Multi-sequence alignment using the Quantum Approximate Optimization Algorithm

• URL: http://arxiv.org/abs/2308.12103v1
• Date: Wed, 23 Aug 2023 12:46:24 GMT
• Title: Multi-sequence alignment using the Quantum Approximate Optimization Algorithm
• Authors: Sebastian Yde Madsen, Frederik Kofoed Marqversen, Stig Elkj{\ae}r Rasmussen and Nikolaj Thomas Zinner
• Abstract summary: We present a Hamiltonian formulation and implementation of the Multiple Sequence Alignment problem with the variational Quantum Approximate Optimization Algorithm (QAOA) We consider a small instance of our QAOA-MSA algorithm in both a quantum simulator and its performance on an actual quantum computer. While the ideal solution to the instance of MSA investigated is shown to be the most probable state sampled for a shallow p5 quantum circuit, the level of noise in current devices is still a formidable challenge.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The task of Multiple Sequence Alignment (MSA) is a constrained combinatorial optimization problem that is generally considered a complex computational problem. In this paper, we first present a binary encoding of MSA and devise a corresponding soft-constrained cost-function that enables a Hamiltonian formulation and implementation of the MSA problem with the variational Quantum Approximate Optimization Algorithm (QAOA). Through theoretical analysis, a bound on the ratio of the number of feasible states to the size of the Hilbert space is determined. Furthermore, we consider a small instance of our QAOA-MSA algorithm in both a quantum simulator and its performance on an actual quantum computer. While the ideal solution to the instance of MSA investigated is shown to be the most probable state sampled for a shallow p<5 quantum circuit in the simulation, the level of noise in current devices is still a formidable challenge for the kind of MSA-QAOA algorithm developed here. In turn, we are not able to distinguish the feasible solutions from other states in the quantum hardware output data at this point. This indicates a need for further investigation into both the strategy utilized for compiling the quantum circuit, but also the possibility of devising a more compact ansatz, as one might achieve through constraint-preserving mixers for QAOA.

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