Quantum Optimization Driven Solution



Packages travel across locations through interconnected stations, hubs, gateways, ramps etc. Last mile logistics is the final step of the delivery process from a depot to the end customer (Residential or Commercial) and stations assign packages and design routes for its last mile delivery fleet daily. The fleet size, capacity utilization and route length are major cost drivers to manage operational costs. The challenge is to reduce the cost involved for every trip through optimized delivery planning. There are various stages in the logistics process of delivering goods from the time a parcel leaves the Sender up to the moment it arrives at its destination. The last mile delivery stage is where the goods from a transportation hub move to their final delivery destination. The goal of last-mile delivery is to transport an item to its recipient in the quickest and cost-effective way possible. It is important to remove inefficiencies in this process and needs optimisation across a fleet of vehicles, delivery personnel, input costs such as fuel, end customer delivery preferences, missed deliveries, route changes due to emergencies etc. Vehicle route optimization is important for effective route planning, on-time deliveries, increased customer frustration, and lower costs.




The Mphasis Capacitated Vehicle Route Optimizer helps assign packages and design delivery routes for last mile delivery. The solution focuses on finding an optimized route with minimal fleet size and maximum capacity utilization. The objective function is to minimize the cost of running the trucks while satisfying customer preferred time windows and vehicle capacities constraints. This helps reduce the operational costs along with % of failed deliveries and increases customer satisfaction. The solution makes use of Quantum Optimization techniques which finds more accurate solutions in a shorter time in comparison to classical optimization techniques. Quantum Optimization techniques fare well in comparison to classical techniques as problem size grows.


  • 68.74 % Reduced Time taken in optimization
  • 2-5% improvement in accuracy
  • Reduced cost of operations and improved productivity, improved Customer experience



Mphasis EON is a patent pending, classical-quantum hybrid network, consisting of energy optimization, quantum circuit and deep neural network layers. A quantum-assisted, deep learning architecture is the recommended approach. The deep learning part handles the data preprocessing step, while the quantum hardware performs the task of parameter search. The efficiency of quantum assisted, deep learning system is much higher than the efficiency of two systems, when used separately.

Mphasis EON standardizes the classical data to bring all the values in a range of [0,1], to reduce the big number effect on machine learning. After standardization, input data is manipulated to prepare enhanced feature space that can better represent classical data on quantum systems for predictive tasks. The transformed feature space is mapped onto quantum systems using quantum state preparation such as angle embedding, amplitude embedding etc. Quantum circuits perform a defined series of operations on quantum data and measure the system information using the measurement function. The output from measurement functions becomes the input to deep neural network layers. The resultant cost function resides on the classical machine. The measured error is reduced by back propagation and different gradient descent methods.

Mphasis EON follows an iterative process to select the best suited feature space transformation, by reducing the overall energy of the network and capturing as much information spread as possible. For classical data to input on quantum computational systems, data encoding is a necessary step, and the strategy of how to represent classical data on quantum systems influence the quantum circuit design and its efficiency. A better expression of data on quantum systems, for a given machine learning task, leads to low information loss, faster convergence and better solution, due to quantum efficient optimization as compared to their classical counter parts. Mphasis EON achieves the optimal information representation for quantum using feature space transformation and batch sampling.


Significantly reduces the need for higher configuration quantum systems with increased data encoding efficiencies

Prepares the feature space specifically and adaptively for the quantum prediction, making the process more outcome-oriented and suitable for quantum prediction tasks

Learns data patterns and performs quantum predictive tasks in an iterative mode, enabling quantum to manage the challenging task of handling the big data effectively.

Better learning of complex data patterns

Generates more orthogonal features with reduced intra-feature correlation

Reduces non-linear dimensionality of the data, making quantum circuit training feasible in less available qubits

Generates batches that guides the quantum circuit to strategically converge to optimal weights, making training faster with better accuracy