Title: TITAN: A Trajectory-Informed Technique for Adaptive Parameter Freezing in Large-Scale VQE
Venue: NeurIPS 2025
Accepted: yes
Keywords: Barren Plateau

Variational Quantum Algorithms

Circuit Optimization

Measurement Overhead

VQE

Parameter Freezing
Abstract: Variational quantum Eigensolver (VQE) is a leading candidate for harnessing quantum computers to advance quantum chemistry and materials simulations, yet its training efficiency deteriorates rapidly for large Hamiltonians. Two issues underlie this bottleneck: (i) the no-cloning theorem imposes a linear growth in circuit evaluations with the number of parameters per gradient step; and (ii) deeper circuits encounter barren plateaus (BPs), leading to exponentially increasing measurement overheads. To address these challenges, here we propose a deep learning framework, dubbed Titan, which identifies and freezes inactive parameters of a given ansätze at initialization for a specific class of Hamiltonians, reducing the optimization overhead without sacrificing accuracy. The motivation of Titan starts with our empirical findings that a subset of parameters consistently has negligible influence on training dynamics. Its design combines a theoretically grounded data construction strategy, ensuring each training example is informative and BP-resilient, with an adaptive neural architecture that generalizes across ansätze of varying sizes. Across benchmark transverse-field Ising models, Heisenberg models, and multiple molecule systems up to $30$ qubits, Titan  achieves up to $3\times$ faster convergence and $40$–$60\%$ fewer circuit evaluations than state-of-the-art baselines, while matching or surpassing their estimation accuracy. By proactively trimming parameter space, Titan lowers hardware demands and offers a scalable path toward utilizing VQE to advance practical quantum chemistry and materials science.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nTITAN is the work proposed in this paper to reduce the number of measurements required by VQEs by freezing some of the parameters statically and a priori so that the parameter shift doesn't have to be applied for their gradient calculation, saving circuit runs, time, and resources. The work also supports the prior work in reducing barren plateaus by showing that parameter freezing can also help reduce them in the optimization landscape. TITAN trains a RestNet model with input features as circuit parameters and their freezing intensities and outputs which parameters should be frozen before the VQE is executed.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\nParameter freezing of VQE is a bit of an underexplored area, and the thought of freezing the parameters a priori is especially interesting.\n\nThe empirical analysis indicates that there is a large scope for parameter freezing without losing performance in terms of achieving the ground state energy of the VQE Hamiltonian.\n\nWeaknesses:\n\nWe don’t know if the baseline technique reaches the minimum eigenvalue (the ground state energy in VQE) since only the difference between the baseline and TITAN is shown. Both techniques could be performing poorly and have a low differential. Please provide the results as raw numbers or provide the differential as a percentage of the raw minimum eigenvalue.\n\nNo error bars are provided for any values, even though they are all statistical quantities. For instance, the intensity of frozen parameters is a fractional quantity that varies from ansatz to ansatz, even if the two ansatzes have the same number of qubits (e.g., in Figure 2). So, some sort of variation metric or visualization should be provided, as these are not deterministic numbers. Also, Figure 2 just conveys that the number of frozen parameters increases linearly with the number of qubits and the number of layers. I'm not sure if this is a novel insight.\n\nShouldn’t the Hamiltonian itself be an input to the TITAN model training (currently, the input is only circuit features and freezing intensity of the parameters), because not just the circuit features but also the optimization loss affect the frozen parameters? So, the Hamiltonian itself should be included as an input? This might also help generalize the model. A similar case can be made for initial parameter values. They also affect the freezing intensity and should be included in the training.\n\nThe frozen parameters vary dynamically over time. I'm not sure if it is the best idea to freeze them statically a priori. \n\nIn most cases, the number of parameters frozen seems to be very low (Table 1), having a negligible impact on measured parameters.\n\nQUESTIONS:\nHow were 100-qubit circuits evaluated using simulators when it is impossible to simulate them on even the largest supercomputers? Were they purely Clifford?\n\nWould a different type of TITAN model need to be trained for different types of ansatz? An alternative to HEA, for example?\n\nWhat is the overall overhead of training and all the measurements that need to be done for training? Is the saving in inference worth it if each trained model only serves a limited class of VQE instances?\n\nDid you observe any interesting trends in which parameters got frozen (e.g., beginning layers, end layers, etc.)?\n\nWould TITAN need a large training dataset? Does a new model have to be trained for different ansatz sizes, number of qubits, number of layers, etc.? Do different VQE domains require different Titan models?\n\nLIMITATIONS:\nThe paper does not have direct negative societal impacts. Some limitations of the work are discussed, such as the scaling issues; others are highlighted above in the form of questions and weaknesses.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper focuses on the expense related to sampling overhead in VQE approaches on quantum computers, especially as it pertains in scaling with respect to number of parameters as general backpropagation is known not to be possible due to consequences of the no-cloning theorem.  Hence, reducing the number of actively trained parameters has the potential to dramatically reduce overall training costs for a commonly used method, which is exploited here.  Previous strategies have focused on simple parameter elimination or layerwise freezing.  This work introduces a new method based on machine learning from data on other optimization runs in order to predict optimized, adaptive freezing schedules to reduce costs while maintaining speed and accuracy as much as possible.  Across a range of systems up to 30 qubits, it achieves faster convergence and 40-60% fewer circuit evaluations to reach or surpass current accuracy.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\nThe paper is clear in the setup of the problem and motivation.  The conceptual novelty of using an ML approach to help decide the freezing strategy and optimize for cost is interesting, and different than previous metalearning approaches for guessing the parameters outright.\n\nWeaknesses\n\nThe major weakness of the paper is that for the added implementation complexity, the improvements are not as striking as one would hope.  In many of the presented results, Titan does a little bit worse or about the same as much simpler approaches, and only decreases the cost by a small constant factor.  It certainly appears to help in some cases, but it looks like it's not very obvious at the outset when it will, so for near experiments, one is likely to have to run the baseline anyways.  The results are presented in a way that make it a bit hard to see the potential advantages, and there is not much discussion of the size of training set or time required to reach the improvements reported.\n\nQUESTIONS:\n1. Can you try to better quantify in a single plot the typical expected improvement (or penalty) for time and energy when using Titan?  Right now it seems like there is substantial chance the energy gets worse in 50% of the cases for a modest decrease in cost, but I can't quite tell because it's in so many different plots for so many different models.  A summary statstic showing a high likelihood of maintaining quality, while clearly stating averaged reduced resources would be helpful for improving the significance and quality scores.\n\n2. Can you say more specifically what models and trajectories the Titan model itself was trained on, how much data was used, and what the training time was like?  Were the models exactly those tested in the paper, but with different parameters? Were they totally unrelated? If they were totally unrelated, or at much smaller sizes, this would strengthen the case this approach would generalize.\n\n3. The plotted freezing intensity suggests a somewhat deterministic pattern being discovered.  How does Titan compare to a freezing strategy that is not uniformly random, but rather. freezes early layers with much higher probability than later layers? Does Titan substantially beat such a baseline? See Figure 4 for my intuition.\n\nLIMITATIONS:\nThe authors could perhaps benefit from\n1. Further discussing the costs of training their approach to get a holistic view of cost\n2. Mention the additional problems in variational circuits related to local minima in the cost function", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-27"}

