RESEARCH

The performance of quantum annealing depends critically on how the available annealing time is distributed along the evolution. Although the Roland–Cerf local-adiabatic schedule is theoretically optimal, it requires complete knowledge of the instantaneous spectral gap, making it impractical for large optimization problems. We propose a computationally inexpensive surrogate schedule based on the worldline magnetization susceptibility measured during simulated quantum annealing. The susceptibility is obtained directly from equilibrium Monte Carlo sampling and identifies the critical region of the anneal without requiring spectral information. Using exact diagonalization of Sherrington–Kirkpatrick spin-glass instances as ground truth, we show that the resulting schedule consistently outperforms conventional linear annealing and, for a substantial fraction of instances, also surpasses the exact Roland–Cerf schedule. We demonstrate that this unexpected behaviour originates from two finite-time failure modes of exact local-adiabatic scheduling: a boundary-gap trap, in which the minimum spectral gap occurs at the end of the anneal, and an oscillatory instability caused by excessively localized time allocation around an interior minimum gap. These results suggest that robust scheduling based on inexpensive equilibrium observables can outperform exact spectral-gap-based strategies under realistic finite-time conditions. The complete methodology is implemented in the open-source Qanneal framework.

Interconnected financial systems are vulnerable to cascading failures arising from cross-holdings and nonlinear contagion, making the analysis and mitigation of systemic risk a challenging computational problem. We develop a unified optimization framework for financial network analysis based on Ising models and Quadratic Unconstrained Binary Optimization (QUBO). Starting from the Elliott–Golub–Jackson financial network model, we extend equilibrium valuation to incorporate threshold-induced failures, formulate the Maximum Cascade Failure Problem, and derive an equivalent QUBO representation. We then formulate the Optimal Bailout Allocation Problem as a controlled Ising model and transform the resulting bi-level optimization into a single joint QUBO that simultaneously determines equilibrium failures and optimal interventions under budget constraints. To characterize the influence of individual institutions, we introduce bailout susceptibility as a response-based measure of systemic importance and develop a susceptibility-driven greedy intervention strategy. Numerical simulations demonstrate equilibrium valuation, worst-case cascade identification, optimal bailout allocation, and susceptibility analysis on financial networks of varying sizes, establishing a unified approach for systemic risk analysis compatible with classical annealing, quantum-inspired optimization, and emerging quantum annealing technologies.

Exact fermion-to-qubit transformations are conventionally regarded as algorithmic tools that translate many-body Hamiltonians into qubit representations for quantum simulation. Here we show that they also define intrinsic geometric representations whose structure encodes physically meaningful information beyond spectral equivalence. We develop a geometric framework based on weighted hypergraphs and coupling-space representations constructed from the Bravyi–Kitaev (BK) and Xia–Bian–Kais (XBK) encodings. Applications to the Hubbard, spinless t–V, single-impurity Anderson, and Kitaev models demonstrate that these connectivity- and transport-based geometric descriptions consistently capture the structural evolution of encoded quantum Hamiltonians across distinct classes of many-body systems.

We present an end-to-end, symmetry-aware pipeline that converts interacting fermionic and quantum-spin models into annealer-ready QUBOs while preserving low-energy physics. The workflow combines Bravyi–Kitaev encoding, exact Z2 symmetry tapering, Xia–Bian–Kais (XBK) diagonalization to a Z-only form, and k→2 local quadratization, with ground energies recovered via a Dinkelbach fixed-point over the resulting Ising objective. We validate the approach across a complexity ladder spanning a frustrated 2D Ising model run on a D-Wave Advantage QPU, finite-temperature 1D Ising checks, a genuinely quantum XXZ spin target, and interacting t–V fermions in 1D and 2D, establishing a practical pathway for mapping quantum matter to current annealers.

This paper addresses the adaptation of fermionic encodings for quantum annealers, focusing on efficient mappings that mitigate hardware constraints through techniques like quadratization.

We present a coupled reduction strategy that integrates the ReduceMin algorithm with an XBK-inspired mapping to systematically transform high–order fermionic terms into quadratic form.

We report enhanced phase sensitivity in a Mach-Zehnder interferometer using single-photon-added coherent states (SPACS), surpassing the Standard Quantum Limit (SQL) in the low-photon-number regime.

Development of constrained optimization routines tailored for frustrated spin glass systems using quantum annealers and hybrid solvers.