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ADR-002: Quantum-Inspired Genomics Engine

Status: Proposed (Revised - Implementable Today) Date: 2026-02-11 Authors: ruv.io, RuVector Team Deciders: Architecture Review Board SDK: Claude-Flow

Version History

Version Date Author Changes
0.1 2026-02-11 ruv.io Initial quantum genomics engine proposal
0.2 2026-02-11 ruv.io Revised to focus on implementable quantum-inspired algorithms

Context

The Genomics Computational Bottleneck

Modern genomics confronts a data explosion that outpaces Moore's Law. A single human genome contains approximately 3.2 billion base pairs. The critical computational tasks -- sequence alignment, variant calling, haplotype phasing, de novo assembly, phylogenetic inference, and protein structure prediction -- each pose optimization problems whose classical complexity ranges from O(N log N) to NP-hard.

Genomic Operation Classical Complexity Bottleneck
k-mer exact search O(N) per query Linear scan over 3.2B base pairs
Sequence alignment (BWA-MEM2) O(N log N) with FM-index Index construction and seed extension
Variant calling (GATK HaplotypeCaller) O(R * H * L) per active region Local assembly of haplotype candidates
Haplotype assembly NP-hard (MEC formulation) Minimum error correction on read fragments
De novo genome assembly O(N) edge traversal on de Bruijn graph Graph construction and Eulerian path finding
Phylogenetic tree inference (ML) NP-hard (Felsenstein, 1978) Tree topology search over super-exponential space
Protein folding energy minimization NP-hard (Crescenzi & Pode, 1998) Conformational search in continuous space

Quantum-Inspired Classical Algorithms: Implementable Today

While fault-tolerant quantum computers remain decades away, quantum-inspired classical algorithms provide the same algorithmic insights and computational structures as their quantum counterparts, running on classical hardware today. RuVector's quantum crates (ruQu, ruqu-algorithms, ruqu-core, ruqu-wasm) enable:

  1. Quantum circuit simulation for algorithm design and validation (up to 25 qubits)
  2. Quantum-inspired optimization via tensor network contractions and variational methods
  3. Classical implementations of quantum algorithmic patterns with similar complexity benefits

Why Quantum-Inspired Algorithms Work

Quantum algorithms provide computational advantages through:

  • Amplitude amplification patterns that inform hierarchical pruning strategies
  • Variational optimization that maps to classical gradient descent with structured ansätze
  • Superposition concepts that translate to parallel ensemble methods
  • Entanglement structures that guide tensor network decompositions

We implement these algorithmic insights classically, using quantum simulation only for validation and algorithm design at tractable scales.


Decision

Architecture Overview

Introduce a quantum-genomics module within ruqu-algorithms that implements quantum-inspired classical algorithms for genomic data processing, with quantum simulation for validation.

                    ┌─────────────────────────────────────────────┐
                    │    Quantum-Inspired Genomics Engine          │
                    │       (ruqu-algorithms::genomics)            │
                    ├─────────────────────────────────────────────┤
                    │                                              │
                    │  ┌─────────┐  ┌──────────┐  ┌───────────┐ │
                    │  │ HNSW    │  │ Simulated│  │ Bayesian  │ │
                    │  │ k-mer   │  │ Annealing│  │ Haplotype │ │
                    │  │ Search  │  │ Phylo    │  │ Assembly  │ │
                    │  └────┬────┘  └────┬─────┘  └─────┬─────┘ │
                    │       │            │              │        │
                    │  ┌────┴────┐  ┌────┴─────┐  ┌────┴─────┐ │
                    │  │ Classical│  │ Tensor   │  │ Variational│
                    │  │ VQE      │  │ Network  │  │ Optimization│
                    │  │ Molecular│  │ Assembly │  │ Variant  │ │
                    │  └────┬────┘  └────┬─────┘  └────┬─────┘ │
                    │       │            │              │        │
                    │  ┌────┴────────────┴──────────────┴─────┐ │
                    │  │    ruQu Quantum Simulation (25 qubits)│ │
                    │  │    (Algorithm Validation Only)        │ │
                    │  └──────────────────────────────────────┘ │
                    └────────────────┬────────────────────────┬──┘
                                     │                        │
                    ┌────────────────┴────┐    ┌─────────────┴───────┐
                    │     ruqu-core       │    │  Classical backends │
                    │  (quantum simulator)│    │  - HNSW indexing    │
                    ├─────────────────────┤    │  - Tensor networks  │
                    │  ruqu-wasm          │    │  - Simulated        │
                    │  (browser target)   │    │    annealing        │
                    └─────────────────────┘    └─────────────────────┘

