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.
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.
We report the largest trapped-ion hardware demonstration of lattice protein-folding optimization to date, using bias-field digitized counterdiabatic quantum optimization (BF-DCQO) on a fully connected 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. Six peptide sequences with 14-16 amino-acid residues are encoded using a coarse-grained tetrahedral lattice model, yielding higher-order spin-glass Hamiltonians with long-range interactions involving up to five-body terms and mapped to 46-61 qubits. The resulting instances are demanding for near-term quantum hardware because low-energy configurations must satisfy backbone-geometry constraints while optimizing dense residue-contact interactions. BF-DCQO uses a non-variational bias-feedback mechanism, where low-energy samples from each round define longitudinal fields that guide subsequent quantum evolutions. Across the studied instances, BF-DCQO shifts raw sampled energy distributions toward lower energies than uniform random sampling, with the strongest improvements appearing in residue-contact variables. To preserve this signal, we introduce a consensus-based post-processing pipeline that combines quantum-learned contact information with feasible backbone geometries. The resulting hybrid workflow reaches the classical reference energy in multiple instances and improves over the corresponding random-seeded pipeline. These results show that BF-DCQO can generate structured samples for dense protein-folding Hamiltonians at previously unexplored trapped-ion scales.
Portfolio diversification - a cornerstone of modern investment management - can be formulated as a Maximum Independent Set (MIS) problem on asset correlation graphs. Solving this problem at scale is computationally challenging, motivating the exploration of quantum algorithms for practical financial optimization. We propose an end-to-end pipeline leveraging qReduMIS, a recursive hybrid quantum-classical algorithm. Rather than using quantum optimization to directly produce a final solution, qReduMIS leverages independent set measurements from the Quantum Approximate Optimization Algorithm (QAOA) to identify frozen nodes - vertices likely to belong to optimal solutions - thereby guiding and unblocking subsequent (provably optimal) classical reductions on the remaining graph. We benchmark qReduMIS on real financial data from four major market indices with up to 225 assets, executing experiments on Quantinuum's 98-qubit trapped-ion Helios system, with QAOA circuits acting on kernels of up to 78 qubits and 1016 two-qubit gates. While standalone QAOA fails to find the optimal solution for two of the largest indices (S&P 100 and Nikkei 225), qReduMIS achieves success probabilities of 0.40 and 0.95, respectively, with average approximation ratios ≥0.96 across all four indices. We perform a systematic benchmark on the Quantinuum H2-1 noisy emulator over 73 asset correlation graphs of varying size showing that, for p=2 QAOA layers, the optimal time-to-solution scaling exponent of qReduMIS is 3.2 times smaller than that of standalone QAOA.
Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline targeting portfolio optimization and rebalancing problems with constraints. The pipeline decomposes the optimization problem into constrained subproblems, which are then solved separately and aggregated to give a final result. Our pipeline includes three main components: preprocessing of correlation matrices based on random matrix theory, modified spectral clustering based on Newman's algorithm, and risk rebalancing. Our empirical results show that our pipeline consistently decomposes real-world portfolio optimization problems into subproblems with a size reduction of approximately 80%. Since subproblems are then solved independently, our pipeline drastically reduces the total computation time for state-of-the-art solvers. Moreover, by decomposing large problems into several smaller subproblems, the pipeline enables the use of near-term quantum devices as solvers, providing a path toward practical utility of quantum computers in portfolio optimization.
Cardinality-constrained portfolio selection is routinely cast as a quadratic unconstrained binary optimization (QUBO) and submitted to a quantum processing unit (QPU) for direct annealing. We show that this standard penalty encoding is the binding constraint for direct-QPU execution on current D-Wave Pegasus and Zephyr hardware. Expanding the exact cardinality penalty contributes a dense rank-one term that makes the logical interaction graph complete regardless of the covariance, producing chain-break fractions from 83% at small universes up to 92% at the full forty-nine-industry Fama--French universe, and zero feasible raw samples at every tested scale. Topology-aware sparsification reduces chain breaks to near zero, but any sparsifier that removes off-diagonal entries also dilutes the cardinality constraint; an ablation reveals that this sparsify-and-project pipeline is dominated by the classical projector, not the QPU. We propose removing the penalty entirely: sample an objective-only QUBO built from expected returns and the risk-scaled covariance on hardware, and enforce cardinality classically through a deterministic feasibility projector. Across 4,468 saved embedding records on live Pegasus and Zephyr hardware, spanning equities up to forty-nine assets and football-betting instances up to forty-eight, this penalty-free pipeline reduces mean chain-break fractions from 71%--92% down to at most 0.04%, and post-processed regret is at most 0.03% relative to greedy classical references at every tested scale. We do not claim quantum advantage; the penalty encoding, not the sparse hardware topology, is the limiting factor for direct-QPU portfolio optimization at currently accessible scales.
We present a scalable, hardware-aware methodology for extending the Variational Quantum Eigensolver (VQE) to large, realistic Dynamic Portfolio Optimization (DPO) problems. Building on the scaling strategy from our previous work, where we tailored a VQE workflow to both the DPO formulation and the target QPU, we now put forward two significant advances. The first is the implementation of the Ising Sample-based Quantum Configuration Recovery (ISQR) routine, which improves solution quality in Quadratic Unconstrained Binary Optimization problems. The second is the use of the VQE Constrained method to decompose the optimization task, enabling us to handle DPO instances with more variables than the available qubits on current hardware. These advances, which are broadly applicable to other optimization problems, allow us to address a portfolio with a size relevant to the financial industry, consisting of up to 38 assets and covering the full Spanish stock index (IBEX 35). Our results, obtained on a real Quantum Processing Unit (IBM Fez), show that this tailored workflow achieves financial performance on par with classical methods while delivering a broader set of high-quality investment strategies, demonstrating a viable path towards obtaining practical advantage from quantum optimization in real financial applications.
Direct quantum-annealer portfolio optimization is commonly formulated as a penalty-encoded QUBO and submitted to D-Wave hardware. We show that this standard formulation fails on current devices and identify the structural reason: the cardinality penalty A(1^T x - K)^2 contributes a dense rank-one matrix A·11^T that makes the logical graph complete regardless of the underlying covariance structure, producing chain-break fractions of 83% at N=24 rising to 92% at N=49 on both Pegasus and Zephyr, and zero feasible samples. Attempting to fix this through topology-aware sparsification reveals a second problem: any sparsifier that removes off-diagonal entries also dilutes the cardinality constraint. Raw samples remain infeasible even when chains no longer break. An ablation shows that for structurally favorable cases (betting with settlement-graph priors), the classical feasibility projector alone explains the result, not the QPU. We propose dropping the penalty entirely: build the objective-only QUBO Q_obj = -diag(mu) + lambda*Sigma, sample on hardware, and enforce cardinality classically. On D-Wave Advantage and Advantage2 for equities up to N=49 (full FF49 universe) and betting up to N=48, mean chain-break fractions (per sample, averaged overreads) drop from 71-92% to at most 0.04%. The QPU returns lower-energy feasible portfolios than the greedy heuristic on betting at N in {39, 48} (an energy comparison, not a proof of optimality), and equity post-processed regret is at most 0.03% at all tested scales. These results establish that the penalty encoding, not the sparse hardware topology, is the binding constraint for direct QPU portfolio optimization at currently accessible scales.