and analyze a qubit which uses a meander inductor instead of a Josephson junction. Implications for qubit performance and fabrication are discussed. Given a choice for an effective phase operator, relevant parameters such as anharmonicity, frequency, and dispersive shifts are calculated for this meander inductor based qubit.