Quantifying the advantages of applying quantum approximate algorithms to portfolio optimisation

summary

Video file (mp4)

The gist

A quantum algorithm for portfolio optimisation, specifically an end-to-end Quantum Approximate Optimization Algorithm (QAOA), is presented to solve the discrete global minimum variance portfolio

In short

This quantum algorithm uses QAOA to solve discrete global minimum variance portfolio problems (DGMVP) by encoding asset weights into binary variables. The method involves designing specific initial states, cost operators, and mixing operators for the circuit. Results show that warm-started initial states improve solution quality, though achieving significant quantum advantage requires drastically reducing noise.

Key concepts

Discrete Global Minimum Variance Portfolio (DGMVP) Model
This model seeks the lowest possible risk portfolio when you can only trade a specific, discrete number of assets. It involves minimizing a quadratic function subject to constraints like a fixed total budget and ensuring weights are non-negative and adhere to specific trading lot sizes.
Binary Block Encoding Method
To run the problem on a quantum computer, asset weights are converted into binary variables using an 'l'-length block of qubits. This encoding maps the continuous weight vector onto discrete Pauli-Z measurements, allowing the quantum circuit to process the portfolio optimization task.
QAOA Ansatz
The QAOA is a parameterized circuit structure used for optimization problems. It alternates between applying a cost operator (which measures how good a potential solution is) and a mixing operator (which explores the solution space). The number of alternating layers determines the circuit's depth.

Terminology used across episodes

This episode discusses

The paper

Quantifying the advantages of applying quantum approximate algorithms to portfolio optimisation · Read on arXiv

Haomu Yuan, *Christopher K. Long, *Hugo V. Lepage, *Crispin H. W. Barnes

Cavendish Laboratory, Department of Physics, University of Cambridge

We present a quantum algorithm for portfolio optimisation. Specifically, We present san end-to-end quantum approximate optimisation algorithm to solve the discrete global minimum variance portfolio model. This model finds a portfolio of risky assets with the lowest possible risk contingent on the number of traded assets being discrete. We provide a complete pipeline for this model and analyse its viability for noisy intermediate-scale quantum computers. We design initial states, a cost operator, and ansätze within a binary encoding. Further, we perform numerical simulations to analyse several optimisation routines, including layerwise optimisation, utilising constrained optimisation by linear approximation and dual annealing. Finally, we consider the impacts of thermal relaxation and stochastic measurement noise. We find dual annealing with a layerwise optimisation routine provides the most robust performance. We observe that realistic thermal relaxation noise levels preclude quantum advantage. However, stochastic measurement noise will dominate when hardware sufficiently improves. Within this regime, we numerically demonstrate a favourable scaling in the number of shots required to obtain the global minimum -- an indication of quantum advantage in portfolio optimisation.

DOI: 10.1088/2058-9565/ae4a48

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Quantifying the advantages of applying quantum approximate algorithms to portfolio optimisation".

Mira: A quantum algorithm for portfolio optimisation, specifically an end-to-end Quantum Approximate Optimization Algorithm (QAOA), is presented to solve the discrete global minimum variance portfolio (DGMVP) model,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: Essentially, the main thesis is that they’ve built this entire system from scratch to tackle the DGMVP model using QAOA, and they want to demonstrate how well this approach scales when you look at asset numbers or the level of discretization required. They're showing how it compares to classical methods in terms of performance metrics.

Mira: What really matters here is their focus on quantifying the advantage; they aren't just claiming it works, but they are numerically simulating and analyzing several optimization routines, like dual annealing versus layerwise optimization using COYLA or DA, to establish which strategy is most efficient.

Lev: That comparative analysis between different optimisers sounds important for real-world deployment because you can't rely on just one specific classical method working perfectly; you need a robust strategy that doesn't break down easily.

Kai: And they found that dual annealing paired with a layerwise optimization routine gives the most robust performance, which tells us there’s a specific way to combine the quantum and classical parts to get better results. They also analyzed how thermal relaxation and stochastic measurement noise affect these outcomes.

Mira: The analysis regarding noise is significant because they find that only limited quantum advantage can be achieved unless those noise levels are reduced by orders of magnitude, which puts practical constraints on what we expect from near-term devices right now.

Lev: That's a sobering thought; it suggests that while the theoretical potential is there, the engineering hurdle for achieving useful results on current NISQ hardware is substantial and requires significant error mitigation.

Conclusion: Kai: To summarize what this means in simpler terms is that they’ve moved beyond just showing a small proof of concept; they've built a full system designed to solve a complex financial optimization problem, and their analysis shows exactly where this approach shines compared to existing classical methods.

Mira: The implication I see is that for discrete problems like this portfolio selection, we might be able to see how quantum approximate algorithms can offer an advantage in finding solutions that are genuinely near the optimum, even if the full solution isn't perfectly found in one go.

Lev: From an error correction standpoint, the findings about noise levels give us a clear picture of what kind of hardware improvements we need to see before this specific approach becomes practically applicable for solving these kinds of problems reliably.

Kai: So, while they show potential on current NISQ devices, the title points to their work being about quantifying that advantage precisely, which is a necessary step before we expect widespread adoption in finance or other fields.

Mira: Ultimately, the paper suggests that the combination of a well-designed ansatz and a smart classical optimization routine can lead to better solutions than relying on simpler classical solvers for these constrained integer problems.

Lev: We need to keep watching how these scaling analyses evolve; if they can show improvements in sample reduction over classical methods as asset numbers grow, that’s the kind of practical result that would really move the needle for us in error correction research.

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