Derivative Pricing using Quantum Signal Processing

ArXiv ID: 2307.14310 “View on arXiv”

Authors: Unknown

Abstract

Pricing financial derivatives on quantum computers typically includes quantum arithmetic components which contribute heavily to the quantum resources required by the corresponding circuits. In this manuscript, we introduce a method based on Quantum Signal Processing (QSP) to encode financial derivative payoffs directly into quantum amplitudes, alleviating the quantum circuits from the burden of costly quantum arithmetic. Compared to current state-of-the-art approaches in the literature, we find that for derivative contracts of practical interest, the application of QSP significantly reduces the required resources across all metrics considered, most notably the total number of T-gates by $\sim 16$x and the number of logical qubits by $\sim 4$x. Additionally, we estimate that the logical clock rate needed for quantum advantage is also reduced by a factor of $\sim 5$x. Overall, we find that quantum advantage will require $4.7$k logical qubits, and quantum devices that can execute $10^9$ T-gates at a rate of $45$MHz. While in this work we focus specifically on the payoff component of the derivative pricing process where the method we present is most readily applicable, similar techniques can be employed to further reduce the resources in other applications, such as state preparation.

Keywords: Quantum Computing, Quantum Signal Processing, Derivative Pricing, Quantum Resource Estimation, T-gate Reduction, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper presents advanced quantum signal processing (QSP) theory with significant mathematical derivations, but focuses on resource estimation for future quantum hardware rather than providing backtest-ready code or empirical market data.

  flowchart TD
    A["Research Goal<br>Determine if Quantum Signal Processing (QSP)<br>can reduce quantum resources for derivative pricing"] --> B["Methodology: QSP Approach"]
    
    B --> C["Data Inputs<br>Financial derivative payoff functions"]
    
    C --> D["Key Process<br>Encode payoff directly into quantum amplitudes<br>via QSP unitary, bypassing quantum arithmetic"]
    
    D --> E["Comparison Benchmark<br>Compare against current state-of-the-art<br>quantum arithmetic methods"]
    
    E --> F["Resource Estimation<br>Calculate logical qubits, T-gates,<br>and clock rate requirements"]
    
    F --> G["Key Outcomes<br>1. T-gates reduced by ~16x<br>2. Logical qubits reduced by ~4x<br>3. Quantum advantage threshold: 4.7k qubits,<br>45MHz clock rate for 10^9 T-gates"]
    
    G --> H["Future Applications<br>Extensible to state preparation<br>and other quantum finance algorithms"]