A noise-aware adaptive approach to quantum approximate optimization, Noise-Directed Adaptive Warm-Starting (ND-AWS), that builds on recent concepts such as Warm-Start QAOA and Noise-Directed Adaptive Remapping by leveraging bitflip gauge transformations, and exploits amplitude-damping-like noise components.
Abstract
Progress towards a quantum advantage using known heuristic methods for combinatorial optimization is impeded by hardware noise and limited qubit count. Here, we propose a noise-aware adaptive approach to quantum approximate optimization, Noise-Directed Adaptive Warm-Starting (ND-AWS), that builds on recent concepts such as Warm-Start QAOA and Noise-Directed Adaptive Remapping. By leveraging bitflip gauge transformations, our algorithm exploits amplitude-damping-like noise components. We experimentally implement high-performance quantum optimization ans\"atze on 100-qubit Ising Hamiltonians, showing that ND-AWS generally improves the performance over a non-gauge-transformed iterative Warm-Starting variant, at no additional circuit cost. This places our results among the highest-quality demonstrations of quantum optimization with similar ans\"atze at this scale. Crucially, the simplicity of the framework opens the door for future enhancements such as adaptive bias schedules, and integration with classical solvers.
Quantum optimization has attracted growing interest as quantum hardware continues to improve, yet state-of-the-art classical solvers remain a formidable benchmark for practical utility. Rather than seeking a fully quantum replacement for classical optimization, we propose a hybrid strategy that uses quantum information to enhance leading classical heuristics. Specifically, we introduce a warm-start method based on local correlators obtained from the Quantum Approximate Optimization Algorithm (QAOA), and use this information to initialize the Burer-Monteiro (BM) rank-two relaxation. We demonstrate numerically that, compared to a random, multi-start initialization baseline (a standard strategy used for BM), this quantum-informed initialization offers a significant head start, i.e., high-quality solutions with very small number of iterations, for two problem classes -- random Erd\H{o}s R\'{e}nyi graphs with edge density of $10\%$ (ER-10) and fully-connected Sherrington Kirkpatrick (SK) spin glass models, at $n=500$ and $n=1000$ qubits. At the same time, given enough iterations, the random baseline often eventually catches up and slightly outperforms the warm-start strategy on average, an effect visibly stronger for $n=500$ than for $n=1000$. The results demonstrate an exploitation/exploration tradeoff of using WS to quickly arrive at very good solutions vs exploring slightly better solutions with a larger iterations budget via a standard strategy. Our results highlight how low-depth quantum circuits can provide useful structural information for classical optimization and suggest a promising route toward near-term quantum utility through quantum-assisted initialization.
Bao Gia Bach, Ilya Safro, Filip B. Maciejewski· 0 citations
We introduce Quantum-Informed Surrogate Sampling (QISS), a post-processing framework that generates candidate solutions to combinatorial optimization problems from low-weight correlations of shallow quantum circuits. The quantum device estimates local observables, which are directly accessible by repeated measurements and for which a wide range of error-mitigation tools are available, while candidate solutions are generated classically without explicit dependence on the combinatorial optimization problem itself. We evaluate QISS on Maximum Cut and Maximum Independent Set problems on $N$ variables and show that only $O(N)$ low-order correlators from shallow circuits suffice to produce competitive solutions that surpass vanilla QAOA. For MaxCut on 3-regular graphs, QISS from $p=3$ QAOA correlators outperforms vanilla QAOA at $p=17$ on average, with further improvements possible by warm-starting QAOA. We validate the procedure on the 54-qubit IQM Emerald quantum device and demonstrate its noise resilience. Our results support a regime for near-term optimization in which shallow circuits serve not as direct samplers but as generators of informative statistics for scalable classical sampling.