Module Structure

ruqu-algorithms/
  src/
    genomics/
      mod.rs                     # Public API and genomic type definitions
      hnsw_kmer_search.rs        # HNSW-based k-mer search (O(log N) heuristic)
      haplotype_assembly.rs      # Variational optimization for phasing
      classical_vqe_molecular.rs # Classical variational molecular simulation
      tensor_network_assembly.rs # Tensor network for de Bruijn graphs
      simulated_annealing.rs     # Simulated annealing for phylogenetics
      pattern_matching.rs        # Quantum-inspired pattern recognition
      encoding.rs                # DNA base-pair to qubit encoding schemes
      hybrid_pipeline.rs         # Classical-quantum decision boundary logic
      quantum_validation.rs      # Quantum simulation for algorithm validation

Implementation Status

Algorithm Status Classical Implementation Quantum Validation Production Ready
HNSW k-mer search ✅ Implemented HNSW with O(log N) ruQu 8-12 qubits Yes
Haplotype assembly ✅ Implemented Variational MinCut QAOA simulation 20 qubits Yes
Molecular docking 🔄 In Progress Classical VQE (DFT-level) ruQu 12-16 qubits Q2 2026
Tensor network assembly 🔄 In Progress MPS/PEPS contractions N/A (classical-only) Q3 2026
Simulated annealing phylo ✅ Implemented Metropolis-Hastings 8-10 qubits validation Yes
Pattern matching ✅ Implemented GNN + attention N/A Yes

1. HNSW-Based k-mer Search (Quantum-Inspired)

Problem Statement

Classical k-mer search uses hash tables (O(1) lookup after O(N) preprocessing) or FM-indices (O(k) lookup). Grover's algorithm offers O(sqrt(N)) query complexity on quantum hardware, but we implement this algorithmic insight classically using hierarchical navigable small world (HNSW) graphs.

Classical Implementation: HNSW Search

Key Insight: Grover's amplitude amplification creates a hierarchical search pattern. HNSW replicates this structure through layered graph navigation.

/// HNSW-based k-mer search inspired by Grover's hierarchical amplification.
///
/// Grover: O(sqrt(N)) queries with amplitude amplification
/// HNSW: O(log N) average-case with hierarchical graph traversal
///
/// The hierarchical structure mimics Grover's iteration pattern.
pub struct HnswKmerIndex {
    /// HNSW index for k-mer vectors
    index: HnswIndex<KmerVector>,
    /// k-mer length
    k: usize,
    /// Reference genome encoded as 2-bit per base
    reference: Vec<u8>,
    /// M parameter (connections per layer)
    m: usize,
    /// ef_construction parameter
    ef_construction: usize,
}

impl HnswKmerIndex {
    /// Build HNSW index from reference genome.
    ///
    /// Preprocessing: O(N log N) to build index
    /// Query: O(log N) average case
    pub fn from_reference(reference: &[u8], k: usize) -> Self {
        let mut index = HnswIndex::new(
            /*dim=*/ k * 2, // 2 bits per base
            /*m=*/ 16,
            /*ef_construction=*/ 200,
        );

        // Extract all k-mers and build index
        for i in 0..reference.len().saturating_sub(k) {
            let kmer = &reference[i..i + k];
            let vector = encode_kmer_to_vector(kmer);
            index.insert(i, vector);
        }

        Self { index, k, reference: reference.to_vec(), m: 16, ef_construction: 200 }
    }

    /// Search for k-mer matches using HNSW.
    ///
    /// Returns all positions matching within Hamming distance threshold.
    pub fn search(&self, query_kmer: &[u8], max_hamming: usize) -> Vec<usize> {
        let query_vector = encode_kmer_to_vector(query_kmer);

        // HNSW search with hierarchical navigation (Grover-inspired)
        let candidates = self.index.search(&query_vector, /*k=*/ 100, /*ef=*/ 200);

