Large-scale portfolio optimization on a trapped-ion quantum computer

TL;DR

Overall, the results establish a hardware-tested route for scaling financial optimization problems, defined by a trade space in which executable problem size and circuit cost are balanced against the resulting solution quality.

Abstract

We present an end-to-end pipeline for large-scale portfolio selection with cardinality constraints and experimentally demonstrate it on trapped-ion quantum processors using hardware-aware decomposition. Building on RMT-based correlation-matrix denoising and community detection, we identify correlated asset groups and introduce a correlation-guided greedy splitting scheme that caps each cluster by the executable qubit budget. Each cluster defines a hardware-embeddable QUBO subproblem that we solve using bias-field digitized counterdiabatic quantum optimization (BF-DCQO), a non-variational method that avoids classical parameter-training loops. We recombine low-energy candidates into global portfolios and enforce feasibility with a two-stage post-processing routine: fast repair followed by a cardinality-preserving swap local search. We benchmark the workflow on a 250-asset universe taken from the S&P 500 and execute subproblems on a 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. We observe that larger executable subproblem sizes reduce decomposition error and systematically improve final objective values and risk-return trade-offs relative to randomized baselines under identical post-processing. Overall, the results establish a hardware-tested route for scaling financial optimization problems, defined by a trade space in which executable problem size and circuit cost are balanced against the resulting solution quality.

Figures (6)

• Figure 1: Schematic of the end-to-end pipeline: (a) original problem; (b) community detection and size-bounded splitting produce clusters with $|\mathcal{C}_m|\le Q_{\max}$; (c) each cluster is mapped to an Ising instance and solved via BF-DCQO (or classically for small clusters); (d--e) low-energy cluster candidates are recombined into global portfolios and refined using a cardinality-preserving local search.
• Figure 2: Energy distribution of global candidate portfolios under different hardware and pruning configurations. From top to bottom, the panels correspond to (a) the 36-qubit decomposition with high pruning on IonQ Forte, (b) the 36-qubit decomposition with medium pruning on IonQ Forte, and (c) the 64-qubit decomposition with medium pruning on the IonQ 64-qubit Barium development system. Orange histograms show the energy distribution obtained by running BF-DCQO on the largest subproblem, applying the two-phase local search at the cluster level and then, recombining into global candidates. Blue histograms show the corresponding distributions after applying the two-phase local-search post-processing. Red dotted vertical lines indicate the energy of the recombined optimal solution obtained by merging the individually optimal subproblem solutions, while blue dash-dotted lines denote this recombined optimum after local search. The black dashed lines mark the global optimum of the full problem, obtained by the Gurobi solver.
• Figure 3: Return-risk distribution of global candidate portfolios generated by the clustered BF-DCQO pipeline under different hardware and pruning configurations. From top to bottom, the panels correspond to (a) the 36-qubit decomposition with high pruning, (b) the 36-qubit decomposition with medium pruning, and (c) the 64-qubit decomposition with medium pruning. Square markers denote portfolios obtained from random initialization followed by classical post-processing, while circular markers represent post-processed candidates. The global reference portfolio is indicated by a red star, and the recombined reference portfolio is shown as a blue ×. The color scale encodes the objective value of each portfolio. The post-processing budget is intentionally small (Sec. \ref{['subsec:local_search_cardinality']}) so that differences primarily reflect the quality of the initial candidate pools.
• Figure 4: Superposed top-$10$ samples of each iteration of BF-DCQO on IonQ Forte using high pruning. We show the distributions before and after cluster-level local search for (a) the first $36$-qubit cluster, (b) the second $36$-qubit cluster and (c) the last $36$-qubit cluster.
• Figure 5: Superposed top-$10$ samples of each iteration of BF-DCQO on IonQ Forte using medium pruning. We show the distributions before and after cluster-level local search for (a) the first $36$-qubit cluster, (b) the second $36$-qubit cluster and (c) the last $36$-qubit cluster.