The Invention of Circuit Quantum Electrodynamics
Around fifteen years ago, a team led by professors Robert Schoelkopf and Steven Girvin at Yale University introduced the Circuit Quantum Electrodynamics architecture (Circuit QED). Loosely speaking, Circuit QED emerges from the recognition of a natural mapping between quantum optics, describing the interaction between Nature’s atoms and photons, and superconducting quantum circuits. Conceived as a flexible test-bed for quantum optics on a chip, as well as a solid-state quantum-computing architecture, this platform has enabled spectacular progress both in the fundamental understanding of light-matter interaction at the quantum level and in quantum information processing. Through the years, Circuit QED has served as a powerful toolbox for quantum engineering, with an impact on the development of novel quantum devices and protocols for the generation, filtering, amplification, routing and readout of microwave quantum signals. Circuit QED is now a very active field of research, and one of the leading quantum-computing hardware architectures developed in universities and companies worldwide.
The emergence of a new technology
Circuit QED is the study of cm-wavelength microwave photons interacting with mesoscopic superconducting quantum circuits at dilution-refrigerator temperatures. With dimensions approximately between 1 μm and 1 cm, and operating at frequencies in the microwave-frequency range of 1–20 GHz, these devices are fabricated by depositing aluminum (or niobium) on a low-loss dielectric substrate such as sapphire or silicon, by a process similar to that in the microelectronics industry. Superconductivity, which allows for dissipation-free current flow, arises when these circuits are cooled down below the critical temperature of the superconductor and conduction electrons are bound together into Cooper pairs. Transition to the superconducting state constitutes a dramatic reduction of complexity in the system, in which billions of electrons are now described by a unique and collective degree of freedom. Remarkably, this simplification leads to the existence of quantized energy levels in a superconducting quantum circuit and enables such a device to eventually behave as an artificial atom. The existence of atom-like energy levels was predicted by the Nobel Prize winner Anthony J. Leggett and demonstrated in 1985 by the group of John Clark at UC Berkeley, in an experiment conducted by John Martinis and Michel Devoret.
A simple example of a quantum superconducting circuit is a wire of inductance L shunted by a capacitance C, realizing an LC harmonic oscillator. By choosing L and C such that the resonance frequency is in the microwave domain, LC circuits play the role of cavities in which microwave photons can be stored. However, in order to realize an artificial atom, some anharmonicity (also called nonlinearity) is needed. This, again, is provided by superconductivity and more precisely by Josephson junctions. A Josephson junction consists of two superconductors separated by a nanometer-thin insulating layer. Cooper pairs in the superconductors can coherently tunnel through the insulator, establishing a supercurrent across a classically forbidden region. When embedded in a circuit, the Josephson junction behaves as an inductance with nonlinear current-flux dispersion. This nonlinearity allows for the engineering of artificial atoms with anharmonic spectra.
In the late ‘90s, Josephson-junction-based artificial atoms were suggested as candidates to realize a quantum bit, or qubit for short. In these proposals, the qubit subspace would be composed of the ground and first excited states of the artificial atom. Moreover, the anharmonicity of the atom’s energy spectrum would prevent leakage of the encoded information out of the qubit subspace and facilitate qubit control. These ideas were soon followed by the experimental demonstration of quantum coherence in a superconducting qubit in 1999 by Y. Nakamura and collaborators, then at NEC in Japan. With this milestone achievement, it did not take much longer for the field of superconducting qubits to gain greater popularity.
Josephson junctions were rapidly incorporated in many other qubit designs, including the flux qubit introduced in 1999 at Delft, the phase qubit in 2002 at NIST-Boulder, and the quantronium, also in 2002, at CEA-Saclay. However, during this time significant challenges remained to be surmounted. In particular, superconducting qubits were being measured using non-optimal readout schemes that introduced noise. The search for better strategies powered the next breakthrough.
Circuit QED emerged at Yale in 2003–2004 as an architecture integrating superconducting microwave resonators (cavities) and Josephson quantum circuits (artificial atoms). This platform provided excellent and single-package control and readout solutions for superconducting quantum-information-processing devices. Furthermore, Circuit QED realized a mesoscopic analogy to Cavity QED (Nobel Prize-winning Cavity QED work by Serge Haroche), where optical or microwave photons interact with single atoms in a three-dimensional cavity. Inspired by this correspondence, the work at Yale introduced solid-state analogues to the methods developed in quantum optics. In particular, these techniques included the formalism of master equations for the treatment of dissipation and decoherence — this time applied to mesoscopic devices.
A centerpiece of the Circuit-QED architecture are the superconducting coplanar-waveguide resonators (see Fig. 1). Qubits are fabricated in proximity to such resonators, which allow for qubit control and readout. Moreover, the resonators filter the qubits’ electromagnetic environment thereby increasing the qubits’ coherence time — the time in which qubits can faithfully preserve encoded quantum information. In 2004, a breakthrough experiment at Yale employed a single qubit in a resonator to demonstrate the coherent exchange of microwave photons between these two systems. This experiment served as a clear evidence of the quantum optical nature of superconducting circuits, opening avenues for new applications bridging the two respective research fields.
