Boson Sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require a universal control over the quantum system, which favours current photonic experimental platforms. Here, we introduce Gaussian Boson Sampling, a classically hardto-solve problem that uses squeezed states as a non-classical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson Sampling, a #P hard problem, using squeezed states. This approach leads to a more efficient photonic boson sampler with significant advantages in generation probability and measurement time over currently existing protocols.

Since the development of Boson sampling, there has been a quest to construct more efficient and experimentally feasible protocols to test the computational complexity of sampling from photonic states. In this paper we interpret and extend the results presented in [Phys. Rev. Lett. 119, 170501 (2017)]. We derive an expression that relates the probability to measure a specific photon output pattern from a Gaussian state to the hafnian matrix function and us it to design a Gaussian Boson sampling protocol. Then, we discuss the advantages that this protocol has relative to other photonic protocols and the experimental requirements for Gaussian Boson Sampling. Finally, we relate it to the previously most general protocol, Scattershot Boson Sampling [Phys. Rev. Lett. 113, 100502 (2014)].

Boson Sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require a universal control over the quantum system, which favours current photonic experimental platforms. Here, we introduce Gaussian Boson Sampling, a classically hardto-solve problem that uses squeezed states as a non-classical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson Sampling, a #P hard problem, using squeezed states. This approach leads to a more efficient photonic boson sampler with significant advantages in generation probability and measurement time over currently existing protocols.

The effects of projective measurements on the quantum mechanical evolution of a particle can be simulated with coherent light.

Quantum optics in combination with integrated optical devices shows great promise for efficient manipulation of single photons. New physical concepts, however, can only be found when these fields truly merge and reciprocally enhance each other. Here we work at the merging point and investigate the physical concept behind a two-coupled-waveguide system with an integrated parametric down-conversion process. We use the eigenmode description of the linear system and the resulting modification in momentum conservation to derive the state generation protocol for this type of device. With this new concept of state engineering, we are able to effectively implement a two-in-one waveguide source that produces the useful two-photon NOON state without extra overhead such as phase stabilization or narrow-band filtering. Experimentally, we benchmark our device by measuring a two-photon NOON state fidelity of $\mathcal{F} = (84.2 \pm 2.6) \%$ and observe the characteristic interferometric pattern directly given by the doubled phase dependence with a visibility of $V_{\mathrm{NOON}} = (93.3 \pm 3.7) \%$.Comment: 6 pages, 3 figure

High dimensional quantum states are of fundamental interest for quantum information processing. They give access to large Hilbert spaces and, in turn, enable the encoding of quantum information on multiple modes. One method to create such quantum states is parametric down-conversion (PDC) in waveguide arrays (WGAs) which allows for the creation of highly entangled photon pairs in controlled, easily accessible spatial modes, with unique spectral properties.In this paper we examine both theoretically and experimentally the PDC process in a lithium niobate WGA. We measure the spatial and spectral properties of the emitted photon pairs, revealing correlations between spectral and spatial 6

Sampling the distribution of bosons that have undergone a random unitary evolution is strongly believed to be a computationally hard problem. Key to outperforming classical simulations of this task is to increase both the number of input photons and the size of the network. We propose driven boson sampling, in which photons are input within the network itself, as a means to approach this goal. We show that the mean number of photons entering a boson sampling experiment can exceed one photon per input mode, while maintaining the required complexity, potentially leading to less stringent requirements on the input states for such experiments. When using heralded single-photon sources based on parametric down-conversion, this approach offers an ∼e-fold enhancement in the input state generation rate over scattershot boson sampling, reaching the scaling limit for such sources. This approach also offers a dramatic increase in the signal-to-noise ratio with respect to higher-order photon generation from such probabilistic sources, which removes the need for photon number resolution during the heralding process as the size of the system increases.

We introduce and experimentally implement a method for the absolute detector calibration of photon-number-resolving time-bin multiplexing layouts based on the measured click statistics of superconduncting nanowire detectors. In particular, the quantum efficiencies, the dark count rates, and the positive operator-valued measures of these measurement schemes are directly obtained with high accuracy. The method is based on the moments of the click-counting statistics for coherent states with different coherent amplitudes. The strength of our analysis is that we can directly conclude -- on a quantitative basis -- that the detection strategy under study is well described by a linear response function for the light-matter interaction and that it is sensitive to the polarization of the incident light field. Moreover, our method is further extended to a two-mode detection scenario. Finally, we present possible applications for such well characterized detectors, such as sensing of atmospheric loss channels and phase sensitive measurements