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Kristel Michielsen

Publications and source records attributed to Kristel Michielsen.

At least 19 recordsLinked to original sources
arXiv2026

Generalized Mean-Field Ising Model as a Benchmark Family with Exact Solutions

Exactly solvable models provide opportunities to understand complex optimization problems while offering controlled benchmarks for computational methods. However, nontrivial models that combine analytical tractability with challenging optimization structure remain scarce. Here, we introduce the Generalized Mean-Field Ising (GMFI) family, a densely connected and inhomogeneous class of Ising Hamiltonians whose ground states can nevertheless be obtained exactly. This exact solution reveals a hidden low-dimensional structure and enables a complete number-theoretic classification of different system sizes and degenerate ground states. Uniquely, the GMFI family can be used to benchmark both quantum and classical optimization methods over system sizes far beyond exact diagonalization. We investigate the GMFI family using several approaches, including theoretical analysis of quantum annealing, experiments on a D-Wave quantum processor, the quantum approximate optimization algorithm (QAOA), imaginary-time evolution (ITE), greedy algorithm, simulated annealing, and a quantum-inspired greedy algorithm. Despite the GMFI model's exact solvability, it exhibits nontrivial algorithmic behavior: although the quantum-annealing gap is expected to decrease with increasing system size, it shows pronounced and unexpected system-size-dependent oscillatory signatures. These results establish GMFI models as a rare bridge between exact many-body theory, number theory, optimization, and quantum hardware, providing a scalable benchmark for identifying and understanding algorithmic limitations in classical and quantum computing.

quant-ph↗
arXiv2026

Empirical Quantum Advantage in Constrained Optimization from Encoded Unitary Designs

We introduce the Constraint-Enhanced Quantum Approximate Optimization Algorithm (CE-QAOA), a shallow, constraint-aware ansatz that operates inside the one-hot product space [n]^m, where m is the number of blocks and each block is initialized in an n-qubit W_n state. We give an ancilla-free, depth-optimal encoder that prepares W_n using n-1 two-qubit rotations per block, and a two-local block-XY mixer that preserves the one-hot manifold and has a constant spectral gap on the one-excitation sector. At the level of expressivity, we establish per-block controllability, implying approximate universality per block. At the level of distributional behavior, we show that, after natural block and symbol permutation twirls, shallow CE-QAOA realizes an encoded unitary 1-design and supports approximate second-moment (2-design) behavior; combined with a Paley-Zygmund argument, this yields finite-shot anticoncentration guarantees. Algorithmically, we wrap constant-depth sampling with a deterministic feasibility checker to obtain a polynomial-time hybrid quantum-classical solver (PHQC) that returns the best observed feasible solution in O(S n^2) time, where S is a polynomial shot budget. We obtain two advantages. First, when CE-QAOA fixes r >= 1 locations different from the start city, we achieve a Theta(n^r) reduction in shot complexity even against a classical sampler that draws uniformly from the feasible set. Second, against a classical baseline restricted to raw bitstring sampling, we show an exp(Theta(n^2)) minimax separation. In noiseless circuit simulations of traveling salesman problem instances with n in {4,...,10} locations from the QOPTLib benchmark library, we recover the global optimum at depth p = 1 using polynomial shot budgets and coarse parameter grids defined by the problem size.

cs.ET↗
arXiv2026

Fundamental Limitations of QAOA on Constrained Problems and a Route to Exponential Enhancement

We study the feasibility limitations of generic QAOA for permutation-constrained optimization, where valid configurations occupy an exponentially small fraction of the Boolean hypercube. Using random edge-cost TSP/ATSP ensembles, we establish high-probability bounds showing that optimized generic QAOA retains exponentially small feasible probability over specified parameter domains. At depth one, the bound holds uniformly over all mixer angles and a cost-angle grid that may be exponentially large in n^2. The analysis combines Walsh-Fourier/Krawtchouk estimates, which suppress low- and high-degree contributions, with transition-feature collision bounds controlling objective-dependent interference. Complementary cost-angle averaging, fourth-moment estimates, and light-cone analysis characterize energy-fibre coherence, typical-angle concentration, and constraint-correlation geometry. We compare generic QAOA with a constraint-enhanced kernel (CE-QAOA) initialized in a product one-hot subspace and evolved with a block-local XY mixer. For N = n^2 binary variables, CE-QAOA attains feasible probability at least n!/n^n at every depth, yielding an exp[Omega(n^2)] advantage over optimized generic QAOA at depth one with high probability. For linked cost-angle schedules with independently optimized mixer angles, the generic feasibility obstruction and exponential CE-QAOA separation extend throughout linear-depth windows p <= alpha*n, for fixed alpha > 0. These parameter-uniform bounds also imply exponential raw-sample requirements for adaptive feasible sampling within the prescribed domains.