        // Filter by exact Hamming distance
        candidates.into_iter()
            .filter(|(idx, _dist)| {
                let ref_kmer = &self.reference[*idx..*idx + self.k];
                hamming_distance(query_kmer, ref_kmer) <= max_hamming
            })
            .map(|(idx, _)| idx)
            .collect()
    }
}

/// Encode k-mer as vector for HNSW.
fn encode_kmer_to_vector(kmer: &[u8]) -> Vec<f32> {
    kmer.iter()
        .flat_map(|&base| match base {
            b'A' => [1.0, 0.0],
            b'C' => [0.0, 1.0],
            b'G' => [-1.0, 0.0],
            b'T' => [0.0, -1.0],
            _ => [0.0, 0.0],
        })
        .collect()
}

Complexity Analysis

Approach Preprocessing Per-Query Space
Linear scan None O(N * k) O(1)
Hash table O(N) O(k) average O(N)
FM-index (BWT) O(N) O(k) O(N)
HNSW (quantum-inspired) O(N log N) O(log N) O(N)
Grover (quantum) None O(sqrt(N) * k) O(n) qubits

Practical speedup for human genome (N = 3.2B):

  • Linear scan: 3.2B comparisons
  • HNSW: ~32 comparisons (log₂(3.2e9) ≈ 32)
  • Speedup: 100M× over linear scan

Quantum Validation (ruQu)

/// Validate HNSW search pattern against Grover's algorithm at small scale.
pub fn validate_against_grover(reference: &[u8], k: usize) {
    assert!(reference.len() <= 256, "Grover validation limited to 8 qubits (2^8 = 256 bases)");

    // Build HNSW index
    let hnsw_index = HnswKmerIndex::from_reference(reference, k);

    // Build Grover oracle for validation
    let oracle = GroverKmerOracle::new(reference, k);
    let grover_result = grover_search(&oracle, /*iterations=*/ 12);

    // Compare results
    let test_kmer = &reference[42..42 + k];
    let hnsw_matches = hnsw_index.search(test_kmer, 0);
    let grover_matches = grover_result.marked_states;

    assert_eq!(hnsw_matches.len(), grover_matches.len());
}

2. Variational Haplotype Assembly (QAOA-Inspired)

Problem Statement

Haplotype assembly partitions reads into two groups (maternal/paternal) that minimize read-allele conflicts -- the Minimum Error Correction (MEC) problem, proven NP-hard.

Classical Implementation: Variational MinCut

Key Insight: QAOA encodes MEC as a MaxCut Hamiltonian. We implement classical variational optimization with the same cost function structure.

/// Variational haplotype assembly inspired by QAOA MaxCut.
///
/// Uses gradient-based optimization over the same cost landscape
/// as QAOA, but with classical bitstring representation.
pub struct VariationalHaplotypeAssembler {
    /// Fragment-SNP matrix
    fragment_matrix: Vec<Vec<i8>>,
    /// Quality scores (Phred-scaled)
    quality_matrix: Vec<Vec<f64>>,
    /// Number of variational layers
    layers: usize,
}

impl VariationalHaplotypeAssembler {
    /// Build fragment-conflict graph (same as QAOA formulation).
    pub fn build_conflict_graph(&self) -> WeightedGraph {
        let n_fragments = self.fragment_matrix.len();
        let mut edges = Vec::new();

        for i in 0..n_fragments {
            for j in (i + 1)..n_fragments {
                let mut weight = 0.0;
                for s in 0..self.fragment_matrix[i].len() {
                    let a_i = self.fragment_matrix[i][s];
                    let a_j = self.fragment_matrix[j][s];
                    if a_i >= 0 && a_j >= 0 && a_i != a_j {
                        let q = (self.quality_matrix[i][s]
                                + self.quality_matrix[j][s]) / 2.0;
                        weight += q;
                    }
                }
                if weight > 0.0 {
                    edges.push((i, j, weight));
                }
            }
        }

        WeightedGraph { vertices: n_fragments, edges }
    }

    /// Solve using classical variational optimization.
    ///
    /// Mimics QAOA cost landscape but uses gradient descent
    /// over continuous relaxation of the cut.
    pub fn solve(&self) -> HaplotypeResult {
        let graph = self.build_conflict_graph();

        // Initialize random partition
        let mut partition = random_bitstring(graph.vertices);

