Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

The study of light-matter interaction has led to many fundamental discoveries as well as numerous important technologies. Over the last decades, great strides have been made in increasing the strength of this interaction at the single-photon level, leading to a continual exploration of new physics and applications. Recently, a major achievement has been the demonstration of the so-called strong coupling regime [1, 2], a key advancement enabling great progress in quantum information science. Here, we demonstrate light-matter interaction over an order of magnitude stronger than previously reported, reaching the nonperturbative regime of ultrastrong coupling (USC). We achieve this using a superconducting artificial atom tunably coupled to the electromagnetic continuum of a one-dimensional waveguide. For the largest coupling, the spontaneous emission rate of the atom exceeds its transition frequency. In this USC regime, the description of atom and light as distinct entities breaks down, and a new description in terms of hybrid states is required [4, 8]. Our results open the door to a wealth of new physics and applications. Beyond light-matter interaction itself, the tunability of our system makes it a promising tool to study a number of important physical systems such as the well-known spin-boson [9] and Kondo models [12]. * These authors contributed equally to this work.

We have embedded an artificial atom, a superconducting transmon qubit, in an open transmission line and investigated the strong scattering of incident microwave photons (∼6  GHz). When an input coherent state, with an average photon number N≪1 is on resonance with the artificial atom, we observe extinction of up to 99.6% in the forward propagating field. We use two-tone spectroscopy to study scattering from excited states and we observe electromagnetically induced transparency (EIT). We then use EIT to make a single-photon router, where we can control to what output port an incoming signal is delivered. The maximum on-off ratio is around 99% with a rise and fall time on the order of nanoseconds, consistent with theoretical expectations. The router can easily be extended to have multiple output ports and it can be viewed as a rudimentary quantum node, an important step towards building quantum information networks.

Quantum computers are expected to be more efficient in performing certain computations than any classical machine. Unfortunately, the technological challenges associated with building a fullscale quantum computer have not yet allowed the experimental verification of such an expectation. Recently, boson sampling has emerged as a problem that is suspected to be intractable on any classical computer, but efficiently implementable with a linear quantum optical setup. Therefore, boson sampling may offer an experimentally realizable challenge to the Extended Church-Turing thesis and this remarkable possibility motivated much of the interest around boson sampling, at least in relation to complexity-theoretic questions. In this work, we show that the successful development of a boson sampling apparatus would not only answer such inquiries, but also yield a practical tool for difficult molecular computations. Specifically, we show that a boson sampling device with a modified input state can be used to generate molecular vibronic spectra, including complicated effects such as Duschinsky rotations.

We propose different designs of switchable coupling between a superconducting flux qubit and a microwave transmission line. They are based on two or more loops of Josephson junctions which are directly connected to a closed (cavity) or open transmission line. In both cases the circuit induces a coupling that can be modulated in strength, reaching the so-called ultrastrong coupling regime in which the coupling is comparable to the qubit and photon frequencies. Furthermore, we suggest a wide set of applications for the introduced architectures. DOI: 10.1103/PhysRevLett.105.023601 PACS numbers: 42.50.Àp, 03.67.Lx, 85.25.Àj Superconducting quantum circuits [1] possess ingredients for quantum information processing and for developing on-chip microwave quantum optics [2]. After the first manipulations of few-level superconducting systems (qubits) [3][4][5], the real boost came with the achievement of the strong coupling regime between qubits and confined microwave photons [6][7][8]. The initial qubit-cavity couplings of 10-100 MHz exceeded by orders of magnitude the rate at which photons leak out of the resonator, but the use of the transmon qubit [9] improved those numbers by a factor of 2-3 reaching a strength that is comparable only to the state of the art in microwave quantum optics [10,11]. More recently, proof-of-principle theoretical and experimental studies have paved the way to the ultrastrong coupling regime [12][13][14], where the coupling approaches the qubit transition frequency and the Jaynes-Cummings model of cavity QED [10,14] breaks down [15,16], and a door opens to the rather unexplored physics beyond the rotating-wave approximation [17,18].The strong coupling regime in circuit QED has made possible an incredible variety of experiments, such as dispersive readouts of qubits [19], resolving the photon numbers in cavity [20], multiphoton excitations of the Jaynes-Cummings model [21], preparing nonclassical states of a resonator [22], full quantum tomography of the microwave radiation field [23], or the TavisCummings model [24], etc. However, all those experiments have something in common: The microwave field is confined inside a resonator. In other words, the transmission line spectrum is discrete and the coupling between qubits and photons could be switched on and off by tuning the qubit [25] or cavity frequency [26]. While the switchability of the coupling has been proposed for open lines [27,28], this has not been achieved in the ultrastrong coupling regimes.In this work, we will introduce a novel circuit QED design where the qubit is ultrastrongly coupled to a transmission line, open or not, with a coupling that can be tuned in strength and kind by applying an external flux bias. Our proposal uses the type of designs shown in Fig. 1, where the qubit is built in direct contact with the transmission line. It has been shown theoretically [14], and demonstrated experimentally [13], that the system admits an effective description based on a two-level system-the current in the loop-ultrastrongly coup...