quant-ph↗
arXiv2026

Enhanced analogue quantum computation with a logically-encoded XX gadget

The introduction of two-body XX interactions has been shown to improve the performance of quantum annealing in solving certain combinatorial optimisation problems and would enable the simulation of a broader class of many-body Hamiltonians. Due to experimental constraints, such interactions are typically not natively available on analogue quantum devices. To overcome this limitation we introduce the truss gadget. This is an exact construction that generates two-body XX interactions using only one-body X and Z fields and two-body ZZ interactions which are readily accessible on, for instance, superconducting quantum annealers. We experimentally validate the construction by reproducing the dynamics of a target XX Hamiltonian on a trapped-ion quantum processor. We then apply the gadget to an illustrative set of instances of the weighted maximum-independent-set problem on a superconducting quantum annealer. We empirically determine an approximate thousand-fold improvement in the probability of finding a state close to the ground state for these instances, over implementation without an XX interaction.

quant-ph↗
arXiv2026

Separating Geometry From Interference in Constrained Quantum Optimization

We study the separation of geometric effects from quantum interference in quantum optimization algorithms. Constrained optimization problems such as routing, assignment, and scheduling are often encoded as product spaces of local variables, together with global feasibility penalties. The central algorithmic question we address is how a constraint-preserving mixing operator transports quantum amplitude across an exponential search space in the presence of local and global constraints. We develop a framework that separates three effects that are usually intermixed: amplitude transport, coherent interference among transported amplitudes, and problem-dependent classical postprocessing. We show that the mixing operator alone does not have a target-seeking ability. Concretely, the normalized distribution induced by its amplitude transport moves toward the distance profile of a uniformly random configuration. Thus, quantum sampling advantage may only arise when the phases of the many computational paths reaching a target configuration are sufficiently aligned for their amplitudes to reinforce. We show that, when the cost phases are engineered so that these paths add coherently, a number of circuit alternations growing only logarithmically with problem size suffices to convert the sum of their absolute contributions into a lower bound on the target amplitude, yielding a certified success probability independent of the ambient Hilbert-space dimension, the search-space size, or the feasible-set cardinality. We develop applications to problem-specific transpilation diagnostics, scalable hardware probes, constraint-induced classical maps of quantum-generated samples, the attribution of solution quality between the quantum distribution and classical post-processing in hybrid quantum-classical workflows and connections to distance-partitioned product spaces from classical coding theory.

quant-ph↗
arXiv2026

Evaluating the performance of QEC primitives on quantum processors at large width and depth

Quantum error correction (QEC) relies on repeated parity extraction, mid-circuit measurement (MCM), reset, feed-forward, and scheduling, yet these primitives are usually assessed either in isolation or through resource-demanding experiments. We introduce a few-sample benchmark of QEC-relevant primitives based on an MCM implementation of the quantum approximate optimization algorithm (QAOA) with a fixed set of linear parameters (LR-QAOA). For a chosen code, the QAOA Hamiltonian is constructed from its check structure, such that the resulting circuit mimics the syndrome-extraction connectivity and MCM pattern while producing a direct algorithmic signal, the approximation-ratio r. The LR-QAOA depth, defined by the number of QAOA layers, plays a role analogous to the number of repeated syndrome-extraction rounds in a QEC experiment. From QPU executions, the decay of r with depth defines an effective hardware error, which we map to an equivalent two-qubit depolarizing rate λeff. We compare direct and MCM-mediated implementations across 10 QPUs from IBM, IQM, and Quantinuum, with circuits containing up to 2950 MCM operations. On Quantinuum's Helios-1 and H2-1, we run code-structured LR-QAOA benchmarks for surface-code, triangular color-code, and bivariate-bicycle qLDPC Hamiltonians up to 81, 91, and 48 data qubits, respectively, using up to 480 MCM operations. On IBM ibm_phoenix, we implement the surface-code structure and compare the LR-QAOA response with logical-memory experiments, observing a correlation between the benchmark and the logical performance across different regions of the QPU. Its construction and low resource requirements provide a practical benchmark for comparing hardware generations and QEC implementations before full logical-memory experiments are performed.

