We study how hardware noise changes the p=1 Quantum Approximate Optimization Algorithm (QAOA) landscape for cardinality-constrained portfolio problems on ibm_fez (IBM Heron r2): seven instances from n=6 to 16 qubits, each on a 7x7 parameter grid at 4,096 and 8,192 shots per point. The first version of this paper proposed Landscape Span Compression (LSC), the fractional loss of energy range across the grid, as a device benchmark, based on stable values of 0.24-0.30 at n<=8. The larger study shows why that does not hold. Hardware LSC rises to 0.72-0.81 at n=16, growing with circuit size (R^2=0.96 and 0.88 for an exponential decay in CZ count). Because the landscape energy averages over all shots, it is nearly linear in the feasible fraction, and a statistic built only from that fraction reproduces LSC (Pearson r=0.954). For these penalty-encoded problems, landscape compression is a circuit-fidelity effect expressed as loss of feasible samples, as noise-flattening models of QAOA predict. The same mechanism biases the usual test of parameter transfer: grid verdicts on whether the optimum moves agree across shot counts for only 2 of 7 instances, and hardware optima move toward higher feasibility. Even in noiseless simulation, p=1 QAOA samples the feasible set of these instances almost uniformly, so best-feasible approximation ratios (>=0.9993) are uninformative and the only effect noise can remove is a raised feasible fraction. We withdraw the benchmark and noise-model-gap claims of the first version, correct its solution-quality figures, and describe a protocol that separates feasibility loss from solution quality.We study how hardware noise changes the p=1 Quantum Approximate Optimization Algorithm (QAOA) landscape for cardinality-constrained portfolio problems on ibm_fez (IBM Heron r2): seven instances from n=6 to 16 qubits, each on a 7x7 parameter grid at 4,096 and 8,192 shots per point. The first version of this paper proposed Landscape Span Compression (LSC), the fractional loss of energy range across the grid, as a device benchmark, based on stable values of 0.24-0.30 at n<=8. The larger study shows why that does not hold. Hardware LSC rises to 0.72-0.81 at n=16, growing with circuit size (R^2=0.96 and 0.88 for an exponential decay in CZ count). Because the landscape energy averages over all shots, it is nearly linear in the feasible fraction, and a statistic built only from that fraction reproduces LSC (Pearson r=0.954). For these penalty-encoded problems, landscape compression is a circuit-fidelity effect expressed as loss of feasible samples, as noise-flattening models of QAOA predict. The same mechanism biases the usual test of parameter transfer: grid verdicts on whether the optimum moves agree across shot counts for only 2 of 7 instances, and hardware optima move toward higher feasibility. Even in noiseless simulation, p=1 QAOA samples the feasible set of these instances almost uniformly, so best-feasible approximation ratios (>=0.9993) are uninformative and the only effect noise can remove is a raised feasible fraction. We withdraw the benchmark and noise-model-gap claims of the first version, correct its solution-quality figures, and describe a protocol that separates feasibility loss from solution quality.

quant-pharXiv:2604.19426Apr 22, 20260 citations

Molecular Energy Landscapes of Hardware-Efficient Ansätze in Quantum Computing

Choy Boy, David J. Wales

Rapid advances in quantum computing have opened up new opportunities for solving the central electronic structure problem in computational chemistry. In the noisy intermediate-scale quantum (NISQ) era, where qubit coherence times are limited, it is essential to exploit quantum algorithms with sufficiently short quantum circuits to maximize qubit efficiency. The procedural construction of hardware-efficient ansätze provides one approach to design such circuits. However, refining the accuracy of the global minimum by increasing circuit depth may lead to a proliferation of local minima that hinders global optimization. To investigate this phenomenon, we explore the energy landscapes of hardware-efficient circuits to identify ground-state energies of the hydrogen, lithium hydride, and beryllium hydride molecules. We also propose a simple dimensionality reduction procedure that reduces quantum gate depth while retaining high accuracy for the global minimum, simplifying the energy landscape, and hence speeding up optimization from both software and hardware perspectives.Rapid advances in quantum computing have opened up new opportunities for solving the central electronic structure problem in computational chemistry. In the noisy intermediate-scale quantum (NISQ) era, where qubit coherence times are limited, it is essential to exploit quantum algorithms with sufficiently short quantum circuits to maximize qubit efficiency. The procedural construction of hardware-efficient ansätze provides one approach to design such circuits. However, refining the accuracy of the global minimum by increasing circuit depth may lead to a proliferation of local minima that hinders global optimization. To investigate this phenomenon, we explore the energy landscapes of hardware-efficient circuits to identify ground-state energies of the hydrogen, lithium hydride, and beryllium hydride molecules. We also propose a simple dimensionality reduction procedure that reduces quantum gate depth while retaining high accuracy for the global minimum, simplifying the energy landscape, and hence speeding up optimization from both software and hardware perspectives.

