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Register a new userCoherent states in Quantum Optics: An oriented overview
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Authors
Jean Pierre Gazeau
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In this survey, various generalisations of Glauber-Sudarshan coherent states are described in a unified way, with their statistical properties and their possible role in non-standard quantisations of the classical electromagnetic field. Some statistical photon-counting aspects of Perelomov SU(2) and SU(1,1) coherent states are emphasized.
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The general transformation of the product of coherent states $prod_{i=1}^N|alpha_i>$ to the output state $prod_{i=1}^M|beta_i>$ ($N=M$ or $N eq M$), which is realizable with linear optical circuit, is characterized with a linear map from the vector $(alpha^{ast}_1,...,alpha^{ast}_N)$ to $(beta^{ast}_1,...,beta^{ast}_M)$. A correspondence between the transformations of a product of coherent states and those of a single photon state is established with such linear maps. It is convenient to apply this linear transformation method to design any linear optical scheme working with coherent states. The examples include message encoding and quantum database searching. The limitation of manipulating entangled coherent states with linear optics is also discussed.
The last few decades have seen significant breakthroughs in the fields of deep learning and quantum computing. Research at the junction of the two fields has garnered an increasing amount of interest, which has led to the development of quantum deep learning and quantum-inspired deep learning techniques in recent times. In this work, we present an overview of advances in the intersection of quantum computing and deep learning by discussing the technical contributions, strengths and similarities of various research works in this domain. To this end, we review and summarise the different schemes proposed to model quantum neural networks (QNNs) and other variants like quantum convolutional networks (QCNNs). We also briefly describe the recent progress in quantum inspired classic deep learning algorithms and their applications to natural language processing.
The current shift in the quantum optics community towards large-size experiments -- with many modes and photons -- necessitates new classical simulation techniques that go beyond the usual phase space formulation of quantum mechanics. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. As a toy model, we extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.
A coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs), in which the strongest collective mode of oscillation at well above threshold corresponds to an optimum solution of a given Ising problem. When a pump rate or network coupling rate is increased from below to above threshold, however, the eigenvectors with a smallest eigenvalue of Ising coupling matrix [J_ij] appear near threshold and impede the machine to relax to true ground states. Two complementary approaches to attack this problem are described here. One approach is to utilize squeezed/anti-squeezed vacuum noise of OPOs below threshold to produce coherent spreading over numerous local minima via quantum noise correlation, which could enable the machine to access either true ground states or excited states with eigen-energies close enough to that of ground states above threshold. The other approach is to implement real-time error correction feedback loop so that the machine migrates from one local minimum to another during an explorative search for ground states. Finally, a set of qualitative analogies connecting the CIM and traditional computer science techniques are pointed out. In particular, belief propagation and survey propagation used in combinatorial optimization are touched upon.
We propose and experimentally demonstrate non-destructive and noiseless removal (filtering) of vacuum states from an arbitrary set of coherent states of continuous variable systems. Errors i.e. vacuum states in the quantum information are diagnosed through a weak measurement, and on that basis, probabilistically filtered out. We consider three different filters based on on/off detection phase stabilized and phase randomized homodyne detection. We find that on/off etection, optimal in the ideal theoretical setting, is superior to the homodyne strategy in a practical setting.
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