        // Variational optimization (inspired by QAOA parameter optimization)
        for _layer in 0..self.layers {
            // Compute gradient of MaxCut cost
            let gradient = self.compute_cut_gradient(&graph, &partition);

            // Update partition via simulated annealing moves
            self.apply_gradient_moves(&mut partition, &gradient);
        }

        HaplotypeResult {
            haplotype_assignment: partition,
            mec_score: self.compute_cut_cost(&graph, &partition),
        }
    }

    fn compute_cut_cost(&self, graph: &WeightedGraph, partition: &[bool]) -> f64 {
        graph.edges.iter()
            .filter(|(i, j, _)| partition[*i] != partition[*j])
            .map(|(_, _, w)| w)
            .sum()
    }
}

Quantum Validation (ruQu QAOA)

/// Validate classical variational approach against QAOA at small scale.
pub fn validate_against_qaoa(fragment_matrix: &[Vec<i8>], quality_matrix: &[Vec<f64>]) {
    assert!(fragment_matrix.len() <= 20, "QAOA validation limited to 20 qubits");

    let assembler = VariationalHaplotypeAssembler {
        fragment_matrix: fragment_matrix.to_vec(),
        quality_matrix: quality_matrix.to_vec(),
        layers: 3,
    };

    // Classical variational result
    let classical_result = assembler.solve();

    // QAOA quantum simulation result
    let graph = assembler.build_conflict_graph();
    let qaoa_result = qaoa_maxcut(&graph, /*p=*/ 3, &LbfgsOptimizer::new());

    // Compare cut quality (should be within 5%)
    let quality_ratio = classical_result.mec_score / qaoa_result.best_cost;
    assert!((0.95..=1.05).contains(&quality_ratio), "Classical variational within 5% of QAOA");
}

3. Classical VQE for Molecular Interaction

Problem Statement

Understanding DNA-protein binding and drug-nucleic acid interactions requires computing molecular ground-state energies. Classical force fields approximate quantum effects; VQE computes from first principles.

Classical Implementation: Density Functional Theory

Key Insight: VQE's variational principle is the same as classical DFT. We use classical DFT libraries with VQE-inspired ansatz optimization.

/// Classical molecular energy calculation using VQE principles.
///
/// Uses DFT (PySCF backend) with variational optimization structure
/// identical to VQE, but without quantum hardware.
pub struct ClassicalVqeMolecular {
    /// Molecular geometry (XYZ coordinates)
    geometry: Vec<Atom>,
    /// Basis set (e.g., "def2-TZVP")
    basis: String,
    /// Functional (e.g., "B3LYP")
    functional: String,
}

impl ClassicalVqeMolecular {
    /// Compute ground state energy using classical DFT.
    ///
    /// Variational optimization over molecular orbitals (same principle as VQE).
    pub fn compute_energy(&self) -> f64 {
        // Initialize DFT calculation (via FFI to PySCF or similar)
        let mut dft_calc = DftCalculation::new(&self.geometry, &self.basis, &self.functional);

        // Variational optimization (SCF iterations)
        dft_calc.run_scf(/*max_iterations=*/ 100, /*convergence=*/ 1e-6);

        dft_calc.total_energy()
    }

    /// Compute molecular binding energy for DNA-protein interaction.
    pub fn compute_binding_energy(
        &self,
        dna_geometry: &[Atom],
        protein_geometry: &[Atom],
    ) -> f64 {
        let complex_energy = self.compute_energy();

        let dna_alone = ClassicalVqeMolecular {
            geometry: dna_geometry.to_vec(),
            ..self.clone()
        };
        let protein_alone = ClassicalVqeMolecular {
            geometry: protein_geometry.to_vec(),
            ..self.clone()
        };

        complex_energy - dna_alone.compute_energy() - protein_alone.compute_energy()
    }
}

Quantum Validation (ruQu VQE)

/// Validate classical DFT against quantum VQE at small scale.
pub fn validate_against_vqe(geometry: &[Atom]) {
    assert!(geometry.len() <= 6, "VQE validation limited to small molecules (12-16 qubits)");

    // Classical DFT result
    let classical_calc = ClassicalVqeMolecular {
        geometry: geometry.to_vec(),
        basis: "sto-3g".to_string(),
        functional: "B3LYP".to_string(),
    };
    let classical_energy = classical_calc.compute_energy();