comments: SUMMARY:
To tackle challenges faced by Variational quantum Eigensolver (VQE), this paper introduces a deep learning framework called TITAN. The proposed method detects and freezes inactive parameters of a given ansatz at initialization for a targeted class of Hamiltonians.

STRENGTHS AND WEAKNESSES:
S1. The proposed method TITAN significantly speeds up the convergence, uses fewer circuit evaluations, while maintaining the accuracy. The methodology and experimental results demonstrate a non-trivial contribution.

S2. This paper is well-written and logically structured, making it accessible and easy to read even for readers who are not experts in the field.

S3.  The appendix and codebase are clear and well-structured, providing rich and important information.

W1. Can this method efficiently achieve accurate results for larger molecules?

W2. The frozen parameter is innovative, but the model architecture shows limited novelty.

QUESTIONS:
See Strengths And Weaknesses

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-03

comments: SUMMARY:
The paper first observes a phenomenon that in variational quantum circuits many parameters do not have drastic dynamics and hence can be frozen once optimized. Then the authors propose a learning-based framework to predict which parameters can be frozen to what values as initialization of variational quantum circuits. This prediction saves many resources in the training of variational quantum circuits and leads to faster convergence, which is demonstrated in experiments.

STRENGTHS AND WEAKNESSES:
Pros
1. The observation of the phenomenon of frozen parameters is interesting and insightful.
2. With the observation, it is also interesting to propose a learning-based method to predict frozen parameters from the description of the variational task.
3. The experiments conducted are comprehensive and illustrative. 

Cons
1. The data presented in Table 1 shows only a small portion of the parameters are frozen, possibly because of the high threshold. I would like to see how these thresholds affect the performance of the proposed method.
2. The color in Figure 6 is fainted for Random and TITAN, especially when printed. I suggest the authors make the transition smoother. 
3. The details on how TITAN complements Zero initialization and others are missing. I cannot fully understand what Figure 5 means, since I do not know the experiment setting.

QUESTIONS:
For a frozen parameter, the reason that it does not move significantly is that the gradients tend to be zero for them. As observed in the paper, this phenomenon happens more in the shallower layers. I wonder if there is any connection between this phenomenon and the gradient vanishing problem in classical NN training.

LIMITATIONS:
There are limited discussions on the limitation of the proposed method in the paper.
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-03