Quantum Circuit-Based Adaptation for Credit Risk Analysis

TL;DR

This work addresses the challenge of running credit risk analysis algorithms on NISQ hardware by developing hardware-aware variational quantum circuits that load Gaussian latent-factor distributions for a Gaussian Conditional Independence (GCI) framework. The approach maps conditional default probabilities to quantum amplitudes via PD_k(z)=sin^2(α z+β) with the latent factor encoded on an n-qubit register and uses pulse-level, hardware-aware transpilation to minimize gate depth and connectivity constraints. Through two- and three-qubit Gaussian loaders and a GCI circuit, the study demonstrates that hardware-specific rotation angles and transpilation choices are crucial to closely reproduce target distributions and align VaR/CDF outcomes with classical baselines within hardware noise. The results provide a practical pathway for implementing quantum adaptations of financial algorithms on current devices and offer guidance for hardware-aware compiler strategies in quantum finance.

Abstract

Noisy and Intermediate-Scale Quantum, or NISQ, processors are sensitive to noise, prone to quantum decoherence, and are not yet capable of continuous quantum error correction for fault-tolerant quantum computation. Hence, quantum algorithms designed in the pre-fault-tolerant era cannot neglect the noisy nature of the hardware, and investigating the relationship between quantum hardware performance and the output of quantum algorithms is essential. In this work, we experimentally study how hardware-aware variational quantum circuits on a superconducting quantum processing unit can model distributions relevant to specific use-case applications for Credit Risk Analysis, e.g., standard Gaussian distributions for latent factor loading in the Gaussian Conditional Independence model. We use a transpilation technique tailored to the specific quantum hardware topology, which minimizes gate depth and connectivity violations, and we calibrate the gate rotations of the circuit to achieve an optimized output from quantum algorithms. Our results demonstrate the viability of quantum adaptation on a small-scale, proof-of-concept model inspired by financial applications and offer a good starting point for understanding the practical use of NISQ devices.

Figures (30)

• Figure 1: Quantum circuit for the target GCI model with one asset and one risk factor. The green box underlines the Gaussian loading sub-circuit.
• Figure 2: Two-qubit quantum circuit for the Gaussian distribution loading.
• Figure 3: Three-qubit quantum circuit for the Gaussian distribution loading.
• Figure 4: Schematics of the processor, with focus on three qubit register A6, D3, C4. The processor has 4 feedlines for multiplexed readout: feedline A (light green), coupled to $6$ qubits, and feedlines B (pink), C (indigo), and D (purple), each coupled to $5$ qubits. In green: low frequency qubits; in blue: mid frequency qubits; in red: high frequency qubits; in yellow: isolated qubits. White color identifies qubits that are not operational.
• Figure 5: Comparison between probability amplitudes of $|00\rangle,|01\rangle,|10\rangle,|11\rangle$ states and theoretical model as a function of $\theta_{1} \in \left\{90^{\circ},450^{\circ}\right\}$ and fixed $\theta_{0}=90^{\circ}$.