As a direct consequence, superconducting quantum devices have reemerged as a microwave-quantum-optics platform, where the Josephson junction provides the necessary nonlinearity to make microwave photons interact. Furthermore, the two-dimensional confinement of the electromagnetic field in a superconducting chip has allowed Circuit-QED setups to display an extraordinarily strong light-matter coupling in flexible geometries. Importantly, these strong, nonlinear engineered interactions have enabled quantum optics to be explored in previously inaccessible regimes.
From a historical point of view, Circuit QED was, perhaps, the result of combining an interdisciplinary team and opportune timing. Indeed, while similar ideas were being discussed in a handful of groups, it is worth mentioning that at the time the concept of microwave photons stored in superconducting circuits was not unanimously accepted by the experts. The work at Yale helped to formalize this concept and provided the first clear demonstration.
Quantum information processing with superconducting qubits
Circuit QED was recognized early on as a promising platform for quantum information processing (QIP). Broadly speaking, QIP entails the encoding and manipulation of information in long-lived quantum states, with the purpose of computing or communicating. Importantly, QIP promises computers exponentially faster at some tasks than current classical computers. The work at Yale concentrated on implementing what is known as gate-based universal quantum computation in the Circuit QED architecture, and it was later extended to other QIP schemes.
Gate-based universal quantum computation requires performing high-fidelity single- and two-qubit operations (also called gates), in addition to qubit readout. Moreover, a protocol for qubit initialization is needed and usually provided by thermal equilibrium with a cold environment. The implementation of universal gates in the Circuit-QED architecture was originally examined in a setup consisting of two superconducting qubits coupled to a common resonator, and is discussed below.
Single qubits are manipulated by irradiating the resonator with a microwave voltage pulse tuned to the qubit frequency — analogous to shining a laser on an atom. Using this concept, state-of-the-art single-qubit-gate fidelities are now above 99.9%. Regarding two-qubit gates, the resonator plays the role of a communication channel or “quantum bus”. As S. Girvin explains, a superconducting qubit can be thought of as a small antenna with two superconducting halves connected by a Josephson junction. When the qubit is in the excited state, Cooper pairs tunnel back and forth between the two antennae halves. The frequency of this tunneling is in the GHz range and the qubit, which looks like a classical dipole, can radiate (emit) a microwave photon through the resonator. Now in the resonator, the photon can reach a second qubit and inversely, be absorbed by it. This mechanism represents a resonator-mediated qubit-qubit interaction which forms the basis of quantum two-qubit operations between qubits separated by as much as a centimeter. State-of- the-art two-qubit gate fidelities are now above 99%.
Due to a noninvasive scheme known as dispersive readout, resonator-based qubit measurement is also possible. With state-of-the-art fidelities exceeding 99%, this technique is one of the most important achievements of the Circuit-QED architecture. Indeed, recall that the low performance of early readout protocols was one of the main motivations that led to the development of Circuit QED. As a result, the dispersive readout has offered a fast, high-fidelity and relatively simple alternative, where the qubit state is revealed by detecting a shift of the resonator frequency.
The availability and experimental demonstration of a complete set of high-fidelity universal quantum operations have enabled Circuit QED to become one of the leading and most developed QIP platforms at the moment. Furthermore, the generality of such control and readout protocols has gathered attention from developers of solid-state architectures beyond superconducting qubits. For example, Circuit QED is now used with spin qubits in semiconductors, and might potentially serve in Majorana-qubit devices. However, important challenges remain to be overcome with respect to the development of a truly fault-tolerant QIP architecture. This fact motivates large part of the current Circuit QED research.
Present and future of the Circuit-QED technology
In recent years, Circuit QED has powered astonishing progress in several areas ranging from QIP to fundamental mesoscopic physics. Superconducting QIP devices have been scaled from one- and two-qubit chips in 2004–2007 to more than 50-qubit devices in 2018. This has been possible thanks in part to the development of the so-called transmon qubit (with state-of-the-art coherence times exceeding 100 μs) and advances in microwave engineering and fabrication. Furthermore, quantum processors have been used to implement early quantum-chemistry and quantum-machine-learning algorithms, in addition to small-scale quantum error correcting codes. Some of these Circuit-QED-based devices are now available to the public via Cloud services, and have already produced significant amounts of research and interdisciplinary interest.
Circuit QED has also helped to achieve long-desired milestones. For instance, the coherent coupling between a spin qubit and a single microwave photon was recently demonstrated. Moreover, it is now possible to realize microwave quantum states in resonators, which can encode and preserve quantum information even longer than the resonator coherence time. Additionally, a new era of quantum-limited devices capable of detecting a single microwave photon with energy 10,000 smaller than a visible one, or amplifying signals at the quantum limit, has emerged. These devices have direct applications to QIP, and are currently in use to improve detection in experiments ranging from quantum metrology to the search of dark-matter and signatures of quantum gravity.
These groundbreaking achievements have contributed to the development of Circuit QED into a research field in its own right, holding promises of fundamental discoveries and new technological applications in the near future!
Acknowledgments
I thank my advisor Alexandre Blais for insightful discussions and comments on the text.
Note
A version of the text with citations is available here.
