[Paper Review] Towards Prediction of Financial Crashes with a D-Wave Quantum Computer

Yongcheng Ding, Gonzalez-Conde, Javier+8 more|arXiv (Cornell University)|Apr 11, 2019

Quantum Computing Algorithms and Architecture38 references9 citations

TL;DR

This paper proposes using a D-Wave 2000Q quantum annealer to predict financial crashes by solving a higher-order unconstrained binary optimization (HUBO) problem derived from a nonlinear financial network model. The HUBO is mapped to a QUBO using ancilla qubits for two-qubit interactions, enabling quantum annealing to find the equilibrium state; the experiment demonstrates proof-of-concept accuracy on a small-scale network, validating the approach against classical exhaustive search.

ABSTRACT

Prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can guarantee to find optimal solutions efficiently. We experimentally explore a novel approach to this problem by using a D-Wave quantum computer, benchmarking its performance for attaining financial equilibrium. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed to a spin-$1/2$ Hamiltonian with at most two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. The size of the simulation is mainly constrained by the necessity of a large quantity of physical qubits representing a logical qubit with the correct connectivity. Our experiment paves the way to codify this quantitative macroeconomics problem in quantum computers.

Motivation & Objective

• To address the NP-hard problem of predicting financial crashes in complex networks using quantum computing.
• To implement a quantum annealing approach for simulating financial network equilibria under perturbation.
• To benchmark the performance of a D-Wave 2000Q quantum annealer on a real-world financial modeling problem.
• To explore strategies for reducing ancilla qubit overhead in HUBO-to-QUBO mappings to improve scalability.
• To validate the quantum approach against classical exhaustive search on a small-scale financial network.

Proposed method

• The financial network equilibrium problem is formulated as a higher-order unconstrained binary optimization (HUBO) problem.
• The HUBO is transformed into a quadratic unconstrained binary optimization (QUBO) problem using ancilla qubits to encode three-body interactions as two-body interactions.
• The QUBO is mapped to a spin-1/2 Ising Hamiltonian with at most two-qubit interactions, suitable for D-Wave's Chimera architecture.
• The ground state of the resulting Hamiltonian is approximated via quantum annealing on the D-Wave 2000Q processor.
• The solution is compared to results from classical exhaustive search to validate accuracy.
• An efficient three-to-two qubit mapping protocol is applied, reducing ancilla qubit count to ~7,000 for improved scalability.

Experimental results

Research questions

• RQ1 Can a D-Wave quantum annealer accurately predict financial crash equilibria in a nonlinear financial network model?
• RQ2 How does the performance of quantum annealing compare to classical exhaustive search on a small-scale financial network?
• RQ3 What is the impact of ancilla qubit overhead on the scalability of HUBO-to-QUBO mappings in quantum annealing?
• RQ4 Can an optimized qubit mapping protocol reduce ancilla qubit requirements while preserving solution fidelity?
• RQ5 To what extent can quantum annealing provide a speedup in forecasting financial network equilibria compared to classical methods?

Key findings

• The D-Wave 2000Q quantum annealer successfully computed the equilibrium state of a small financial network, matching results from classical exhaustive search.
• The quantum approach demonstrated feasibility for predicting financial crashes by identifying network state changes under perturbation.
• The use of a three-to-two qubit mapping protocol reduced ancilla qubit requirements, improving potential scalability.
• The study confirmed that quantum annealing can approximate the ground state of a complex financial Hamiltonian, validating the HUBO-to-QUBO mapping strategy.
• The results support the potential of future specialized quantum annealers with enhanced connectivity and multi-qubit couplings for faster financial risk forecasting.
• The authors estimate that a future quantum annealer with ~5,000 qubits and Pegasus topology could significantly improve network size and accuracy.