We present a method to implement fast two-qubit gates valid for the ultrastrong coupling (USC) and deep strong coupling (DSC) regimes of light-matter interaction, considering state-of-the-art circuit quantum electrodynamics (QED) technology. Our proposal includes a suitable qubit architecture and is based on a four-step sequential displacement of the intracavity field, operating at a time proportional to the inverse of the resonator frequency. Through ab initio calculations, we show that these quantum gates can be performed at subnanosecond time scales, while keeping a fidelity above 99%.Introduction.-With the advent of quantum information science [1], there have been enormous efforts in the design of devices with high level of quantum control and coherence [2]. Circuit QED [3][4][5] has become a leading technology for solidstate based quantum computation and its performance is approaching that of trapped ions [6] and all-optical implementations [7]. Considerable progress has been made in recent circuit QED experiments involving ultrastrong coupling [8,9], two-qubit gate and algorithms [11][12][13][14][15][16], three-qubit gate and entanglement [17][18][19]. Most of the proposed gates are based on slow dispersive interactions or faster resonant gates, and would require operation times of about tens of nanoseconds.To speed up gate operations, the latest circuit-QED technology offers the USC regime of light-matter interactions [8-10, 20, 21], where the coupling strength g is comparable to the resonator frequency ω r (0.1 < ∼ g/ω r < ∼ 1). This should open the possibility to achieve fast gates operating at subnanosecond time scales [22,23] . In this sense, the design of these novel gates becomes a challenge as the rotating-wave approximation (RWA) breaks down and the complexity of the quantum Rabi Hamiltonian emerges [24,25]. Preliminary efforts have been done in this direction involving different configurations of superconducting circuits [26][27][28]. Likewise, in a recent contribution, it has been discussed the possibility of performing protected quantum computing [29].In this Letter, we propose a realistic scheme to realize fast two-qubit controlled phase (CPHASE) gates between two newly designed flux qubits [30], coupled galvanically to a single-mode transmission line resonator (Fig. 1). Our proposal includes: (i) a CPHASE gate protocol operating at times proportional to the inverse of the resonator frequency; (ii) the design of the qubit-resonator system, allowing for high controllability on both the qubit transition frequency and the qubit-resonator coupling, in USC [8,9] and potentially the DSC regime [31] of light-matter interaction. Through ab initio numerical analysis, we discuss the main features of this scheme in detail and show that the fidelity could reach 99.6%. This is an important step in the reduction of resources requirement for fault-tolerant quantum computation [32].Design of a versatile flux qubit.-The junction array is schematically depicted in Fig. 1. It consists of a six-

We propose a method to get experimental access to the physics of the ultrastrong (USC) and deep strong (DSC) coupling regimes of light-matter interaction through the quantum simulation of their dynamics in standard circuit QED. The method makes use of a two-tone driving scheme, using state-of-the-art circuit-QED technology, and can be easily extended to general cavity-QED setups. We provide examples of USC/DSC quantum effects that would be otherwise inaccessible.

Path entanglement constitutes an essential resource in quantum information and communication protocols. Here, we demonstrate frequency-degenerate entanglement between continuous-variable quantum microwaves propagating along two spatially separated paths. We combine a squeezed and a vacuum state using a microwave beam splitter. Via correlation measurements, we detect and quantify the path entanglement contained in the beam splitter output state. Our experiments open the avenue to quantum teleportation, quantum communication, or quantum radar with continuous variables at microwave frequencies.

We provide the quantum-mechanical description of the excitation of surface plasmon polaritons on metal surfaces by single photons. An attenuated-reflection setup is described for the quantum excitation process in which we find remarkably efficient photon-to-surface plasmon wave-packet transfer. Using a fully quantized treatment of the fields, we introduce the Hamiltonian for their interaction and study the quantum statistics during transfer with and without losses in the metal.