@article{quantum-advantage-bounds,
    title = {Information-Theoretic Bounds on Quantum Advantage in Machine
             Learning },
    author = {Huang, Hsin-Yuan and Kueng, Richard and Preskill, John},
    journal = {Phys. Rev. Lett.},
    volume = {126},
    issue = {19},
    pages = {190505},
    numpages = {7},
    year = {2021},
    month = {May},
    publisher = {American Physical Society},
    doi = {10.1103/PhysRevLett.126.190505},
    url = {https://link.aps.org/doi/10.1103/PhysRevLett.126.190505},
}

@article{quantum-advantage-learning,
    author = {Hsin-Yuan Huang and Michael Broughton and Jordan Cotler and Sitan
              Chen and Jerry Li and Masoud Mohseni and Hartmut Neven and Ryan
              Babbush and Richard Kueng and John Preskill and Jarrod R. McClean },
    title = {Quantum advantage in learning from experiments},
    journal = {Science},
    volume = {376},
    number = {6598},
    pages = {1182-1186},
    year = {2022},
    doi = {10.1126/science.abn7293},
    URL = {https://www.science.org/doi/abs/10.1126/science.abn7293},
    eprint = {https://www.science.org/doi/pdf/10.1126/science.abn7293},
    abstract = {Quantum technology promises to revolutionize how we learn about
                the physical world. An experiment that processes quantum data
                with a quantum computer could have substantial advantages over
                conventional experiments in which quantum states are measured and
                outcomes are processed with a classical computer. We proved that
                quantum machines could learn from exponentially fewer experiments
                than the number required by conventional experiments. This
                exponential advantage is shown for predicting properties of
                physical systems, performing quantum principal component analysis
                , and learning about physical dynamics. Furthermore, the quantum
                resources needed for achieving an exponential advantage are quite
                modest in some cases. Conducting experiments with 40
                superconducting qubits and 1300 quantum gates, we demonstrated
                that a substantial quantum advantage is possible with today’s
                quantum processors. There is considerable interest in extending
                the recent success of quantum computers in outperforming their
                conventional classical counterparts (quantum advantage) from some
                model mathematical problems to more meaningful tasks. Huang et
                al. show how manipulating multiple quantum states can provide an
                exponential advantage over classical processing of measurements
                of single-quantum states for certain learning tasks. These
                include predicting properties of physical systems, performing
                quantum principal component analysis on noisy states, and
                learning approximate models of physical dynamics (see the
                Perspective by Dunjko). In their proof-of-principle experiments
                using up to 40 qubits on a Google Sycamore quantum processor, the
                authors achieved almost four orders of magnitude of reduction in
                the required number of experiments over the best-known classical
                lower bounds. —YS Quantum-enhanced strategies can provide a
                dramatic performance boost in learning useful information from
                quantum experiments.},
}

@article{expressibility-and-entanglement,
    author = {Sim, Sukin and Johnson, Peter D. and Aspuru-Guzik, Alán},
    title = {Expressibility and Entangling Capability of Parameterized Quantum
             Circuits for Hybrid Quantum-Classical Algorithms},
    journal = {Advanced Quantum Technologies},
    volume = {2},
    number = {12},
    pages = {1900070},
    keywords = {quantum algorithms, quantum circuits, quantum computation},
    doi = {https://doi.org/10.1002/qute.201900070},
    url = {
           https://advanced.onlinelibrary.wiley.com/doi/abs/10.1002/qute.201900070
           },
    eprint = {
              https://advanced.onlinelibrary.wiley.com/doi/pdf/10.1002/qute.201900070
              },
    abstract = {Abstract Parameterized quantum circuits (PQCs) play an essential
                role in the performance of many variational quantum algorithms.
                One challenge in implementing such algorithms is choosing an
                effective circuit that well represents the solution space while
                maintaining a low circuit depth and parameter count. To
                characterize and identify expressible, yet compact, circuits,
                several descriptors are proposed, including expressibility and
                entangling capability, that are statistically estimated from
                classical simulations. These descriptors are computed for
                different circuit structures, varying the qubit connectivity and
                selection of gates. From these simulations, circuit fragments
                that perform well with respect to the descriptors are identified.
                In particular, a substantial improvement in performance of
                two-qubit gates in a ring or all-to-all connected arrangement,
                compared to that of those on a line, is observed. Furthermore,
                improvement in both descriptors is achieved by sequences of
                controlled X-rotation gates compared to sequences of controlled
                Z-rotation gates. In addition, it is investigated how
                expressibility “saturates” with increased circuit depth, finding
                that the rate and saturated value appear to be distinguishing
                features of a PQC. While the correlation between each descriptor
                and algorithm performance remains to be investigated, methods and
                results from this study can be useful for algorithm development
                and design of experiments.},
    year = {2019},
}

