Approximate Solutions of Combinatorial Problems via Quantum Relaxations

Combinatorial problems are formulated to find optimal designs within a fixed set of constraints and are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial optimization remains an ongoing area of study. Here, we propose new methods for producing approximate solutions to quadratic unconstrained binary optimization problems, […]

Analysis of the Vehicle Routing Problem Solved via Hybrid Quantum Algorithms in the Presence of Noisy Channels

The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with optimal efficiency. Classical tools and methods provide good approximations to reach the optimal global […]

Benchmarking Hamiltonian Noise in the D-Wave Quantum Annealer

Various sources of noise limit the performance of quantum computers by altering qubit states in an uncontrolled manner throughout computations and reducing their coherence time. In quantum annealers, this noise introduces additional fluctuations to the parameters defining the original problem Hamiltonian, such that they find the ground states of problems perturbed from those originally programmed. […]

O(N^3) Measurement Cost for Variational Quantum Eigensolver on Molecular Hamiltonians

Variational quantum eigensolver (VQE) is a promising algorithm for near-term quantum machines. It can be used to estimate the ground state energy of a molecule by performing separate measurements of O(N 4 ) terms. This quartic scaling appears to be a significant obstacle to practical applications. However, we note that it empirically reduces to O(N 3 ) when we […]

Quantum Approximate Optimization With Parallelizable Gates

The quantum approximate optimization algorithm (QAOA) has been introduced as a heuristic digital quantum computing scheme to find approximate solutions of combinatorial optimization problems. We present a scheme to parallelize this approach for arbitrary all-to-all connected problem graphs in a layout of quantum bits (qubits) with nearest-neighbor interactions. The protocol consists of single qubit operations […]