Abstract
Several classes of quantum circuits have been shown to provide a quantum computational advantage under certain assumptions. The study of ever more restricted classes of quantum circuits capable of quantum advantage is motivated by possible simplifications in experimental demonstrations. In this paper we study the efficiency of measurement-based quantum computation with a completely flat temporal ordering of measurements. We propose new constructions for the deterministic computation of arbitrary Boolean functions, drawing on correlations present in multi-qubit Greenberger, Horne, and Zeilinger (GHZ) states. We characterize the necessary measurement complexity using the Clifford hierarchy, and also generally decrease the number of qubits needed with respect to previous constructions. In particular, we identify a family of Boolean functions for which deterministic evaluation using non-adaptive MBQC is possible, featuring quantum advantage in width and number of gates with respect to classical circuits.

Abstract
Secure multiparty computation (SMC) provides collaboration among multiple parties, ensuring the confidentiality of their private information. However, classical SMC implementations encounter significant security and efficiency challenges. Resorting to the entangled Greenberger-Horne-Zeilinger (GHZ) state, we propose a quantum-based two-party protocol to compute binary Boolean functions, with the help of a third party. We exploit a technique in which a random Z-phase rotation on the GHZ state is performed to achieve higher security. The security and complexity analyses demonstrate the feasibility and improved security of our scheme compared to other SMC Boolean function computation methods. Additionally, we implemented the proposed protocol on the IBM QisKit and found consistent outcomes that validate the protocol's correctness.

Abstract
This research explores the trainability of Parameterized Quantum Circuit-based policies in Reinforcement Learning, an area that has recently seen a surge in empirical exploration. While some studies suggest improved sample complexity using quantum gradient estimation, the efficient trainability of these policies remains an open question. Our findings reveal significant challenges, including standard Barren Plateaus with exponentially small gradients and gradient explosion. These phenomena depend on the type of basis-state partitioning and the mapping of these partitions onto actions. For a polynomial number of actions, a trainable window can be ensured with a polynomial number of measurements if a contiguous-like partitioning of basis-states is employed. These results are empirically validated in a multi-armed bandit environment.

Abstract
This research addresses the trainability of Parameterized Quantum Circuit-based Softmax policies in Reinforcement Learning. We assess the trainability of these policies by examining the scaling of the expected value of the partial derivative of the log policy objective function. Here, we assume the hardware-efficient ansatz with blocks forming local 2-designs. In this setting, we show that if each expectation value representing the action's numerical preference is composed of a global observable, it leads to exponentially vanishing gradients. In contrast, for n-qubit systems, if the observables are log(n)-local, the gradients vanish polynomially with the number of qubits provided O(log n) depth. We also show that the expectation of the gradient of the log policy objective depend on the entire action space. Thus, even though global observables lead to concentration, the gradient signal can still be propagated in the presence of at least a single local observable. We validate the theoretical predictions in a series of ansatze and evaluate the performance of local and global observables in a multi-armed bandit setting.

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