quant-ph↗
arXiv2026

Repairability of Inexact Solvers in Recursive State Estimation with Machine Learning

Recursive state estimation often executes approximate numerical solutions inside a feedback loop, where highly accurate local steps do not guarantee better overall results. For a fixed linear Kalman model, we characterize when a correction within a prescribed subspace and norm budget can meet a local admissibility tolerance, and how the defects actually executed affect the finite-horizon covariance response. Centering each defect on the exact gain for the implemented covariance separates current solve error from inherited gain drift. Expanding the exact residual-drift identity reveals opposing quartic contributions beyond the quadratic response: innovation-covariance inflation enters positively, while local-gain reoptimization enters subtractively. Under matched initialization, an absolute sixth-order remainder bound, uniform over bounded defect sequences at fixed horizon, gives sufficient conditions for quadratic under- or overprediction. Machine learning proposes bounded corrections, while a learner-independent residual certificate and verified fallback govern execution of classical and quantum candidates without changing the reference estimator. In a power-grid tolerance study, learned correction lowers the minimum conjugate-gradient iteration count for deployment without fallback relative to uncorrected solves under the same residual certificate. Gains reconstructed from a variational quantum linear solver and from an annealing-based binary encoding, with small-scale terminal measurements on superconducting hardware and sampling on a quantum annealer, are executed through the same interface. By linking local repairability to nonlinear error propagation, the framework evaluates approximate solvers and learned corrections through independent certification and finite-horizon response, providing a practical basis for studying hybrid quantum--classical computation.

quant-ph↗
arXiv2026

Exposing Finite-Depth, Finite-Shot Guarantees for Constrained Quantum Optimization via Fejér Filtering

Constrained quantum optimization algorithms need quantitative guarantees that connect circuit resources to the probability of actually sampling feasible or optimal solutions in finitely many shots. We establish such a connection by exposing a positive sampling law in which mixer-driven exploration and spectral selection can be controlled separately. We show that after removing interference between distinct cost eigenspaces as an analytic device, the measurement distribution becomes the normalized product of a mixer-induced exploration envelope and a Fejér spectral weight, with the former describing how the mixer spreads probability over the encoded manifold and the latter enhancing the target cost phase while suppressing spectrally separated nontarget phases. In this model, finite-shot success becomes a tractable competition between target weight and off-target leakage, yielding an explicit lower bound on the probability of sampling an optimum. For the primary bound, we rescale the cost Hamiltonian to an integer-valued spectrum, placing the wrapped cost phases on a controlled lattice for Fejér filtering. We then define $δ$ as the minimum circular separation between the optimal phase and every nontarget phase. The single-shot success probability $q_0$ satisfies \[ q_0 \ge \frac{x}{1+x}, \qquad x = (p+1)^2 \sin^2\!\left(\fracδ{2}\right) C_β, \] where $p$ is the filter order and $C_β$ is the mixer-envelope mass on the optimal set, exposing a finite-resource compensation law in which weaker phase separation or smaller envelope mass can be compensated by increased filter order and additional shots. The same filtering principle exposes a feasibility guarantee when applied to penalty phases. We further prove analogous bounds for nonlattice spectra through off-target suppression, extending our results beyond exact lattice normalization.

quant-ph↗
arXiv2026

Optimizing QAOA circuit transpilation with parity twine and SWAP network encodings

