The quantum computing landscape in 2025 presents both promising advances and sobering realities. While the technology has moved beyond pure research into early commercial deployments, it remains years away from the transformative applications often promised in popular media. For the Fidelity framework, this creates an interesting design opportunity: how can we architect our system to potentially leverage quantum acceleration when it becomes practical, without over-committing to a technology still finding its footing?

This vision document examines how F#’s functional basis, combined with the Program Semantic Graph architecture and our interaction net foundations, creates a natural path for future quantum-classical integration. While we recognize that fault-tolerant quantum computers remain on the horizon (expert consensus suggests 2030 ± 2 years), we believe in preparing architectural foundations that could adapt to quantum acceleration when specific use cases demonstrate genuine advantage.

The Current Quantum Reality

Before exploring integration possibilities, it’s important to acknowledge where quantum computing stands today. Government agencies are leading concrete deployments, with the U.S. Department of Defense awarding contracts like IonQ’s $54.5 million Air Force Research Lab project. Financial institutions, particularly JPMorgan Chase with their dedicated quantum team, have achieved specific milestones like demonstrating Certified Quantum Randomness on Quantinuum’s 56-qubit system.

However, current systems face significant technical barriers. Error rates remain 1-2 orders of magnitude above fault-tolerance thresholds, and coherence times vary dramatically by technology. The path to practical quantum computing requires massive overhead - current estimates suggest 100-1,000 physical qubits per logical qubit for effective error correction.

This reality shapes our approach: rather than assuming imminent quantum supremacy, we’re designing for selective integration where quantum acceleration could provide genuine computational advantages for specific subroutines within larger classical applications.

The Convergence of Paradigms

Interaction Nets Meet Quantum Computing

The same interaction net principles that optimize pure functional computations reveal interesting parallels with quantum computation. Both paradigms emphasize:

• Local rewriting rules that can execute in parallel
• Reversible operations preserving information
• Minimal state with maximal parallelism

Consider how quantum gate operations mirror interaction net reductions:

// Interaction net rules for quantum gate fusion
type QuantumInteraction =
    | HadamardAnnihilation    
    | CNOTInvolution         
    | PhaseCommutation       

These correspond to fundamental quantum identities:

These aren’t theoretical abstractions - they’re mathematical laws that enable optimization. The deep connections through category theory and linear logic suggest natural integration points when quantum hardware matures.

Pure Functional Operations as Quantum Candidates

The PSG’s purity analysis could identify computations potentially suitable for quantum acceleration:

// Pure operations that may benefit from quantum computation
type PureComputation =
    | SearchProblem of searchSpace: int
    | OptimizationProblem of constraints: Constraint[]
    | LinearAlgebra of matrix: SparseMatrix
    | FourierTransform of signal: Complex[]

// DFG analysis determines quantum advantage
let analyzeDataFlow (computation: PureComputation) =
    match computation with
    | SearchProblem n when n > polynomialThreshold ->
        QuantumAdvantage (Grover, speedup = sqrt n)
    | OptimizationProblem constraints ->
        QuantumAdvantage (QAOA, problemDependent)
    | FourierTransform signal ->
        QuantumAdvantage (QFT, exponential)
    | _ ->
        ClassicalOptimal

Integration Pathways: Beyond QIR

While the Quantum Intermediate Representation (QIR) Alliance shows signs of reduced activity (with key repositories dormant since 2022-2024), the quantum ecosystem continues to evolve. Our architecture remains flexible to integrate with various quantum backends as they mature:

Direct Quantum Assembly Integration

Rather than depending solely on QIR, Fidelity’s MLIR pipeline could target quantum assembly languages directly:

// F# quantum computation identified by PSG
let quantumAlgorithm (input: ClassicalData) =
    quantum {
        let! qubits = allocate 10
        let! encoded = encode input qubits
        let! processed = quantumProcess encoded
        return! measure processed
    }

// PSG identifies quantum block and pure operations
PSGNode.Quantum {
    Operations = [Allocate; Encode; Process; Measure]
    PureRegions = [Process]  // Suitable for optimization
    Effects = [Allocate; Measure]
}

This could flow through multiple compilation paths:

The key insight is architectural flexibility - as quantum backends mature and standardize, Fidelity’s modular design can adapt without fundamental restructuring.

