Quantum Hoare Logic with Classical Variables

Hoare logic provides a syntax-oriented method to reason about program correctness and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness or support only quantum variables, thus limiting their capability in practical use. In this article, we propose a quantum Hoare logic for a simple while language that involves both classical and quantum variables. Its soundness and relative completeness are proven for both partial and total correctness of quantum programs written in the language. Remarkably, with novel definitions of classical-quantum states and corresponding assertions, the logic system is quite simple and similar to the traditional Hoare logic for classical programs. Furthermore, to simplify reasoning in real applications, auxiliary proof rules are provided that support standard logical operation in the classical part of assertions and super-operator application in the quantum part. Finally, a series of practical quantum algorithms, in particular the whole algorithm of Shor’s factorisation, are formally verified to show the effectiveness of the logic.

LogicSNN: A Unified Spiking Neural Networks Logical Operation Paradigm

LogicSNN, a unified spiking neural networks (SNN) logical operation paradigm is proposed in this paper. First, we define the logical variables under the semantics of SNN. Then, we design the network structure of this paradigm and use spike-timing-dependent plasticity for training. According to this paradigm, six kinds of basic SNN binary logical operation modules and three kinds of combined logical networks based on these basic modules are implemented. Through these experiments, the rationality, cascading characteristics and the potential of building large-scale network of this paradigm are verified. This study fills in the blanks of the logical operation of SNN and provides a possible way to realize more complex machine learning capabilities.

Band-Gap Solitons in Nonlinear Photonic Crystal Waveguides and Their Application for Functional All-Optical Logic Gating

This review paper summarizes our previous findings regarding propagation characteristics of band-gap temporal solitons in photonic crystal waveguides with Kerr-type nonlinearity and a realization of functional and easily scalable all-optical NOT, AND and NAND logic gates. The proposed structure consists of a planar air-hole type photonic crystal in crystalline silicon as the nonlinear background material. A main advantage of proposing the gap-soliton as a signal carrier is that, by operating in the true time-domain, the temporal soliton maintains a stable pulse envelope during each logical operation. Hence, multiple concatenated all-optical logic gates can be easily realized paving the way to multiple-input ultrafast full-optical digital signal processing. In the suggested setup, due to the gap-soliton features, there is no need to amplify the output signal after each operation which can be directly used as a new input signal for another logical operation. The efficiency of the proposed logic gates as well as their scalability is validated using our original rigorous theoretical formalism confirmed by full-wave computational electromagnetics.

Logical Operator Estimation

This report proposes an estimation method to find the unknown boolean input variable of a logical operation (AND, OR, XOR). The estimators might help to assess if the association between an input and output signal is the result of simple logical operations.