Journal of Chemical Theory and ComputationFeb 7, 202328 citations

Quantum Hardware for All.

Susan Clark

Jun 1, 20211 citation

Quantum Hardware for All.

Susan Clark

Apr 1, 20210 citations

Landscape-Similarity-Guided Optimization in Divide-and-Conquer QAOA

Sokea Sang, Leanghok Hour, Sanghyeon Lee +4 more

Divide-and-conquer strategies mitigate hardware constraints for the Quantum Approximate Optimization Algorithm (QAOA) on Noisy Intermediate-Scale Quantum (NISQ) devices by partitioning large interaction graphs into smaller, hardware-compatible sub-problems. However, this approach introduces a severe classical training bottleneck: a decomposition across $m$ boundary nodes generates $2^m$ distinct sub-problems that typically require independent optimization. In this work, we demonstrate that across diverse synthetic and real-world interaction graphs, the variational landscapes of these reduced QAOA instances actually exhibit a robust universality. Adapting the replica-overlap framework of spin-glass physics, we define a landscape-overlap order parameter $q$ to quantify geometric correlations between energy landscapes, revealing a sharp landscape-similarity transition as graph connectivity is tuned. Exploiting this, we introduce Doubly Optimized QAOA (DO-QAOA), an adaptive pipeline that collapses the sub-problems from $2^m$ distinct sub-problems into $K=\mathcal{O}(1)$ effective landscape classes. By performing optimization on a single representative sub-problem and dynamically transferring parameters to remaining sub-problems, DO-QAOA lowers runtime and quantum measurement overhead by orders of magnitude while maintaining a competitive Approximation Ratio Gap (ARG).Divide-and-conquer strategies mitigate hardware constraints for the Quantum Approximate Optimization Algorithm (QAOA) on Noisy Intermediate-Scale Quantum (NISQ) devices by partitioning large interaction graphs into smaller, hardware-compatible sub-problems. However, this approach introduces a severe classical training bottleneck: a decomposition across $m$ boundary nodes generates $2^m$ distinct sub-problems that typically require independent optimization. In this work, we demonstrate that across diverse synthetic and real-world interaction graphs, the variational landscapes of these reduced QAOA instances actually exhibit a robust universality. Adapting the replica-overlap framework of spin-glass physics, we define a landscape-overlap order parameter $q$ to quantify geometric correlations between energy landscapes, revealing a sharp landscape-similarity transition as graph connectivity is tuned. Exploiting this, we introduce Doubly Optimized QAOA (DO-QAOA), an adaptive pipeline that collapses the sub-problems from $2^m$ distinct sub-problems into $K=\mathcal{O}(1)$ effective landscape classes. By performing optimization on a single representative sub-problem and dynamically transferring parameters to remaining sub-problems, DO-QAOA lowers runtime and quantum measurement overhead by orders of magnitude while maintaining a competitive Approximation Ratio Gap (ARG).

quant-pharXiv:2602.21689Feb 26, 20260 citations

m

boundary nodes generates

2^m

distinct sub-problems that typically require independent optimization. In this work, we demonstrate that across diverse synthetic and real-world interaction graphs, the variational landscapes of these reduced QAOA instances actually exhibit a robust universality. Adapting the replica-overlap framework of spin-glass physics, we define a landscape-overlap order parameter

q

to quantify geometric correlations between energy landscapes, revealing a sharp landscape-similarity transition as graph connectivity is tuned. Exploiting this, we introduce Doubly Optimized QAOA (DO-QAOA), an adaptive pipeline that collapses the sub-problems from

2^m

distinct sub-problems into

K=\mathcal{O}(1)

effective landscape classes. By performing optimization on a single representative sub-problem and dynamically transferring parameters to remaining sub-problems, DO-QAOA lowers runtime and quantum measurement overhead by orders of magnitude while maintaining a competitive Approximation Ratio Gap (ARG).