We audit how much of D-Wave's hybrid quantum-classical portfolio-optimization service is actually quantum. On cardinality-constrained mean-variance-turnover instances spanning N equal to 10 to 640 with a Gurobi MIQP optimality anchor, the constraint-native LeapHybridCQM service matches Gurobi's proven optimum on all 54 instances where Gurobi proves optimality, but the mean QPU access time is only 0.034 seconds out of a 5-second wall-clock budget, roughly 0.7 percent of the run. The remaining roughly 99 percent is the service's classical decomposition, sub-problem assembly, and feasibility-aware reassembly, so the reported D-Wave hybrid win on this problem class is a constraint-native classical pipeline with a small QPU contribution rather than a quantum-sampling win. Two structural results sharpen this audit. First, the cardinality penalty contributes a dense rank-one term that makes the penalty-encoded logical graph fully connected regardless of the original covariance density, collapsing the intended density benchmark axis for all penalty-encoded paths while leaving the constraint-native sparsity intact. Second, the constraint-native service returns identical solutions at every tested wall-clock budget from 5 to 300 seconds and across 10 repeated calls, a determinism property of the service on this problem class. Together with two classical baselines, namely Gurobi MIQP and simulated annealing, and a comparison against the penalty-encoded hybrid interface, these results extend the prior constraint-native versus penalty-encoded observation of Sakuler et al. from the statement that the constraint-native interface handles constraints natively to the operational decomposition of where the win actually originates, a finding that reframes how D-Wave hybrid performance should be reported in quantum-finance benchmarks.
We audit how much of D-Wave's hybrid quantum-classical portfolio-optimization service is actually quantum. On cardinality-constrained mean-variance-turnover instances spanning N equal to 10 to 640 with a Gurobi MIQP optimality anchor, the constraint-native LeapHybridCQM service matches Gurobi's proven optimum on all 54 instances where Gurobi proves optimality, but the mean QPU access time is only 0.034 seconds out of a 5-second wall-clock budget, roughly 0.7 percent of the run. The remaining roughly 99 percent is the service's classical decomposition, sub-problem assembly, and feasibility-aware reassembly, so the reported D-Wave hybrid win on this problem class is a constraint-native classical pipeline with a small QPU contribution rather than a quantum-sampling win. Two structural results sharpen this audit. First, the cardinality penalty contributes a dense rank-one term that makes the penalty-encoded logical graph fully connected regardless of the original covariance density, collapsing the intended density benchmark axis for all penalty-encoded paths while leaving the constraint-native sparsity intact. Second, the constraint-native service returns identical solutions at every tested wall-clock budget from 5 to 300 seconds and across 10 repeated calls, a determinism property of the service on this problem class. Together with two classical baselines, namely Gurobi MIQP and simulated annealing, and a comparison against the penalty-encoded hybrid interface, these results extend the prior constraint-native versus penalty-encoded observation of Sakuler et al. from the statement that the constraint-native interface handles constraints natively to the operational decomposition of where the win actually originates, a finding that reframes how D-Wave hybrid performance should be reported in quantum-finance benchmarks.
We audit how much of D-Wave's hybrid quantum-classical portfolio-optimization service is actually quantum. On cardinality-constrained mean-variance-turnover instances spanning N = 10 to 640 with a Gurobi MIQP optimality anchor, the constraint-native LeapHybridCQM service matches Gurobi's proven optimum on all 54 instances where Gurobi proves optimality, but mean QPU access time is only 0.034 seconds out of a 5-second wall-clock budget, roughly 0.7% of the run. The remaining ~99% is the service's classical decomposition, sub-problem assembly, and feasibility-aware reassembly. The reported D-Wave hybrid win on this problem class is therefore a constraint-native classical pipeline with a small QPU contribution, not a quantum-sampling win. Two structural results sharpen this audit: (i) the cardinality penalty contributes a dense rank-one term that makes the penalty-encoded logical graph fully connected regardless of the original covariance density, collapsing the intended density benchmark axis for all penalty-encoded paths while leaving CQM's sparsity intact; (ii) the CQM service returns identical solutions at every tested wall-clock budget from 5 to 300 seconds and across 10 repeated calls, a determinism property of the service on this problem class. Together with two classical baselines (Gurobi MIQP and simulated annealing) and a comparison against the penalty-encoded LeapHybridBQM interface, these results extend the prior CQM-vs-BQM observation of Sakuler et al. (2025) from "CQM handles constraints natively" to the operational decomposition of where the win actually originates, a finding that reframes how D-Wave hybrid performance should be reported in quantum-finance benchmarks.
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.
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.
