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Scalability Challenges in Variational Quantum Optimization under Stochastic Noise
Quantum Physics · Submitted 18 Mar 2025
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our findings demonstrate serious scalability challenges for VQAs in optimization stemming from mere uncertainty, indicating potential barriers to achieving practical quantum advantage with current hybrid approaches.
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The abstract, sentence by sentence
With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. Variational Quantum Algorithms (VQAs) have gained significant attention as promising candidates in this pursuit, particularly for combinatorial optimization problems. While reports of their challenges and limitations continue to accumulate, many studies remain optimistic based on small-scale, idealized testing setups, leaving doubt about the scalability of VQAs for large-scale problems. We systematically investigate this scaling behavior by analyzing how classical optimizers minimize variational quantum loss functions for random QUBO instances in the presence of uncertainty, modeled as effective Gaussian noise. We find that the critical noise threshold for successful optimization decreases rapidly as system size grows. This decline exceeds what can be explained solely by shrinking loss variance, confirming deeper, fundamental limitations in the loss landscapes of VQAs beyond barren plateaus. Translating these thresholds into required measurement shots reveals that achieving sufficient precision in the evaluated loss values quickly becomes impractical, even for moderately-sized problems. Our findings demonstrate serious scalability challenges for VQAs in optimization stemming from mere uncertainty, indicating potential barriers to achieving practical quantum advantage with current hybrid approaches.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. | background 1.00 | 0.03 | 0.02 | unclear 0.69 |
| s1 | Variational Quantum Algorithms (VQAs) have gained significant attention as promising candidates in this pursuit, particularly for combinatorial optimization problems. | background 1.00 | 0.03 | 0.02 | asserted 0.73 |
| s2 | While reports of their challenges and limitations continue to accumulate, many studies remain optimistic based on small-scale, idealized testing setups, leaving doubt about the scalability of VQAs for large-scale problems. | gap 0.83 | 0.04 | 0.04 | asserted 0.65 |
| s3 | We systematically investigate this scaling behavior by analyzing how classical optimizers minimize variational quantum loss functions for random QUBO instances in the presence of uncertainty, modeled as effective Gaussian noise. | method 0.68 | 0.92 | 0.04 | asserted 0.91 |
| s4 | We find that the critical noise threshold for successful optimization decreases rapidly as system size grows. | result 1.00 | 0.97 | 0.26 | asserted 1.00 |
| s5 | This decline exceeds what can be explained solely by shrinking loss variance, confirming deeper, fundamental limitations in the loss landscapes of VQAs beyond barren plateaus. | interpretation 0.83 | 0.93 | 0.22 | asserted 1.00 |
| s6 | Translating these thresholds into required measurement shots reveals that achieving sufficient precision in the evaluated loss values quickly becomes impractical, even for moderately-sized problems. | result 0.67 | 0.92 | 0.16 | asserted 0.99 |
| s7 | Our findings demonstrate serious scalability challenges for VQAs in optimization stemming from mere uncertainty, indicating potential barriers to achieving practical quantum advantage with current hybrid approaches. | interpretation 0.99 | 0.91 | 0.94 | asserted 0.72 |
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The paper
Original abstract
With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. Variational Quantum Algorithms (VQAs) have gained significant attention as promising candidates in this pursuit, particularly for combinatorial optimization problems. While reports of their challenges and limitations continue to accumulate, many studies remain optimistic based on small-scale, idealized testing setups, leaving doubt about the scalability of VQAs for large-scale problems. We systematically investigate this scaling behavior by analyzing how classical optimizers minimize variational quantum loss functions for random QUBO instances in the presence of uncertainty, modeled as effective Gaussian noise. We find that the critical noise threshold for successful optimization decreases rapidly as system size grows. This decline exceeds what can be explained solely by shrinking loss variance, confirming deeper, fundamental limitations in the loss landscapes of VQAs beyond barren plateaus. Translating these thresholds into required measurement shots reveals that achieving sufficient precision in the evaluated loss values quickly becomes impractical, even for moderately-sized problems. Our findings demonstrate serious scalability challenges for VQAs in optimization stemming from mere uncertainty, indicating potential barriers to achieving practical quantum advantage with current hybrid approaches.
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References
How the literature uses it
2 arXiv papers cite this in 7 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 1 paper
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Following the methodology of [ref] , one can add i.i.d.
Enabling Lie-Algebraic Classical Simulation beyond Free Fermions · A provably well-behaved VQA for TFIM ground states in a free-fermion DLA · 0.99
Cites it as support 1 paper
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The choice of optimizer is influenced by previous testing [ref] and also for its noise resilience [ref] .
Application-Driven Benchmarking of the Traveling Salesperson Problem: a Quantum Hardware Deep-Dive · Experimental setup · 0.96
What it cites · 26 sentences without a confident label
Uses the method or tool of 2 papers
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To provide a more representative performance indicator, we use the approximation index $x_t$ [ref] , which assesses whether the loss value of $|ψ_max⟩$ is within a specified threshold $t ∈[0,1]$ of the global minimum: [equation] For example, $x_1 = 1$, if and only if the most probable basis state $|ψ_max⟩$ is the exact optimal solution $|q^*⟩$.
Solving Combinatorial Optimization Problems with a Block Encoding Quantum Optimizer · Measures of Solvability · 0.97
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A selection of well-established methods from Qiskit [ref] and SciPy [ref] as chosen (cf. <ref>), along with a normalized gradient descent method (NGD) [ref] , proposed as such by Kuete Meli et al. [ref] , which has demonstrated promising performance in prior studies [ref] .
Quantum computing with Qiskit · State-of-the-Art Optimizers · 0.96
Cites as support 4 papers
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Based on a characterization of their dynamical Lie algebra (DLA) structures, we know neither the Two Local ansatz used here nor the problem-dependent BENQO ansatz exhibit exponentially scaling DLA dimensions [ref] .
Classification of dynamical Lie algebras generated by spin interactions on undirected graphs · Well-Behaved Quantum Loss Functions · 0.96
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This aligns with previous studies reporting exponential resource requirements in variational quantum optimization [ref] .
Exponential challenges in unbiasing quantum Monte Carlo algorithms with quantum computers · The Curse of Finite Sampling · 0.98
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This suggests that a small level of noise can enhance their ability to find optimal solutions by helping to escape saddle points and local minima, a phenomenon also reported in the literature [ref] .
Stochastic noise can be helpful for variational quantum algorithms · Solvability under Additive Gaussian Noise · 0.96
Cites as background 4 papers
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Two of the most widely studied VQAs are the Variational Quantum Eigensolver (VQE) [ref] , initially developed for quantum chemistry, and the Quantum Approximate Optimization Algorithm (QAOA) [ref] , a VQE variant explicitly designed for the field of combinatorial optimization.
A Quantum Approximate Optimization Algorithm · Variational Quantum Optimization · 1.00
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QAOA, in contrast, follows a problem-inspired approach, implementing a trotterized version of adiabatic quantum optimization [ref] .
Quantum Computation by Adiabatic Evolution · Variational Quantum Optimization · 0.89
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Additionally, this study has not yet considered alternative computational models, such as Quantum Boson Sampling [ref] or Quantum Annealing [ref] , which may warrant further investigation.
Solving Combinatorial Optimization Problems on a Photonic Quantum Computer · Conclusions and Outlook · 0.93
Discussion
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