Mapping quantum approximate optimization algorithm (QAOA) circuits with non-trivial connectivity in fixed-layout quantum platforms, such as superconducting quantum processing units (QPUs), requires a transpilation process to match the circuit to the hardware layout. This step is critical for reducing error rates on noisy QPUs. Two approaches that improve the resources required for such transpilation are the SWAP network and parity twine chains (PTC), which reduce the two-qubit gate count and circuit depth needed to represent fully connected circuits. In this work, we introduce a simulated annealing-based method that further reduces the encoding overhead of PTC and SWAP networks for QAOA circuits with non-fully connected two-qubit interactions. The method is benchmarked against various transpilers, including the Qiskit SAT mapper, demonstrating that beyond specific connectivity thresholds it achieves significant reductions in both two-qubit gate count and circuit depth. For example, for a 120-qubit QAOA instance with 25% connectivity, our method achieves an 87\% reduction in depth and a 29% reduction in two-qubit gates compared to the Qiskit transpiler. Finally, the practical impact of PTC encoding is validated by benchmarking QAOA on the ibm_fez and ibm_kingston devices, showing improved performance for systems of up to 20 qubits.

quant-ph↗
arXiv2026

Polynomial Time Quantum Approximation Schemes for Constrained Optimisation

When does a noisy quantum sampler yield an end-to-end polynomial-time optimization algorithm with performance guarantees? Building on finite-depth and finite-shot guarantees for Constraint-Enhanced QAOA, we show that inverse-polynomial ideal probability on the optimal set, together with independent sampling, polynomial-time feasibility repair, and scoring, produces an exact-hit fully polynomial randomized approximation scheme, which we call an FPRASq. This guarantee survives device noise within an instance-dependent window. For effective circuit depth linear in the product of layer count and problem size, preserving an inverse-depth fraction of the ideal optimal mass increases the required shot complexity by one power of the problem size. Beyond this window, deterministic repair guarantees feasibility and provides an instance-dependent approximation guarantee whenever the induced objective inflation is controlled. The resulting NP-HQ algorithm fits the Chen-Cotler-Huang-Li oracle model. On any NP-hard kernel-admissible promise family, reproducing its inverse-polynomial optimal overlap with a polynomial-time classical sampler would imply that NP is contained in BPP, even with identical repair and perfect access to the constraint structure. Thus, the separation lies in generating the sampling distribution. We further introduce Heavy-Hitter QAOA, which preserves these conditional guarantees while reducing the retained candidate set and classical post-processing cost by one power of the problem size. Hardware experiments on IBM Eagle r3 processors cover instances with up to one hundred logical variables and match or improve every tested QOptlib reference tour.

quant-ph↗
arXiv2026

Benchmarking neutral atom-based quantum processors at scale

In recent years, neutral atom-based quantum computation has been established as a competing alternative for the realization of fault-tolerant quantum computation. However, as with other quantum technologies, various sources of noise limit their performance. With processors continuing to scale up, new techniques are needed to characterize and compare them in order to track their progress. In this work, we present two systematic benchmarks that evaluate these quantum processors at scale. We use the quantum adiabatic algorithm (QAA) and the quantum approximate optimization algorithm (QAOA) to solve maximal independent set (MIS) instances of random unit-disk graphs. These benchmarks are scalable, relying not on prior knowledge of the system's evolution but on the quality of the MIS solutions obtained. Rather than isolating individual sources of noise, they provide an application-level figure of merit: improvements in a QPU and its implementation of the protocols should be reflected in higher-quality MIS solutions. We benchmark quera_aquila and pasqal_fresnel on problem sizes up to 102 and 85 qubits, respectively. Overall, quera_aquila performs better on QAOA and QAA instances. Finally, we generate MIS instances of up to 1000 qubits, providing scalable benchmarks for evaluating future, larger processors as they become available. The proposed protocols can therefore serve as a common reference for comparisons, allowing future work to assess whether advances in hardware translate into measurable improvements in MIS solution quality.