    // Quantum VQE simulation result
    let hamiltonian = construct_molecular_hamiltonian(geometry, "sto-3g");
    let ansatz = UccsdAnsatz::new(/*n_electrons=*/ 4, /*n_orbitals=*/ 4);
    let vqe_result = run_vqe(&hamiltonian, &ansatz, &LbfgsOptimizer::new());

    // Compare energies (should be within chemical accuracy: 1 kcal/mol = 0.0016 Hartree)
    let error = (classical_energy - vqe_result.energy).abs();
    assert!(error < 0.002, "Classical DFT within chemical accuracy of VQE");
}

4. Tensor Network Assembly (Quantum-Inspired)

Problem Statement

De novo genome assembly constructs genome sequences from reads. De Bruijn graphs have up to N nodes; finding Eulerian paths is O(N) classically, but repeat resolution is combinatorially hard.

Classical Implementation: Matrix Product State Contraction

Key Insight: Quantum walks explore multiple paths via superposition. Tensor network methods achieve similar multi-path exploration classically.

/// Tensor network assembly for de Bruijn graph traversal.
///
/// Inspired by quantum walk superposition, uses matrix product states (MPS)
/// to efficiently represent exponentially many path hypotheses.
pub struct TensorNetworkAssembler {
    /// de Bruijn graph adjacency
    adjacency: Vec<Vec<usize>>,
    /// k-mer labels
    node_labels: Vec<Vec<u8>>,
    /// MPS bond dimension
    bond_dim: usize,
}

impl TensorNetworkAssembler {
    /// Construct MPS representation of path space.
    ///
    /// Instead of quantum walk, use tensor network to represent
    /// exponentially many paths with polynomial memory.
    pub fn build_path_mps(&self) -> MatrixProductState {
        let n_nodes = self.adjacency.len();
        let mut mps = MatrixProductState::new(n_nodes, self.bond_dim);

        // Initialize MPS tensors from adjacency structure
        for node in 0..n_nodes {
            let out_degree = self.adjacency[node].len();
            let tensor = self.create_node_tensor(node, out_degree);
            mps.set_tensor(node, tensor);
        }

        mps
    }

    /// Contract MPS to find high-probability paths (assembly candidates).
    pub fn assemble(&self) -> Vec<Path> {
        let mps = self.build_path_mps();

        // Contract tensor network to find top-k paths
        let path_probabilities = mps.contract_all();

        // Extract paths with probability above threshold
        path_probabilities.into_iter()
            .filter(|(_, prob)| *prob > 0.01)
            .map(|(path, _)| path)
            .collect()
    }

    fn create_node_tensor(&self, node: usize, out_degree: usize) -> Tensor3D {
        // Create tensor encoding local graph structure
        // Dimension: bond_dim x bond_dim x out_degree
        Tensor3D::from_adjacency(&self.adjacency[node], self.bond_dim)
    }
}

Complexity: MPS with bond dimension χ achieves O(N χ³) assembly vs. O(2^N) for exact enumeration.


5. Simulated Annealing for Phylogenetics

Problem Statement

Phylogenetic tree inference searches super-exponential topology space. For n=20 taxa: (2*20-5)!! = 2.2×10²⁰ topologies.

Classical Implementation: Simulated Annealing

Key Insight: Quantum annealing explores cost landscapes via tunneling. Simulated annealing replicates this via thermal fluctuations.

/// Simulated annealing for phylogenetic tree optimization.
///
/// Inspired by quantum annealing, uses thermal fluctuations
/// to escape local minima in the tree topology landscape.
pub struct PhylogeneticAnnealer {
    /// Sequence alignment
    alignment: Vec<Vec<u8>>,
    /// Number of taxa
    n_taxa: usize,
    /// Annealing schedule
    schedule: AnnealingSchedule,
}

pub struct AnnealingSchedule {
    /// Initial temperature
    pub t_initial: f64,
    /// Final temperature
    pub t_final: f64,
    /// Cooling rate
    pub alpha: f64,
    /// Steps per temperature
    pub steps_per_temp: usize,
}

impl PhylogeneticAnnealer {
    /// Run simulated annealing optimization.
    pub fn anneal(&self) -> PhylogeneticTree {
        // Initialize random tree topology
        let mut current_tree = random_tree(self.n_taxa);
        let mut current_likelihood = self.log_likelihood(&current_tree);
        let mut best_tree = current_tree.clone();
        let mut best_likelihood = current_likelihood;

        let mut temperature = self.schedule.t_initial;

        while temperature > self.schedule.t_final {
            for _ in 0..self.schedule.steps_per_temp {
                // Propose tree modification (NNI, SPR, or TBR move)
                let proposed_tree = self.propose_move(&current_tree);
                let proposed_likelihood = self.log_likelihood(&proposed_tree);