F# and Q# Synergy

Given Q#’s design inspiration from F#, Fidelity could enable cross-compilation scenarios when appropriate:

// Shared algorithmic logic between F# and Q#
let groverOracle (items: int[]) (target: int) (index: int) =
    items.[index] = target

// F# classical simulation
let classicalSearch items target =
    items |> Array.findIndex (fun x -> x = target)

// Same oracle could compile to quantum when beneficial
let searchAlgorithm (items: int[]) (target: int) =
    if items.Length < 1000 then
        classicalSearch items target  // Direct classical search
    else
        quantum {
            // Future: same oracle, quantum acceleration
            let! result = Grover.search (groverOracle items target) items.Length
            return result
        }

INets for Quantum-Classical Boundaries

Pure Parallelism Meets Quantum Coherence

Interaction nets excel at managing theoretical quantum-classical boundaries:

type QuantumInetNode =
    | ClassicalData of Tensor<float32>
    | QuantumState of QubitRegister
    | Measurement of Result[]
    | Superposition of Complex[]

// Interaction rules handle state transitions
let quantumClassicalRules = [
    // Classical data prepares quantum state
    ClassicalData tensor × QuantumEncode →
        QuantumState (encodeTensor tensor)
    
    // Measurement collapses quantum state
    QuantumState qubits × MeasureAll →
        Measurement (collapse qubits)
    
    // Results flow back to classical
    Measurement results × ClassicalDecode →
        ClassicalData (decodeResults results)
]

This provides architectural advantages:

1. Automatic parallelization of classical pre/post-processing
2. Clear boundaries between quantum and classical domains
3. Optimization opportunities at transition points

Hybrid Algorithms Through Inet

Variational quantum algorithms would benefit from interaction net representation:

let vqe (hamiltonian: Hamiltonian) (ansatz: Ansatz) =
    inet {
        // Classical parameter optimization (parallel via Inet)
        let! parameters = inet.classical {
            return optimizeParameters initial
        }
        
        // Quantum energy evaluation
        let! energy = inet.quantum {
            let! state = prepareAnsatz ansatz parameters
            return! expectationValue hamiltonian state
        }
        
        // Interaction net handles classical-quantum feedback loop
        let! optimized = inet.iterate {
            classical (updateParameters parameters energy)
            quantum (evaluateEnergy)
        } until convergence
        
        return optimized
    }

Real-World Scenario: Financial Risk Analysis

The Business Challenge

Consider a major investment bank calculating Value at Risk (VaR) across a portfolio containing millions of positions and complex derivatives. Traditional Monte Carlo simulations face two critical limitations:

1. Computational Time: Hours of processing for daily risk reports
2. Tail Risk Blindness: Rare “black swan” events are undersampled

This represents a genuine quantum opportunity, similar to work being done by JPMorgan Chase’s quantum team.

The Hybrid Solution

Financial risk analysis exemplifies a practical quantum-classical workload partition:

let calculatePortfolioRisk (portfolio: Portfolio) (market: MarketData) =
    // Classical Phase 1: Data preparation and correlation analysis
    let historicalData = 
        market
        |> loadHistoricalPrices
        |> cleanAndNormalize
        |> alignTimeSeriesData
        
    let correlationMatrix = 
        historicalData
        |> computeCorrelations
        |> regularizeMatrix  // Ensure positive semi-definite
        
    // Classical Phase 2: Scenario generation and risk identification
    let scenarios = generateScenarios correlationMatrix 1_000_000
    let (normalScenarios, tailScenarios) = 
        scenarios
        |> partitionByProbability 0.95  // 5% tail events
        
    // PSG would identify this as quantum-suitable (pure computation)
    let quantumEnhancedSamples = quantum {
        // Quantum amplitude amplification for rare events
        let! oracle = constructTailEventOracle tailScenarios
        let! amplified = amplitudeAmplification oracle
        
        // Sample 10,000 tail risk scenarios with enhanced probability
        return! measure amplified 10_000
    }
    
    // Classical Phase 3: Combine samples and calculate metrics
    let allSamples = 
        normalScenarios 
        |> MonteCarloSample 990_000  // Standard sampling
        |> Array.append (quantumEnhancedSamples |> Quantum.run IonQ)
        
    // Final risk calculations
    {
        VaR95 = calculateVaR allSamples 0.95
        VaR99 = calculateVaR allSamples 0.99
        CVaR = calculateCVaR allSamples 0.95
        ExpectedShortfall = calculateES allSamples
        StressScenarios = identifyWorstCases allSamples
    }

