The Leveraging Optimization via Quantum-devices for Internet-security (LOQI) proposal aims to demonstrate the power of hybrid (quantum/classical) optimization approaches for classes of combinatorial optimization problems that are relevant to several cyber-security settings. In Phase 1 (this proposal) we will conduct a feasibility study to develop an analytical framework and algorithms, and prototype them in simulation and software, to explore the power of such hybrid algorithms in solving combinatorial optimization problems can be represented as variations of the Multi-dimensional Knapsack Problem (MKP). One of the main objectives of LOQI is to develop variations of hybrid algorithms that can be executed in the near future on Noisy Intermediate-Scale Quantum (NISQ) devices. MKP based optimization problems have several applications in networking-security and cyber-security. Most of the applications we envision can be ed as variations of a constrained resource allocation problem that can be cast as an MKP instance. The three applications that we will focus on in this proposal are: (i) allocating micro-services in a cloud environment to maintain a certain level of quality-of-service to different jobs, especially if under a heavy load, and in the existence of potentially malicious resource-draining processes, (ii) allocating filtering and rate limiting resources locally or upstream in a network to defend distributed against denial-of-service (DDoS) attacks, and (iii) allocating network routes and forwarding rules in the routing infrastructure, e.g., in Software Defined Networking (SDN) controllers, to ensure resilience and operations in a network under attack.