Training Gaussian Boson Sampling Distributions

Gaussian Boson Sampling (GBS) is a near-term platform for photonic quantum computing. Applications have been developed which rely on directly programming GBS devices, but the ability to train and optimize circuits has been a key missing ingredient for developing new algorithms. In this work, we derive analytical gradient formulas for the GBS distribution, which can be used to train devices using standard methods based on gradient descent. We introduce a parametrization of the distribution that allows the gradient to be estimated by sampling from the same device that is being optimized. In the case of training using a Kullback-Leibler divergence or log-likelihood cost function, we show that gradients can be computed classically, leading to fast training. We illustrate these results with numerical experiments in stochastic optimization and unsupervised learning. As a particular example, we introduce the variational Ising solver, a hybrid algorithm for training GBS devices to sample ground states of a classical Ising model with high probability.Comment: 15 pages, 3 figure

Matrix permanent and quantum entanglement of permutation invariant states

We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing a recently introduced permanent inequality by Carlen, Loss and Lieb, we can prove explicit formulas of the geometric measure for permutation invariant basis states in a simple way.Comment: 10 page

Engineering of reconfigurable integrated photonics for quantum computation protocols

Over the last decade, integrated optics has emerged as one of the main technologies for quantum optics and more generally quantum computation, quantum cryptography and communication. In particular, it is fundamental for the construction of reconfigurable interferometers with a high number of optical modes. In this thesis we present, on the one hand, the development of a new geometry for the creation of integrated reconfigurable devices with a high number of modes and, on the other hand, the development of quantum computation protocols to be realized in integrated photonic chips. In the first part, two algorithms are proposed for the characterization of integrated circuits in terms of implemented unitary matrix. The first uses a so-called Black Box approach, i.e. one that makes no assumptions about the internal structure of the device under consideration, and it is based on second-order correlation measurements with coherent light. The second is specific to a planar rectangular geometry, first proposed by Clements et al., which has a variety of applications in the literature and is also employed in this thesis. Subsequently, we present the realization of a new 32-mode reconfigurable integrated photonic device with a continuously coupled three-dimensional geometry. Its potential in terms of reconfigurability is tested and a Boson sampling experiment with three and four photons is carried out to show its potential in the field of quantum computation. In the second part, we propose the application of integrated photonic devices to two quantum computation protocols. The first was recently proposed and is the quantum extension of a problem called Bernoulli factory. It consists in the construction of a qubit from $n$ qubits in the same unknown state so that there is a predetermined exact relation between the output and input states. In the thesis, we theoretically analyze the computational complexity of the problem in terms of the qubits used and the success probability of the problem. Furthermore, a photonic implementation is proposed and experimentally tested for correctness and resilience to experimental noise. The second application consists of the experimental implementation of a quantum metrology protocol in which three distinct phases are estimated simultaneously, showing that the use of indistinguishable photons leads to an advantage in terms of the variance of the estimates