quant-ph↗
arXiv2026

Resonant false vacuum decay in two dimensions on a 4000-qubit quantum annealer

From cosmology to quantum matter, metastable states often decay through the nucleation and growth of competing domains, with false vacuum decay providing the paradigmatic example of this process. Here we demonstrate a distinct regime in which domain growth outpaces nucleation by orders of magnitude and is controlled by local resonance conditions. Using a programmable quantum annealer with more than 4000 qubits, we realize a two-dimensional quantum Ising model whose metastable spin-polarized state encodes a false vacuum. At a specific value of the longitudinal field, single-spin flips at the boundary of a seeded bubble become resonant, enabling kinetically constrained expansion. Combining experiment with tensor-network simulations and stochastic circuit modeling, we observe nearly ballistic growth of true-vacuum domains with sub-ballistic interface broadening, consistent with Kardar--Parisi--Zhang universality. Our results establish a growth-dominated regime of false vacuum decay and show how large-scale quantum simulation can access nonequilibrium metastable dynamics relevant to quantum field theory, cosmology, and strongly correlated matter.

quant-ph↗
arXiv2026

Hybrid Quantum-Classical Corrective Diffusion Modeling for Meteorological Downscaling

Statistical downscaling is a crucial component of the weather modeling field, where high-resolution outputs must be reconstructed from coarse-resolution inputs with the full cost of dynamical refinement. In this work, we investigate a hybrid quantum-classical corrective diffusion model for probabilistic statistical downscaling of weather fields. The proposed model inserts variational quantum circuit layers into the most compressed bottleneck of the diffusion UNet while leaving the regression branch fully classical. This placement tests whether quantum circuits can act as compact nonlinear feature maps for latent-channel mixing. We evaluate intra-channel and cross-channel ansätze on 10m wind components. On the 2020 validation set, the hybrid models remain stable, preserve the large-scale spatial organization of the generated wind fields, and improve both MAE and CRPS relative to a classical corrective diffusion model in several configurations. Structural diagnostics further show that the hybrid variants preserve kinetic-energy spectra and windspeed distributions similar to its classical counterpart while producing controlled changes in tail behavior, extreme-windspeed localization, and joint wind field components structure. Backend studies on the 2020 validation set show negligible impact from simulated device noise at the tested circuit scale, whereas real-hardware deployment remains limited by qubit availability and execution fidelity. The 2021 out-of-distribution test shows that these in-distribution gains do not transfer uniformly under temporal shift, revealing a generalization gap that motivates future mitigation through stabilization and regularization. These results show that bottleneck-level quantum hybridization can make a nontrivial contribution to weather statistical downscaling, while also highlighting that circuit scale and hardware deployment remain key limiting factors.

cs.LG↗
arXiv2026

Universal Quantum Computer Simulation of 50 Qubits on Europe`s First Exascale Supercomputer Harnessing Its Heterogeneous CPU-GPU Architecture

We have developed a new version of the high-performance Jülich universal quantum computer simulator (JUQCS-50) that leverages key features of the GH200 superchips as used in the JUPITER supercomputer, enabling simulations of a 50-qubit universal quantum computer for the first time. JUQCS-50 achieves this through three key innovations: (1) extending usable memory beyond GPU limits via high-bandwidth CPU-GPU interconnects and LPDDR5 memory; (2) adaptive data encoding to reduce memory footprint with acceptable trade-offs in precision and compute effort; and (3) an on-the-fly network traffic optimizer. These advances result in a 16.6-fold speedup over the previous 48-qubit record on the K computer

quant-ph↗
arXiv2026

Requirements for Early Quantum Utility and Quantum Utility in the Capacitated Vehicle Routing Problem

We introduce a transparent, encoding-agnostic framework for determining when the Capacitated Vehicle Routing Problem (CVRP) can achieve early quantum advantage. Our analysis shows this is unlikely on noisy intermediate scale quantum (NISQ) hardware even in best case scenarios that use the most qubit-efficient direct encodings. Closed-form resource counts, combined with recent device benchmarks, yield three decisive go/no-go figures of merit: the quantum feasibility point and the qubit- and gate-feasibility lines, which place any CVRP instance on a single decision diagram. Contrasting a direct QUBO mapping with a space-efficient higher-order (HOBO) encoding reveals a large gap. Applied to early-advantage benchmarks such as Golden-5, our diagram shows that HOBO circuits require only 7,685 qubits, whereas comparable QUBO encodings still exceed 200,000 qubits. In addition to identifying candidate instances for early quantum advantage in CVRP, the framework provides a unifying go/no-go metric that ingests any CVRP encoding together with any hardware profile and highlights when quantum devices could challenge classical heuristics. Quantum advantage in CVRP would likely require innovative problem decomposition techniques.

