Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

We attempt to estimate the uncertainty in the constraints on the spin independent dark matter-nucleon cross section due to our lack of knowledge of the dark matter phase space in the galaxy. We fit the density of dark matter before investigating the possible solutions of the Jeans equation compatible with those fits in order to understand what velocity dispersions we might expect at the solar radius. We take into account the possibility of non-Maxwellian velocity distributions and the possible presence of a dark disk. Combining all these effects, we still find that the uncertainty in the interpretation of direct detection experiments for high (>100 GeV) mass dark matter candidates is less than an order of magnitude in cross section. *

We introduce a new family of quantum circuits in continuous variables and we show that, relying on the widely accepted conjecture that the polynomial hierarchy of complexity classes does not collapse, their output probability distribution cannot be efficiently simulated by a classical computer. These circuits are composed of input photon-subtracted (or photon-added) squeezed states, passive linear optics evolution, and eight-port homodyne detection. We address the proof of hardness for the exact probability distribution of these quantum circuits by exploiting mappings onto different architectures of sub-universal quantum computers. We obtain both a worst-case and an average-case hardness result. Hardness of Boson Sampling with eight-port homodyne detection is obtained as the zero squeezing limit of our model. We conclude with a discussion on the relevance and interest of the present model in connection to experimental applications and classical simulations.

Reaching the strong coupling regime of light-matter interaction has led to an impressive development in fundamental quantum physics and applications to quantum information processing. Latests advances in different quantum technologies, like superconducting circuits or semiconductor quantum wells, show that the ultrastrong coupling regime (USC) can also be achieved, where novel physical phenomena and potential computational benefits have been predicted. Nevertheless, the lack of effective decoupling mechanism in this regime has so far hindered control and measurement processes. Here, we propose a method based on parity symmetry conservation that allows for the generation and reconstruction of arbitrary states in the ultrastrong coupling regime of light-matter interactions. Our protocol requires minimal external resources by making use of the coupling between the USC system and an ancillary two-level quantum system.

The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the non–classical nature of photon pairs, later generalized to quantum systems with either bosonic or fermionic statistics. We show that a simple modification in the well-known and widely used HOM experiment provides the direct measurement of the Wigner function. We apply our results to one of the most reliable quantum systems, consisting of biphotons generated by parametric down conversion. A consequence of our results is that a negative value of the Wigner function is a sufficient condition for non-gaussian entanglement between two photons. In the general case, the Wigner function provides all the required information to infer entanglement using well known necessary and sufficient criteria. The present work offers a new vision of the HOM experiment that further develops its possibilities to realize fundamental tests of quantum mechanics using simple optical set-ups.

We provide a toolbox for continuous variables quantum state engineering and characterization of biphoton states produced by spontaneous parametric down conversion in a transverse pump configuration. We show that the control of the pump beam's incidence spot and angle corresponds to phase space displacements of conjugate collective continuous variables of the biphoton. In particular, we illustrate with numerical simulations on a semiconductor device how this technique can be used to engineer and characterize arbitrary states of the frequency and time degrees of freedom.PACS numbers: 03.67. Bg, 42.50.Dv, 42.65.Lm, 42.65.Wi Spontaneous parametric down conversion (SPDC) experiments play a prominent role in the field of quantum information and communications. Single and multiple photon pairs generated through SPDC display entanglement in multiple degrees of freedom (DOF) which are fundamentally different from each other. When combined or independently accessed, they constitute a powerful platform for experimental demonstrations of quantum protocols. Discrete DOF, such as polarization and orbital angular momentum, are currently used to implement quantum logic gates and protocols [1], test the non-local properties of quantum mechanics [2][3][4][5], and realize quantum cryptography [6-8] and teleportation [9,10]. DOF associated to observables with a continuous spectrum, like the quadratures of the electromagnetic field, potentially offer the same versatility as discrete ones in the field of quantum information. Continuous DOF in the single photon regime, such as frequency, transverse momentum or position display a perfect analogy with a multi-photon single mode continuous variables (CV) [11,12]. Consequently, they constitute an attractive platform to realize CV quantum information protocols [13] that are usually associated to the single mode multi-photon configuration. For example, an appealing aspect of using single photon's transverse coordinates in this field is their relatively easy manipulation with readily available optical devices, such as spatial light modulators (SLMs) and lenses [12], circumventing the difficulties encountered in multi-photon CV strategies to implement non-gaussian operations, which are essential ingredients of universal quantum computation [13]. For these reasons, the study of entanglement in CV in the single photon regime is a valuable strategy to demonstrate CV-based quantum * These authors have equally contributed to this work. † Current adress: Laboratoire Aimé Cotton, Bâtiment 505-Campus d'Orsay, Univ. Paris-Sud 11, 91405 Orsay Cedex, France gates [14], quantum key distribution [15, 16], error correcting codes [17, 18], quantum metrology protocols [19]and to study quantum to classical transitions [20,21]. Finally, we can mention that continuous DOF can be combined to discrete ones to implement conditional operations [22][23][24].CV entanglement in photon pairs can be generated in different DOF via SPDC; one example are the spatial transverse DOF of photon pairs produced in nonlinear bu...

Continuous-variable (CV) devices are a promising platform for demonstrating large-scale quantum information protocols. In this framework we define a general quantum computational model based on a CV hardware. It consists of vacuum input states, a finite set of gates-including non-Gaussian elements-and homodyne detection. We show that this model incorporates encodings sufficient for probabilistic fault-tolerant universal quantum computing. Furthermore, we show that this model can be adapted to yield sampling problems that cannot be simulated efficiently with a classical computer, unless the polynomial hierarchy collapses. This allows us to provide a simple paradigm for experiments to probe quantum advantage relying on Gaussian states, homodyne detection, and some form of non-Gaussian evolution. We finally address the recently introduced model of instantaneous quantum computing in CV, and prove that the hardness statement is robust with respect to some experimentally relevant simplifications in the definition of that model.

International audienceWe present a theoretical proposal to couple a single nitrogen-vacancy (NV) center to a superconducting flux qubit in the regime where both systems are off resonance. The coupling between both quantum devices is achieved through the strong driving of the flux qubit by a classical microwave field that creates dressed states with an experimentally controlled characteristic frequency. We discuss several applications such as controlling the NV center's state by manipulation of the flux qubit, performing the NV center full tomography and using the NV center as a quantum memory. The effect of decoherence and its consequences to the proposed applications are also analyzed. Our results provide a theoretical framework describing a promising hybrid system for quantum information processing, which combines the advantages of fast manipulation and long coherence times