Hamming Weight Operators and an adaptive QAOA variant confine evolution to feasible states by construction, delivering faster convergence and roughly half the gate count versus penalty methods on finance and physics tasks.
Spin-Boson Mapping of the Quantum Approximate Optimization Algorithm
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abstract
The Quantum Approximate Optimization Algorithm (QAOA) achieves monotonically improving performance with circuit depth $p$, yet the study of the high-depth regime has been obstructed by the exponential in $p$ cost of existing exact evaluation techniques. In this Letter, we prove that, in the infinite-size limit, the depth-$p$ QAOA state for the Sherrington-Kirkpatrick (SK) model converges to the state of a spin coupled to $p$ bosonic modes. We simulate the spin-boson system using matrix product states and provide numerical evidence that QAOA obtains a $(1-\epsilon)$ approximation to the optimal energy of the SK model with circuit depth $O(n/\epsilon^{1.13})$ in the average case. The modest computational cost of our approach allows us to optimize QAOA parameters and observe that QAOA achieves $\varepsilon\lesssim 2.2\%$ at $p=160$ in the infinite-size limit, extending far beyond $p\leq 20$ accessible to prior exact methods. Our mapping provides a many-body route to study and optimize high-depth QAOA in regimes previously inaccessible to exact evaluation.
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2026 3verdicts
UNVERDICTED 3representative citing papers
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
QAOA on qudit-encoded integer graph problems outperforms the Frieze-Jerrum SDP for Max-k-Cut at p≤4 in regimes k=3 d≤10 and k=4 d≤40, while a new degree-of-saturation heuristic beats both on GSet but may be overtaken by QAOA at p≤20.
citing papers explorer
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Constraint-Aware Quantum Optimization via Hamming Weight Operators
Hamming Weight Operators and an adaptive QAOA variant confine evolution to feasible states by construction, delivering faster convergence and roughly half the gate count versus penalty methods on finance and physics tasks.
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Potential Hessian Ascent III: Sampling the Sherrington--Kirkpatrick Model at Beta < 1/2
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
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Quantum Approximate Optimization of Integer Graph Problems and Surpassing Semidefinite Programming for Max-k-Cut
QAOA on qudit-encoded integer graph problems outperforms the Frieze-Jerrum SDP for Max-k-Cut at p≤4 in regimes k=3 d≤10 and k=4 d≤40, while a new degree-of-saturation heuristic beats both on GSet but may be overtaken by QAOA at p≤20.