Why This Architecture Matters

The PSG analysis would automatically identify quantum opportunities:

let analyzeRiskWorkflow (psg: ProgramSemanticGraph) =
    psg.Nodes |> List.map (fun node ->
        match node with
        | DataLoading -> ClassicalIO          // I/O bound
        | CorrelationCalc -> ClassicalCPU      // Memory bandwidth limited
        | ScenarioGen -> ClassicalParallel     // Embarrassingly parallel
        | TailSampling -> QuantumAdvantage     // Amplitude amplification
        | RiskMetrics -> ClassicalReduction    // Simple aggregations
    )

The Mathematics of Quantum Advantage

The quantum advantage for tail risk sampling comes from amplitude amplification. For rare events with probability \(p \ll 1\), classical Monte Carlo requires \(O(1/p)\) samples to observe the event reliably. Quantum amplitude amplification reduces this to \(O(1/\sqrt{p})\):

where \(\delta\) is the desired error probability. For a 5-sigma event (\(p \approx 3 \times 10^{-7}\)), this means:

• Classical: ~3.3 million samples needed
• Quantum: ~1,800 samples needed
• Speedup: ~1,800x for rare event detection

Integration with Existing Systems

Financial institutions could adopt this incrementally:

// Gradual migration path
type RiskEngine =
    | Classical of MonteCarloConfig
    | Hybrid of classicalSamples: int * quantumSamples: int
    
let migrateRiskSystem (current: RiskEngine) =
    match current with
    | Classical config ->
        // Start with 1% quantum sampling when available
        Hybrid(config.Samples * 99 / 100, config.Samples / 100)
    | Hybrid(c, q) ->
        // Gradually increase quantum proportion as hardware improves
        Hybrid(c - 1000, q + 1000)

The Path Forward: Measured Optimism

Near-Term Focus

Rather than betting on immediate quantum breakthroughs, Fidelity’s architecture prepares for gradual integration:

1. Maintain PSG Architecture: The control flow and data flow analysis that identifies pure computations serves classical optimization today and quantum candidates tomorrow
2. Monitor Standards Evolution: While QIR appears dormant, quantum software standards continue evolving
3. Focus on Hybrid Patterns: Design for workflows where small quantum subroutines enhance larger classical applications
4. Build Flexible Backends: Firefly’s PSG with intelligent control and data flow graphs provide extensibility that allows adding quantum targets as they mature

Medium-Term Preparation

As quantum hardware approaches practical thresholds:

• Proof-of-Concept Integration: Target specific algorithms like Grover’s search or VQE
• Performance Modeling: Build cost models for quantum vs classical execution
• Error Mitigation Strategies: Integrate with emerging error correction techniques

Long-Term Vision

When fault-tolerant quantum computers become available:

• Transparent Acceleration: PSG-guided automatic offloading to quantum hardware
• Heterogeneous Execution: Seamlessly mix CPU, GPU, and QPU resources
• Domain-Specific Optimization: Specialized quantum kernels for finance, chemistry, and other industries

Engineering Realities and Considerations

Our approach acknowledges several key realities:

1. Quantum Winter Risk: While the industry shows resilience (funding rebounded to $1.9 billion in 2024), we’re not dependent on quantum for core functionality

2. Hardware Diversity: Different quantum architectures (superconducting, trapped ion, photonic) require different compilation strategies - our approach provides needed flexibility

3. Limited Near-Term Applications: Current quantum advantage exists only for specific problems - our hybrid approach targets these precisely

4. Integration Complexity: Quantum-classical boundaries involve complex engineering - our functional approach with clear effect boundaries helps manage this

Conclusion

Quantum optionality in the Fidelity framework represents thoughtful architectural preparation rather than premature optimization. By recognizing the deep connections between interaction nets, pure functional computation, and quantum algorithms, we create a foundation that can adapt as quantum technology matures.

The key is maintaining architectural flexibility without over-committing. Our PSG-based approach to identifying pure computations serves immediate classical optimization needs while naturally extending to quantum acceleration when hardware and algorithms align. Whether through revived standards like QIR or direct integration with quantum assembly languages, Fidelity’s design enables exploration of quantum advantages where they genuinely exist.

This isn’t about chasing quantum hype - it’s about engineering a system that can evolve with the technology landscape. As quantum computing transitions from research curiosity to practical tool for specific applications, Fidelity will be ready to leverage these capabilities while continuing to deliver value through classical optimization today.

The future of high-performance computing will involve more than the binary choice between classical and quantum, but through intelligently combining techniques based on rigorous analysis of computational characteristics, cost and return of value. Fidelity’s architecture, grounded in functional programming principles and designed for heterogeneous hardware, provides exactly this roadmap - quantum optionality without quantum dependency.