NISQ Portfolio Benchmarks Reveal Inescapable Trade-Off Between Expressibility and Coherence

The June 2026 arXiv preprint (not yet peer-reviewed) delivers the first systematic hardware benchmark pitting a Hardware-Efficient Variational Quantum Neural Network against Warm-Start QAOA on a hybrid Mean-Variance plus CVaR objective using up to 16 NIFTY-50 assets mapped to IBM heavy-hex processors. By introducing a classical proxy matrix that sidesteps the auxiliary-qubit overhead of exact CVaR, the authors quantify how routing-induced SWAP layers rapidly erode WS-QAOA’s theoretical fidelity while HE-VQNN remains coherent yet mathematically too restrictive to capture dense tail-risk correlations. This finding extends earlier theoretical warnings in Farhi et al. (2014) on QAOA depth scaling and empirical NISQ routing studies (e.g., IBM’s own heavy-hex topology papers) by grounding them in realistic portfolio risk metrics rather than toy Max-Cut instances. What the source underplays is the compounding effect of market-regime shifts: NIFTY-50 correlations are themselves non-stationary, so even an all-to-all device would still face expressibility limits unless variational ansatze incorporate dynamic feature maps—an avenue left unexplored. The coherence-expressibility dilemma therefore appears structural, not merely topological, implying that near-term quantum advantage in finance will require either radically improved connectivity or hybrid algorithms that offload tail-risk estimation entirely to classical post-processing.