quant-ph↗
arXiv2026

Optimal, Qubit-Efficient Quantum Vehicle Routing via Colored-Permutations

We formulate a global-position colored-permutation encoding for the capacitated vehicle routing problem. Each of the $K$ vehicles selects a disjoint partial permutation, and the sum of these $K$ color layers forms a full $n\times n$ permutation matrix that assigns every customer to exactly one visit position. This representation uses $n^2K$ binary decision variables arranged as $K$ color layers over a common permutation structure, while vehicle capacities are enforced by weighted sums over the entries of each color class, requiring no explicit load register and hence no extra logical qubits beyond the routing variables. In contrast, many prior quantum encodings introduce an explicit capacity or load representation with additional qubits. Our construction is designed to exploit the Constraint-Enhanced QAOA framework together with its encoded-manifold analyses. Building on a requirements-based view of quantum utility in CVRP, we develop a routing optimization formulation that directly targets one of the main near-term bottlenecks, namely the additional logical-qubit cost of vehicle labels and explicit capacity constraints. Our proposal shows strong algorithmic performance in addition to qubit efficiency. On a standard benchmark suite, our end-to-end pipeline recovers the independently verified optima. The feasibility oracle may also be of independent interest as a reusable polynomial-time decoding and certification primitive for quantum and quantum-inspired routing pipelines.

quant-ph↗
arXiv2026

Large-Scale Quantum Circuit Simulation on an Exascale System for QPU Benchmarking

Recent advances in quantum computing have enabled the development of quantum processors with hundreds of qubits. However, noise continues to limit the amount of useful information that can be extracted from these systems, making it essential to identify the regime in which experimental outputs remain reliable. In this work, we benchmark Quantinuum Helios-1, a 98-qubit trapped-ion quantum processing unit, using the linear ramp quantum approximate optimization algorithm (LR-QAOA). To this end, we perform large-scale noiseless simulations on JUPITER, Europe's first exascale supercomputer, for circuits of up to 48 qubits and 3,384 two-qubit gates. These simulations, executed on 4,096 nodes equipped with 16,384 GH200 superchips and high-bandwidth CPU-GPU interconnects, provide a reference for validating experimental results at the edge of classical tractability. We find that, up to 48 qubits, Helios-1 remains in a noise-tolerant region, i.e., its samples cannot be clearly distinguished from those coming from a noiseless simulation. We then extend the analysis to larger system sizes using experimental data only, and apply a mean-of-means resampling procedure with a 3$σ$ threshold to determine whether the QPU output is statistically distinguishable from random sampling. This analysis identifies a regime of coherent performance up to 93 qubits (12,834 two-qubit gates), beyond which, at 95 qubits, the outputs become statistically indistinguishable from random sampling. These results demonstrate how exascale classical simulation can be used to validate quantum processors, and provide a quantitative boundary between noise-tolerant and random regimes in quantum processors.

quant-ph↗
arXiv2026

Quantum annealing inspired algorithms for the NISQ Era

We study algorithms inspired by quantum annealing that are suited for the NISQ era. First, we analyze approximate quantum annealing (AQA), which employs a discretized annealing ansatz in which the time step and the number of layers are allowed to deviate from a faithful implementation of quantum annealing. Parameter scans identify regimes that reproduce annealing-like behavior with reduced resources, making them more suitable for NISQ devices. The resulting parameters can then be used as an effective warm start for the quantum approximate optimization algorithm (QAOA), improving its performance compared to random initializations. We also introduce evolving Hamiltonian quantum optimization (EHQO), a multistep variational scheme that guides the optimization process through intermediate Hamiltonians derived from the standard annealing Hamiltonian. Numerical simulations on sets of hard 2-SAT instances suggest that quantum annealing-inspired algorithms provide practical strategies for enhancing variational quantum optimization.

quant-ph↗