Abstract

Abstract
Kleene algebras (KA) and Kleene algebras with tests (KAT) provide an algebraic framework to capture the behavior of conventional programming constructs. This paper explores a broader understanding of these structures, in order to enable the expression of programs and tests yielding vague or inconsistent outcomes. Within this context, we introduce the concept of a paraconsistent Kleene Algebra with tests (PKAT), capable of capturing vague and contradictory computations. Finally, to establish the semantics of such a structure, we introduce two algebras, SetP(T) and RelP(K,T), parametric on a class of twisted structures K and T. We believe this sort of structures, for their huge flexibility, have an interesting application potential.

Abstract
Secure Multiparty Computation (SMC) facilitates secure collaboration among multiple parties while safeguarding the privacy of their confidential data. This paper introduces a two-party quantum SMC protocol designed for evaluating binary Boolean functions using single qubits. Complexity analyses demonstrate a reduction of 66.7% in required quantum resources, achieved by utilizing single qubits instead of multi-particle entangled states. However, the quantum communication cost has increased by 40% due to the amplified exchange of qubits among participants. Furthermore, we bolster security by performing additional quantum operations along the y-axis of the Bloch sphere, effectively hiding the output from potential adversaries. We design the corresponding quantum circuit and implement the proposed protocol on the IBM Qiskit platform, yielding reliable outcomes.

Abstract

Abstract

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.