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Quantum feedback algorithms for DNA assembly using FALQON variants

Pedro M. Prado, Lucas A. M. Rattighieri, Rafael Simões do Carmo, Giovanni S. Franco, Guilherme E. L. Pexe, Alexandre Drinko, Erick G. Dorlass, Tatiana F. de Almeida, Felipe F. Fanchini

TL;DR

This work analyzes three versions of the Feedback-based Algorithm, a protocol that eliminates classical optimization loops via measurement feedback using long-read DNA fragments from SARS-CoV-2 and human mitochondrial DNA using standard FALQON, second-order FALQON (SO-FALQON), and time-rescaled FALQON (TR-FALQON).

Abstract

Reconstructing DNA sequences without a reference, known as de novo assembly, is a complex computational task involving the alignment of overlapping fragments. To address this problem, a usual strategy is to map the assembly to a Quadratic Unconstrained Binary Optimization (QUBO) formulation, which can be solved by different quantum algorithms. In this work, we focus on three versions of the Feedback-based Algorithm, a protocol that eliminates classical optimization loops via measurement feedback. We analyze long-read DNA fragments from SARS-CoV-2 and human mitochondrial DNA using standard FALQON, second-order FALQON (SO-FALQON), and time-rescaled FALQON (TR-FALQON). Numerical results show that both variants improve convergence to the ground state and increase success probabilities at reduced circuit depths. These findings indicate that enhanced feedback-driven dynamics are effective for solving combinatorial problems on near-term quantum hardware.

Quantum feedback algorithms for DNA assembly using FALQON variants

TL;DR

This work analyzes three versions of the Feedback-based Algorithm, a protocol that eliminates classical optimization loops via measurement feedback using long-read DNA fragments from SARS-CoV-2 and human mitochondrial DNA using standard FALQON, second-order FALQON (SO-FALQON), and time-rescaled FALQON (TR-FALQON).

Abstract

Reconstructing DNA sequences without a reference, known as de novo assembly, is a complex computational task involving the alignment of overlapping fragments. To address this problem, a usual strategy is to map the assembly to a Quadratic Unconstrained Binary Optimization (QUBO) formulation, which can be solved by different quantum algorithms. In this work, we focus on three versions of the Feedback-based Algorithm, a protocol that eliminates classical optimization loops via measurement feedback. We analyze long-read DNA fragments from SARS-CoV-2 and human mitochondrial DNA using standard FALQON, second-order FALQON (SO-FALQON), and time-rescaled FALQON (TR-FALQON). Numerical results show that both variants improve convergence to the ground state and increase success probabilities at reduced circuit depths. These findings indicate that enhanced feedback-driven dynamics are effective for solving combinatorial problems on near-term quantum hardware.
Paper Structure (23 sections, 32 equations, 3 figures, 1 table)

This paper contains 23 sections, 32 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. DNA Decoding Problem via de novo Assembly
  3. Overlap–Layout–Consensus Model
  4. Problem Formulation as QUBO
  5. FALQON Algorithm
  6. Motivation
  7. Formalism and Dynamics
  8. Characteristics and Convergence
  9. TR-FALQON Algorithm
  10. Temporal Rescaling and TR-FALQON Formalism
  11. Impact and Results
  12. SO-FALQON Algorithm
  13. Mathematical Formalism
  14. Practical Implementation and Results
  15. Implementation
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Directed complete graph constructed from four reads and its corresponding adjacency matrix. Each line(column) $i,j$, corresponds to the connectivity between reads $r_i,r_j$.
  • Figure 2: Performance of FALQON and its variants in the DNA assembly problem. The first panel shows the expected value of the energy $\langle H_p \rangle_k$ as a function of the circuit layer $k$. The second panel presents the values of the control function $\beta_k$. The third panel displays the probability $P_k$ of measuring the state that encodes the optimal solution of the problem in each circuit layer. Each curve corresponds to a different variant of the algorithm, as indicated in the legend. The black dashed curve in the panels of the first row indicates the ground-state energy $E_0$ of $H_p$.
  • Figure 3: Performance of FALQON and its variants in the DNA assembly problem for instances with 4, 5, and 6 reads. The first row shows the expected value of the energy $\langle H_p \rangle_k$ as a function of the circuit layer $k$. The second row presents the values of the control function $\beta_k$. The third row displays the probability $P_k$ of measuring the state that encodes the optimal solution of the problem in each circuit layer. Each curve corresponds to a different variant of the algorithm, as indicated in the legend. The black dashed curve in the panels of the first row indicates the ground-state energy $E_0$ of $H_p$.