First Steps towards Hybrid Quantum-Classical Optimization

András Czégel

Samuel Fernández-Lorenzo, Diego Porras, Juan José García‐Ripoll

Abstract In this work we develop tools to address combinatorial optimization problems with a cardinality constraint, in which only a subset of variables end up having nonzero values. Firstly, we introduce a new heuristic pruning method that iteratively discards variables through a hybrid quantum–classical optimization step. Secondly, we analyse the use of soft constraints in the form of ‘chemical potentials’ to control the number of non-zero variables. We illustrate the power of both techniques using the problem of index tracking, which aims to mimicking the performance of a financial index with a balanced subset of assets. We also compare the performance of different state-of-the-art quantum variational optimization algorithms in our pruning method.

Lian Remme, Alexander Weinert, Andre Waschk

Quantum computers do not run in isolation; rather, they are embedded in quantum-classical hybrid architectures. In these setups, a quantum processing unit communicates with a classical device in near-real time. To enable efficient hybrid computations, it is mandatory to optimize quantum-classical hybrid code. To the best of our knowledge, no previous work on the optimization of hybrid code nor on metrics for which to optimize such code exists. In this work, we take a step towards optimization of hybrid programs by introducing seven optimization routines and three metrics to evaluate the effectiveness of the optimization. We implement these routines for the hybrid quantum language Quil and show that our optimizations improve programs according to our metrics. This lays the foundation for new kinds of hybrid optimizers that enable real-time collaboration between quantum and classical devices.

Yipeng Liu, Gary J. Kœhler

Colton Mikes, Ismael R. de Farias, David H. Gutman +1 more

This paper introduces a quantum-classical hybrid algorithm for generalized pattern search (GPS) algorithms. We introduce a quantum search step algorithm using amplitude amplification, which reduces the number of oracle calls needed during the search step from O(N) classical calls to O(N^(1/2)) quantum calls. This work addresses three fundamental issues with using a quantum search step with GPS. First we address the need to mark an improved mesh point, a requirement of the amplitude amplification algorithm. Second, we introduce a modified version of the amplitude amplification algorithm QSearch, which is guaranteed to terminate using a finite number of iterations. Third, we avoid disrupting the GPS algorithm's convergence by limiting the quantum algorithm to the search step.

Tomoyuki Yamakami