Paper: arXiv 2301.13295

Authors: Cameron Perot

Abstract

In this thesis we explore using the D-Wave Advantage 4.1 quantum annealer to sample from quantum Boltzmann distributions and train quantum Boltzmann machines (QBMs). We focus on the real-world problem of using QBMs as generative models to produce synthetic foreign exchange market data and analyze how the results stack up against classical models based on restricted Boltzmann machines (RBMs). Additionally, we study a small 12-qubit problem which we use to compare samples obtained from the Advantage 4.1 with theory, and in the process gain vital insights into how well the Advantage 4.1 can sample quantum Boltzmann random variables and be used to train QBMs. Through this, we are able to show that the Advantage 4.1 can sample classical Boltzmann random variables to some extent, but is limited in its ability to sample from quantum Boltzmann distributions. Our findings indicate that QBMs trained using the Advantage 4.1 are much noisier than those trained using simulations and struggle to perform at the same level as classical RBMs. However, there is the potential for QBMs to outperform classical RBMs if future generation annealers can generate samples closer to the desired theoretical distributions.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel empirical investigation into using D-Wave quantum annealers for training Quantum Boltzmann Machines on foreign exchange data. While hardware noise limits performance compared to classical RBMs, the rigorous comparative framework and early experimental insights on quantum hardware provide significant value to quantum finance literature.

Research Flowchart

  flowchart TD
    A[Goal: Evaluate QBMs via D-Wave Advantage 4.1 for FX Market Data Generation] --> B[Data Input: FX Market Data & 12-Qubit Synthetic Baseline]
    B --> C[Methodology: Sample Quantum Boltzmann Distributions on D-Wave]
    C --> D[Train & Compare Generative Models: QBMs vs Classical RBMs]
    D --> E[Outcome 1: Hardware noise limits D-Wave's ability to sample true quantum distributions]
    D --> F[Outcome 2: QBMs on current hardware perform below classical RBMs, but hold future potential]