# Portfolio Optimisation Using the D-Wave Quantum Annealer

arXiv: https://arxiv.org/abs/2012.01121 · HTML: https://mlsanity.com/paper/2012.01121/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2020.

## Built on by (most cited first, 10 of 10)

- [Quantum-Enhanced Parameter-Efficient Learning for Typhoon Trajectory Forecasting](https://mlsanity.com/paper/2505.09395/) (2025)
- [D-Wave's Nonlinear-Program Hybrid Solver: Description and Performance Analysis](https://mlsanity.com/paper/2410.07980/) (2024)
- [Solving QUBO on the Loihi 2 Neuromorphic Processor](https://mlsanity.com/paper/2408.03076/) (2024)
- [SWIFT-FMQA: Enhancing Factorization Machine with Quadratic-Optimization Annealing via Sliding Window](https://mlsanity.com/paper/2507.21024/) (2025)
- [Multi-objective QUBO Solver: Bi-objective Quadratic Assignment](https://mlsanity.com/paper/2205.13399/) (2022)
- [A Study of Scalarisation Techniques for Multi-Objective QUBO Solving](https://mlsanity.com/paper/2210.11321/) (2022)
- [Applying Ising Machines to Multi-objective QUBOs](https://mlsanity.com/paper/2305.11648/) (2023)
- [A Quantum Model for Constrained Markowitz Modern Portfolio Using Slack Variables to Process Mixed-Binary Optimization under QAOA](https://mlsanity.com/paper/2601.03278/) (2025)
- [Variational Quantum Circuit-Based Reinforcement Learning for Dynamic Portfolio Optimization](https://mlsanity.com/paper/2601.18811/) (2026)
- [Stage-dependent integer-binary encoding in factorization-machine black-box optimization](https://mlsanity.com/paper/2606.23188/) (2026)

## Abstract (arXiv)

The first quantum computers are expected to perform well at quadratic optimisation problems. In this paper a quadratic problem in finance is taken, the Portfolio Optimisation problem. Here, a set of assets is chosen for investment, such that the total risk is minimised, a minimum return is realised and a budget constraint is met. This problem is solved for several instances in two main indices, the Nikkei225 and the S&P500 index, using the state-of-the-art implementation of D-Wave's quantum annealer and its hybrid solvers. The results are benchmarked against conventional, state-of-the-art, commercially available tooling. Results show that for problems of the size of the used instances, the D-Wave solution, in its current, still limited size, comes already close to the performance of commercial solvers.