Quantum Machine Learning (QML) is a young but rapidly growing field where quantum information meets machine learning. Here, we will introduce a new QML model generalizing the classical concept of Reinforcement Learning to the quantum domain, i.e. Qua
ntum Reinforcement Learning (QRL). In particular we apply this idea to the maze problem, where an agent has to learn the optimal set of actions in order to escape from a maze with the highest success probability. To perform the strategy optimization, we consider an hybrid protocol where QRL is combined with classical deep neural networks. In particular, we find that the agent learns the optimal strategy in both the classical and quantum regimes, and we also investigate its behaviour in a noisy environment. It turns out that the quantum speedup does robustly allow the agent to exploit useful actions also at very short time scales, with key roles played by the quantum coherence and the external noise. This new framework has the high potential to be applied to perform different tasks (e.g. high transmission/processing rates and quantum error correction) in the new-generation Noisy Intermediate-Scale Quantum (NISQ) devices whose topology engineering is starting to become a new and crucial control knob for practical applications in real-world problems. This work is dedicated to the memory of Peter Wittek.
We consider the problem of discriminating quantum states, where the task is to distinguish two different quantum states with a complete classical knowledge about them, and the problem of classifying quantum states, where the task is to distinguish tw
o classes of quantum states where no prior classical information is available but a finite number of physical copies of each classes are given. In the case the quantum states are represented by coherent states of light, we identify intermediate scenarios where partial prior information is available. We evaluate an analytical expression for the minimum error when the quantum states are opposite and a prior on the amplitudes is known. Such a threshold is attained by complex POVM that involve highly non-linear optical procedure. A suboptimal procedure that can be implemented with current technology is presented that is based on a modification of the conventional Dolinar receiver. We study and compare the performance of the scheme under different assumptions on the prior information available.
Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We consider
the problem of quantum state discrimination on such a system, and we solve it by optimizing the network topology weights. Finally, we test it on different quantum network topologies and compare it with optimal theoretical bounds.
A fundamental problem in Quantum Information Processing is the discrimination amongst a set of quantum states of a system. In this paper, we address this problem on an open quantum system described by a graph, whose evolution is defined by a Quantum
Stochastic Walk. In particular, the structure of the graph mimics those of neural networks, with the quantum states to discriminate encoded on input nodes and with the discrimination obtained on the output nodes. We optimize the parameters of the network to obtain the highest probability of correct discrimination. Numerical simulations show that after a transient time the probability of correct decision approaches the theoretical optimal quantum limit. These results are confirmed analytically for small graphs. Finally, we analyze the robustness and reconfigurability of the network for different set of quantum states, and show that this architecture can pave the way to experimental realizations of our protocol as well as novel quantum generalizations of deep learning.
The success of quantum noise sensing methods depends on the optimal interplay between properly designed control pulses and statistically informative measurement data on a specific quantum-probe observable. To enhance the information content of the da
ta and reduce as much as possible the number of measurements on the probe, the filter orthogonalization method has been recently introduced. The latter is able to transform the control filter functions on an orthogonal basis allowing for the optimal reconstruction of the noise power spectral density. In this paper, we formalize this method within the standard formalism of minimum mean squared error estimation and we show the equivalence between the solutions of the two approaches. Then, we introduce a non-negative least squares formulation that ensures the non-negativeness of the estimated noise spectral density. Moreover, we also propose a novel protocol for the design in the frequency domain of the set of filter functions. The frequency-designed filter functions and the non-negative least squares reconstruction are numerically tested on noise spectra with multiple components and as a function of the estimation parameters.
The dynamics of any quantum system is unavoidably influenced by the external environment. Thus, the observation of a quantum system (probe) can allow the measure of the environmental features. Here, to spectrally resolve a noise field coupled to the
quantum probe, we employ dissipative manipulations of the probe, leading to so-called Stochastic Quantum Zeno (SQZ) phenomena. A quantum system coupled to a stochastic noise field and subject to a sequence of protective Zeno measurements slowly decays from its initial state with a survival probability that depends both on the measurement frequency and the noise. We present a robust sensing method to reconstruct the unkonwn noise power spectral density by evaluating the survival probability that we obtain when we additionally apply a set of coherent control pulses to the probe. The joint effect of coherent control, protective measurements and noise field on the decay provides us the desired information on the noise field.
We address the implementation of the positive operator-valued measure (POVM) describing the optimal M-outcomes discrimination of the polarization state of a single photon. Initially, the POVM elements are extended to projective operators by Naimark t
heorem, then the resulting projective measure is implemented by a Knill-Laflamme-Milburn scheme involving an optical network and photon counters. We find the analytical expression of the Naimark extension and the detection scheme that realise it for an arbitrary number of outcomes M = 2^N.
Entangled measurement is a crucial tool in quantum technology. We propose a new entanglement measure of multi-mode detection, which estimates the amount of entanglement that can be created in a measurement. To illustrate the proposed measure, we perf
orm quantum tomography of a two-mode detector that is comprised of two superconducting nanowire single photon detectors. Our method utilizes coherent states as probe states, which can be easily prepared with accuracy. Our work shows that a separable state such as a coherent state is enough to characterize a potentially entangled detector. We investigate the entangling capability of the detector in various settings. Our proposed measure verifies that the detector makes an entangled measurement under certain conditions, and reveals the nature of the entangling properties of the detector. Since the precise characterization of a detector is essential for applications in quantum information technology, the experimental reconstruction of detector properties along with the proposed measure will be key features in future quantum information processing.
We revisit the problem of finding the Naimark extension of a probability operator-valued measure (POVM), i.e. its implementation as a projective measurement in a larger Hilbert space. In particular, we suggest an iterative method to build the project
ive measurement from the sole requirements of orthogonality and positivity. Our method improves existing ones, as it may be employed also to extend POVMs containing elements with rank larger than one. It is also more effective in terms of computational steps.