This paper evaluates whether a native constrained formulation, rather than a penalty-style QUBO conversion, helps D-Wave execution pathways recover fault-tree truth-objective solutions, using the locked 80-instance benchmark cohort from a prior platform-feasibility study (Paper 17), stratified into four problem-size groups of twenty instances each (16, 25, 33, and 42 Paper 17 QUBO variables). Two execution arms operate on the same cohort and the same frozen truth layer. Arm A is a direct-QPU pilot on a constraint-level QUBO (CL-QUBO)-derived penalty-style binary quadratic model (BQM). Arm B is a native constrained quadratic model (CQM) submitted to the D-Wave hybrid CQM solver, in which the fault-tree gate constraints are preserved as explicit constraints rather than compiled into penalties. The truth layer uses a minimum-cardinality criterion: an instance is truth-positive when a returned feasible sample matches the canonical truth objective. On the canonical eight-instance pilot, the direct-QPU Arm A recovered truth on 4 of 8 instances, with zero-truth behavior in the larger pilot strata, whereas the native hybrid CQM Arm B recovered truth on 8 of 8. Arm B recovery extended to a balanced twelve-instance set (12 of 12) and to the full locked cohort, recovering a truth-positive feasible solution on all 80 instances, with zero zero-truth instances and zero objective-below-truth anomalies, including 20 of 20 in every size stratum. This paper does not claim quantum advantage, computational speedup, or isolated QPU contribution within the hybrid solver; because the two arms differ in both formulation and pathway, it does not claim to isolate formulation as the sole causal factor. A retrospective timing audit of the preserved execution artifacts, performed without any resubmission, recovered complete solver timing metadata for all 88 jobs and found that two 16-variable instances were solved entirely by classical presolve with zero QPU access time, which bounds the interpretation of the full-cohort result without changing any recovery count. The results support semantic preservation as a central design requirement: the native constrained CQM pathway recovered the truth objective across the full cohort, while the penalty-style direct-QPU pilot showed size-limited recovery under the tested settings.
This paper evaluates D-Wave execution pathways for QUBO-based recovery of fault-tree minimum-cardinality cut sets using a balanced 80-instance benchmark cohort stratified into four problem-size groups of twenty instances each (16, 25, 33, and 42 QUBO variables). The experimental target is recovery of a minimum-cardinality cut set under a QUBO objective that minimizes the number of active basic events; the study does not enumerate the full minimal cut set family. Four execution arms operate on identical canonical payloads: a strict direct-QPU primary arm (Advantage2_system1, 1000 reads, 20 μs anneal time), a 5000-read direct-QPU replicate, a local classical simulated-annealing (SA) baseline at 1000 reads, and a hybrid BQM arm (LeapHybridSampler, 30 s). A deterministic fault-tree truth layer is used for per-sample validation; exhaustive QUBO ground-state enumeration via dimod.ExactSolver is performed only for the 16-variable stratum (20 of 20 confirmed), with the larger strata verified against deterministic fault-tree evaluation rather than exhaustive enumeration. Direct-QPU truth recovery degrades monotonically with problem size: zero-truth instance counts are 3, 10, 18, and 20 out of 20 under the 1000-read primary, and 0, 3, 11, and 19 under the 5000-read replicate. Classical SA at the same read budget recovers truth more often than direct QPU at every size (zero-truth counts 0, 1, 4, 13). Hybrid BQM recovered the canonical minimum-cardinality cut set on all 80 instances under the tested settings, including all 20 at 42 variables. This paper does not claim quantum advantage, computational speedup, replacement of classical cut-set algorithms, or full minimal-cut-set enumeration; it characterizes platform-level feasibility, minimum-cardinality correctness recovery, and size-stratified behavior across the four tested pathways. A device operation-timing analysis added in this revision shows that the fivefold read-budget increase corresponds to only a 4.18-fold increase in QPU access time, because programming is a fixed per-submission cost; it is reported as resource accounting and supports no time-to-solution, speedup, or cross-pathway equal-time claim.
This study compares the performance of D-Wave’s two quantum-classical hybrid optimization solvers, which integrate quantum computing principles with classical optimization techniques to solve complex optimization problems. It focuses on the Binary Quadratic Model (BQM) solver, which encodes optimization problems using a binary quadratic formulation, and the Constrained Quadratic Model (CQM) solver, which can incorporate constraints into the model. The solvers were tested on five combinatorial optimization problems: Traveling Salesman Problem (TSP), Quadratic Knapsack Problem (QKP), Quadratic Assignment Problem (QAP), Weighted Max-Cut Problem (WMP), and Maximum Clique Problem (MCP). The goal is to quantify the accuracy of solutions compared to the optimal ones. Experiments on multiple instances with known optimal solutions examined solver behavior and solution quality. At default execution durations, the CQM solver generally outperforms BQM with lower error and higher consistency. Across all test problem instances in TSP, QKP, QAP, and WMP, the CQM solver achieved lower average absolute errors by 48.38, 27.83, 21.29, and 0.05 percentage points, respectively, compared to the BQM solver. An exception was found in MCP, where the BQM solver outperformed the CQM solver by 0.75 percentage points. These findings provide a guide for end users to understand the characteristics of the solvers and to select the appropriate solver for their specific optimization problems.