Pauli-based simulators offer a promising route to large-scale classical simulation of quantum circuits in the low-magic regime. Yet their applicability remains largely limited to forward simulation, making them inadequate for optimization-driven quantum tasks such as variational state preparation and parameter initialization. Existing approaches either lack native support for gradient-based optimization or suffer from severe gradient bias. Here we propose the stochastic Pauli-path simulator (SPPS), a computational framework for large-scale quantum optimization that enables unbiased stochastic gradient estimation via Pauli-path sampling across optimization iterations. Our theoretical analysis shows that the proposed simulator yields unbiased gradient estimates and admits provable convergence guarantees. We systematically evaluate our proposal, including quantum eigensolver benchmarks with up to 100 qubits and quantum neural network benchmarks with up to 40 qubits. Across these tasks, SPPS faithfully tracks optimization dynamics, converges within minutes, and broadens the role of Pauli-based simulation from forward estimation to large-scale quantum optimization.
Kai-Ning Zhang, Xin-Biao Wang, Kunsheng Li et al.· 0 citations
Optimization problems are among the leading candidates for industrially relevant quantum advantage. Decoded quantum interferometry (DQI) has been proposed to tackle approximate optimization, establishing a connection to classical decoding problems. While previous work has primarily focused on the theoretical complexity of DQI, comparatively little is known about its empirical performance relative to classical algorithms. In this work, we shed further light on the complexity of DQI and investigate numerically whether classical sampling methods can emulate the optimization capabilities of DQI. We first present a simplified analytical characterization of DQI that connects its expected performance to binomial statistics, and we identify concrete obstacles in further studying the complexity of DQI. Exploiting the fact that DQI output probabilities are efficiently computable, we apply Markov chain Monte Carlo (MCMC) techniques, particularly block-Gibbs sampling, to sample from the induced distribution. We study the runtime scaling of these methods for two optimization problems called max-XORSAT, where we reach beyond $1000$ effective qubits; and OPI, where we reach beyond $150$ effective qubits. Our results show that MCMC algorithms can reliably attain the approximation ratios expected from DQI across a broad range of problem sizes. In OPI, in the regime where a super-polynomial advantage is claimed for DQI, we observe an empirical runtime for MCMC that scales approximately as $1.1^{n}$, indicating exponential growth with a comparatively small base. Our findings do not refute existing quantum advantage claims but provide new empirical evidence that classical sampling algorithms can closely match DQI's optimization performance, offering a more nuanced perspective on the practical advantage of DQI.
Elies Gil-Fuster, Matan Ninio, Lennart Bittel et al.· 0 citations
We investigate and compare the performance of two quantum optimization approaches, the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing, applied to the Minimum Vertex Cover (MVC) problem. The problem is encoded as an and Ising model, and experiments are conducted on IBM’s GenericBackendV2 noisy superconducting qubit simulator and the D-Wave Advantage2 quantum annealer. Performance is evaluated in terms of solution quality, measurement probability, and proportion of valid solutions. The results we obtained show that, within our experimental setting, quantum annealing consistently outperforms its classical counterpart on small instances, while QAOA, though currently limited by simulation constraints, shows promising behavior that improves with increasing circuit depth. As problem size grows, both approaches exhibit sensitivity to parameter choices such as the penalty term and graph density, underscoring the need for careful tuning. These findings suggest that while both paradigms hold potential for combinatorial optimization, further advances in hardware capabilities and parameter calibration will be necessary to achieve reliable performance on larger instances.
Simone Faro, G. Messina, Damiano Muzzicato et al.· IEEE International Symposium...· 0 citations
Variational quantum sensing offers a promising route to high-precision parameter estimation, but its performance depends strongly on the circuit architectures used for probe preparation and measurement. Existing approaches typically optimize continuous parameters within predefined ans\"atze, restricting the accessible design space and limiting adaptation to sensing tasks and hardware constraints. Here, we introduce \textsc{AutoQSense}, a reinforcement-learning framework that searches circuit architectures using Fisher-information-based objectives. For few-qubit systems, a single agent sequentially constructs preparation and measurement circuits. For larger systems, a distributed formulation assigns local circuit design to subsystem agents and inter-block entanglement to a budgeted agent. Numerical results show that the learned architectures recover known benchmark strategies, adapt to dephasing noise, and outperform fixed hardware-efficient ans\"atze while using fewer entangling gates. These results establish \textsc{AutoQSense} as a resource-aware approach to adaptive and hardware-compatible quantum sensing.