We present a simple device based on the controlled-SWAP gate that performs quantum state tomography. It can also be used to determine maximum and minimum eigenvalues, expectation values of arbitrary observables, purity estimation as well as characterizing quantum channels. The advantage of this scheme is that the architecture is fixed and the task performed is determined by the input data.PACS numbers: 03.67. Hk, 03.67.Lx One of the the key issues in quantum information is, given an unknown quantum system, what can we learn about it. In particular, we are concerned not only with the resources needed (number of identical unknown physical systems), but also with the complexity of quantum operations required (number of different devices, networks, etc.), in order to obtain certain information about a quantum state, characterized by its density matrix ̺. There are many interesting parameters of ̺ we can determine, such as its maximum and minimum eigenvalues, its purity or even ̺ itself (state tomography [1]), but we also can use ̺ to determine expectation values of arbitrary observables or to characterize unknown quantum channels. However, this usually involves building separate devices for each task, or even building different devices for different measurements within the same task.In this paper we present a simple, universal device, whose architecture is fixed but whose behaviour is determined by the choice of input data [2] (see also [3] for a quantum optical realization of a similar idea). In fact, with suitable input, we can directly measure all the properties mentioned before.Consider a typical interferometric set-up for a single qubit: Hadamard gate, phase shift ϕ, Hadamard gate, followed by a measurement in the computational basis. Here and in the following, we borrow terminology from quantum information science and describe quantum interferometry in terms of quantum logic gates [4]. We modify the interferometer by inserting a controlled-U operation between the Hadamard gates, with its control on the qubit and with U acting on a quantum system described by some unknown density operator ρ. We do not assume anything about the form of ρ, it can, for example, describe several entangled or separable subsystems. This set-up is shown in Fig. 1. The action of the controlled-U on ρ modifies the interference pattern by the factor,where v is the new visibility and α is the shift of the interference fringes, also known as the Pancharatnam phase [5]. Thus, the observed visibility gives a straightforward way of estimating the average value of unitary operators U in state ρ and has a variety of interesting applications. For example, it can be used to measure some entanglement witnesses W , as long as they are unitary operators and the corresponding controlled-W operations are easy to implement [6]. Here, we focus on the applications related to quantum state state tomography. Clearly the interferometer in Fig. 1 can be used to estimate any d × d

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Complex-valued neural networks have many advantages over their real-valued counterparts. Conventional digital electronic computing platforms are incapable of executing truly complex-valued representations and operations. In contrast, optical computing platforms that encode information in both phase and magnitude can execute complex arithmetic by optical interference, offering significantly enhanced computational speed and energy efficiency. However, to date, most demonstrations of optical neural networks still only utilize conventional real-valued frameworks that are designed for digital computers, forfeiting many of the advantages of optical computing such as efficient complex-valued operations. In this article, we highlight an optical neural chip (ONC) that implements truly complex-valued neural networks. We benchmark the performance of our complex-valued ONC in four settings: simple Boolean tasks, species classification of an Iris dataset, classifying nonlinear datasets (Circle and Spiral), and handwriting recognition. Strong learning capabilities (i.e., high accuracy, fast convergence and the capability to construct nonlinear decision boundaries) are achieved by our complex-valued ONC compared to its real-valued counterpart.