                // Metropolis acceptance criterion
                let delta_e = proposed_likelihood - current_likelihood;
                if delta_e > 0.0 || random::<f64>() < (delta_e / temperature).exp() {
                    current_tree = proposed_tree;
                    current_likelihood = proposed_likelihood;

                    if current_likelihood > best_likelihood {
                        best_tree = current_tree.clone();
                        best_likelihood = current_likelihood;
                    }
                }
            }

            // Cool down (annealing schedule)
            temperature *= self.schedule.alpha;
        }

        best_tree
    }

    fn log_likelihood(&self, tree: &PhylogeneticTree) -> f64 {
        // Felsenstein pruning algorithm
        felsenstein_pruning(tree, &self.alignment)
    }
}

Quantum Validation (ruQu)

/// Validate simulated annealing against quantum annealing at small scale.
pub fn validate_against_quantum_annealing(alignment: &[Vec<u8>]) {
    assert!(alignment.len() <= 8, "Quantum annealing validation limited to 8 taxa (18 qubits)");

    let annealer = PhylogeneticAnnealer {
        alignment: alignment.to_vec(),
        n_taxa: alignment.len(),
        schedule: AnnealingSchedule {
            t_initial: 100.0,
            t_final: 0.1,
            alpha: 0.95,
            steps_per_temp: 100,
        },
    };

    // Classical simulated annealing result
    let classical_tree = annealer.anneal();
    let classical_likelihood = annealer.log_likelihood(&classical_tree);

    // Quantum annealing simulation result
    let qaoa_tree = quantum_phylo_annealing(alignment, /*trotter_slices=*/ 10);
    let quantum_likelihood = annealer.log_likelihood(&qaoa_tree);

    // Compare likelihood quality (should be within 2%)
    let quality_ratio = classical_likelihood / quantum_likelihood;
    assert!((0.98..=1.02).contains(&quality_ratio), "Simulated annealing within 2% of quantum");
}

Crate API Mapping

ruqu-core Functions

Genomic Operation ruqu-core Function Purpose
HNSW k-mer validation grover_search(&oracle, iterations) Validate HNSW search pattern against Grover at 8-12 qubits
Haplotype assembly validation qaoa_maxcut(&graph, p, optimizer) Validate variational MinCut against QAOA at 20 qubits
Molecular energy validation run_vqe(&hamiltonian, &ansatz, &optimizer) Validate classical DFT against VQE at 12-16 qubits
Phylogenetics validation quantum_annealing(&hamiltonian, &schedule) Validate simulated annealing at 8 taxa (18 qubits)

ruqu-algorithms Functions

Genomic Operation ruqu-algorithms Function Purpose
Grover oracle GroverOracle::new(reference, k) k-mer search oracle for validation
QAOA graph qaoa_maxcut_graph(edges) Haplotype conflict graph for QAOA
VQE Hamiltonian construct_molecular_hamiltonian(geometry, basis) Molecular Hamiltonian for VQE
Quantum walk quantum_walk_on_graph(adjacency, steps) de Bruijn graph walk validation

ruqu-wasm Functions

Genomic Operation ruqu-wasm Function Browser Demo
k-mer search demo wasm_grover_kmer(reference, query) Interactive k-mer search (up to 256 bases, 8 qubits)
Haplotype demo wasm_qaoa_haplotype(fragments) Haplotype assembly (up to 20 fragments, 20 qubits)
Molecular demo wasm_vqe_molecule(geometry) Base pair energy (up to 12 orbitals, 24 qubits)

Hybrid Classical-Quantum Pipeline

Decision Boundary Framework

Not every genomic computation benefits from quantum simulation. Route operations based on problem size:

Operation Classical (Primary) Quantum Simulation (Validation) When to Use Quantum
k-mer search HNSW O(log N) Grover simulation ≤256 bases Algorithm design and validation only
Haplotype assembly Variational MinCut QAOA simulation ≤20 fragments Validate cost function structure
Molecular interaction Classical DFT (B3LYP) VQE simulation ≤16 orbitals Validate variational ansatz
Phylogenetics Simulated annealing Quantum annealing ≤8 taxa Compare annealing schedules
Genome assembly Tensor network MPS Quantum walk ≤1K nodes Research exploration only

Production Strategy: Run classical implementations for all real-world problems. Use quantum simulation for algorithm validation and design at tractable scales.


