qnn-option-pricing-nisq

name: qnn-option-pricing-nisq description: "Quantum Neural Network (QNN) approach for option pricing on NISQ hardware - methodology for implementing quantum derivative pricing across multiple quantum processors, benchmarking cross-platform performance, and approximating Black-Scholes-Merton pricing functions using QNNs. arXiv: 2604.19832"

QNN Option Pricing on NISQ Hardware

Quantum Neural Network methodology for option pricing on Noisy Intermediate-Scale Quantum (NISQ) computers. Cross-platform evaluation of QNN-based derivative pricing on real quantum hardware.

Activation

Keywords: quantum option pricing, QNN derivative pricing, NISQ finance, quantum Black-Scholes, quantum neural network pricing, cross-platform quantum benchmark, quantum hardware finance

Core Concepts

Problem Setting

Global derivatives market with notional values in hundreds of trillions of dollars
Accuracy and efficiency of pricing models critical for risk management, capital allocation, regulatory compliance
Black-Scholes-Merton (BSM) framework used as controlled benchmark environment

QNN Architecture

Compact 2-qubit QNN for option pricing function approximation
Exploits geometric structure of Hilbert space to approximate pricing functions
Parameters optimized via classical-quantum hybrid training loop

Hardware Evaluation

Cross-platform study across 4 state-of-the-art quantum processors:

IBM Fez (superconducting)
IQM Garnet (superconducting)
IonQ Forte (trapped-ion)
Rigetti Ankaa-3 (superconducting)

Key Findings

Distinct hardware-dependent performance characteristics revealed
Accurate pricing approximations achievable consistently across different devices
Demonstrates viability of QNN approaches for derivative pricing despite NISQ constraints
Results extendable to more complex models: local volatility, stochastic volatility, interest rate frameworks

Workflow for Agents

Step 1: Define Pricing Problem

# Black-Scholes-Merton parameters
S = spot_price
K = strike_price
T = time_to_maturity
r = risk_free_rate
sigma = volatility

Step 2: Encode into QNN

Map BSM input space to quantum state preparation
Use parameterized quantum circuits as the QNN
Encode asset price, strike, time into qubit rotations

Step 3: Train on Quantum Hardware

Hybrid classical-quantum optimization loop
Classical optimizer updates circuit parameters
Quantum hardware evaluates circuit (expectation values)
Loss function: MSE between QNN output and true BSM price

Step 4: Cross-Platform Benchmarking

Run identical QNN on multiple quantum processors
Compare pricing accuracy, circuit fidelity, noise resilience
Identify hardware-specific performance characteristics

Step 5: Extension to Complex Models

Local volatility models
Stochastic volatility (Heston, etc.)
Interest rate frameworks

Pitfalls

NISQ Hardware Constraints

Coherence times: Limit circuit depth
Gate errors: Accumulate noise in deeper circuits
Qubit count: 2-qubit architecture is minimal; scaling requires error correction
Calibration drift: Hardware performance varies day-to-day

Encoding Challenges

State preparation: Mapping financial parameters to quantum states requires careful encoding
Range normalization: Financial parameters span wide ranges; quantum states require normalized inputs
Measurement precision: Limited shots affect pricing accuracy

Cross-Platform Comparison

Different noise models: Each hardware platform has unique error characteristics
Calibration schedules: Hardware recalibrated regularly, affecting reproducibility
Gate set differences: Different platforms support different native gate sets

Future Directions

Extension to path-dependent options (Asian, barrier, lookback)
Multi-asset option pricing
Real-time pricing with streaming data
Integration with quantum Monte Carlo methods
Hybrid classical-quantum pricing pipelines for production systems