Multi-sequence alignment using the Quantum Approximate Optimization Algorithm

TL;DR

This paper explores using the Quantum Approximate Optimization Algorithm (QAOA) for solving the complex problem of Multiple Sequence Alignment (MSA), including theoretical analysis and initial quantum hardware testing.

Contribution

It introduces a binary encoding and Hamiltonian formulation for MSA tailored for QAOA, and evaluates its performance on quantum simulators and hardware.

Findings

Ideal solutions are most probable in simulations with shallow circuits

Current quantum hardware noise hampers distinguishing feasible solutions

Further research needed on circuit compilation and constraint-preserving strategies

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.