Performance Projections

Classical vs. Quantum-Inspired vs. Quantum Simulation

Operation Classical Baseline Quantum-Inspired Classical Quantum Simulation (ruQu) Practical Use
k-mer search (3.2B bp) O(N) = 3.2×10⁹ HNSW O(log N) ≈ 32 Grover O(√N) ≈ 56,568 @ 8 qubits only HNSW production, ruQu validation
Haplotype (50 fragments) O(2⁵⁰) exact Variational O(F²·iter) QAOA O(F²·p) @ 20 qubits Variational production, QAOA validation
VQE molecular (12 orbitals) DFT O(N⁷) Classical VQE O(N⁴·iter) VQE O(poly·iter) @ 24 qubits Classical VQE production, quantum validation
Phylogenetics (20 taxa) RAxML heuristic Simulated annealing Quantum anneal @ 8 taxa only Simulated annealing production, validation limited

Key Takeaway: Quantum simulation (ruQu) is for algorithm design and validation at small scales. Production uses quantum-inspired classical algorithms.


Consequences

Benefits

  1. Implementable today: All algorithms run on classical hardware without waiting for fault-tolerant quantum computers
  2. Quantum-inspired performance: HNSW k-mer search achieves O(log N) vs. O(N); tensor networks reduce exponential to polynomial
  3. Validation framework: ruQu quantum simulation validates algorithmic correctness at tractable scales (8-25 qubits)
  4. Hardware-ready: When fault-tolerant quantum computers arrive, quantum simulation code becomes production code
  5. Browser accessibility: ruqu-wasm enables quantum algorithm education and validation in-browser
  6. No overpromising: Clear distinction between "implementable today" and "requires quantum hardware"

Limitations

  1. No exponential quantum speedup: Classical implementations do not achieve theoretical quantum advantages (e.g., Grover's O(√N))
  2. Validation scale limited: Quantum simulation capped at ~25 qubits (33M bases for k-mer search, 25 fragments for haplotype assembly)
  3. Quantum simulation overhead: State vector simulation is 10-100× slower than native classical algorithms
  4. Requires classical expertise: Tensor networks, variational optimization, simulated annealing require specialized classical algorithm knowledge

Alternatives Considered

Alternative 1: Wait for Fault-Tolerant Quantum Computers

Rejected: Fault-tolerant quantum computers with >1,000 logical qubits are 10-20 years away. We need solutions today.

Alternative 2: Cloud Quantum Hardware (IBM Quantum, IonQ)

Rejected: Current NISQ hardware (50-100 noisy qubits) cannot achieve quantum advantage for genomic problems due to error rates. Simulation provides exact results for algorithm design.

Alternative 3: Pure Classical Genomics (No Quantum Inspiration)

Rejected: Quantum algorithmic insights (hierarchical amplification, variational optimization, superposition patterns) inform better classical algorithms. We leverage these insights.


References

Quantum Computing

  • Grover, L.K. "A fast quantum mechanical algorithm for database search." STOC 1996.
  • Farhi, E., et al. "A Quantum Approximate Optimization Algorithm." arXiv:1411.4028, 2014.
  • Peruzzo, A. et al. "A variational eigenvalue solver on a photonic quantum processor." Nature Communications 5, 4213, 2014.
  • Malkov, Y., & Yashunin, D. "Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs." IEEE TPAMI, 2018.

Classical Algorithms

  • Verstraete, F., et al. "Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems." Advances in Physics, 2008.
  • Kirkpatrick, S., et al. "Optimization by simulated annealing." Science, 1983.

Genomics

  • Li, H. "Aligning sequence reads with BWA-MEM." arXiv:1303.3997, 2013.
  • Patterson, M. et al. "WhatsHap: Weighted Haplotype Assembly." Journal of Computational Biology, 2015.

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