@article{quantum-dynamics-physical-resource,
    title = {Quantum dynamics as a physical resource},
    author = {Nielsen, Michael A. and Dawson, Christopher M. and Dodd, Jennifer
              L. and Gilchrist, Alexei and Mortimer, Duncan and Osborne, Tobias
              J. and Bremner, Michael J. and Harrow, Aram W. and Hines, Andrew},
    journal = {Phys. Rev. A},
    volume = {67},
    issue = {5},
    pages = {052301},
    numpages = {19},
    year = {2003},
    month = {May},
    publisher = {American Physical Society},
    doi = {10.1103/PhysRevA.67.052301},
    url = {https://link.aps.org/doi/10.1103/PhysRevA.67.052301},
}

@article{scaling-variational-circuit-depth,
    doi = {10.22331/q-2020-05-28-272},
    url = {https://doi.org/10.22331/q-2020-05-28-272},
    title = {Scaling of variational quantum circuit depth for condensed matter
             systems},
    author = {Bravo-Prieto, Carlos and Lumbreras-Zarapico, Josep and Tagliacozzo
              , Luca and Latorre, Jos{\'{e}} I.},
    journal = {{Quantum}},
    issn = {2521-327X},
    publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den
                 Quantenwissenschaften}},
    volume = {4},
    pages = {272},
    month = may,
    year = {2020},
}

@misc{akash,
    title = {Reinforcement learning-assisted quantum architecture search for
             variational quantum algorithms},
    author = {Akash Kundu},
    year = {2024},
    eprint = {2402.13754},
    archivePrefix = {arXiv},
    primaryClass = {quant-ph},
    url = {https://arxiv.org/abs/2402.13754},
}

@article{supernet-qas,
    author = {Du, Yuxuan and Huang, Tao and You, Shan and Hsieh, Min-Hsiu and
              Tao, Dacheng},
    title = {Quantum circuit architecture search for variational quantum
             algorithms},
    journal = {npj Quantum Information},
    year = {2022},
    month = {May},
    day = {23},
    volume = {8},
    number = {1},
    pages = {62},
    abstract = {Variational quantum algorithms (VQAs) are expected to be a path
                to quantum advantages on noisy intermediate-scale quantum
                devices. However, both empirical and theoretical results exhibit
                that the deployed ansatz heavily affects the performance of VQAs
                such that an ansatz with a larger number of quantum gates enables
                a stronger expressivity, while the accumulated noise may render a
                poor trainability. To maximally improve the robustness and
                trainability of VQAs, here we devise a resource and runtime
                efficient scheme termed quantum architecture search (QAS). In
                particular, given a learning task, QAS automatically seeks a
                near-optimal ansatz (i.e., circuit architecture) to balance
                benefits and side-effects brought by adding more noisy quantum
                gates to achieve a good performance. We implement QAS on both the
                numerical simulator and real quantum hardware, via the IBM cloud,
                to accomplish data classification and quantum chemistry tasks. In
                the problems studied, numerical and experimental results show
                that QAS cannot only alleviate the influence of quantum noise and
                barren plateaus but also outperforms VQAs with pre-selected
                ansatze.},
    issn = {2056-6387},
    doi = {10.1038/s41534-022-00570-y},
    url = {https://doi.org/10.1038/s41534-022-00570-y},
}


@article{evolutionary-architecture-search,
    AUTHOR = {Ding, Li and Spector, Lee},
    TITLE = {Multi-Objective Evolutionary Architecture Search for Parameterized
             Quantum Circuits},
    JOURNAL = {Entropy},
    VOLUME = {25},
    YEAR = {2023},
    NUMBER = {1},
    ARTICLE-NUMBER = {93},
    URL = {https://www.mdpi.com/1099-4300/25/1/93},
    PubMedID = {36673234},
    ISSN = {1099-4300},
    ABSTRACT = {Recent work on hybrid quantum-classical machine learning systems
                has demonstrated success in utilizing parameterized quantum
                circuits (PQCs) to solve the challenging reinforcement learning
                (RL) tasks, with provable learning advantages over classical
                systems, e.g., deep neural networks. While existing work
                demonstrates and exploits the strength of PQC-based models, the
                design choices of PQC architectures and the interactions between
                different quantum circuits on learning tasks are generally
                underexplored. In this work, we introduce a Multi-objective
                Evolutionary Architecture Search framework for parameterized
                quantum circuits (MEAS-PQC), which uses a multi-objective genetic
                algorithm with quantum-specific configurations to perform
                efficient searching of optimal PQC architectures. Experimental
                results show that our method can find architectures that have
                superior learning performance on three benchmark RL tasks, and
                are also optimized for additional objectives including reductions
                in quantum noise and model size. Further analysis of patterns and
                probability distributions of quantum operations helps identify
                performance-critical design choices of hybrid quantum-classical
                learning systems.},
    DOI = {10.3390/e25010093},
}

@misc{generative-quantum-eigensolver,
    title = {The generative quantum eigensolver (GQE) and its application for
             ground state search},
    author = {Kouhei Nakaji and Lasse Bjørn Kristensen and Ryota Kemmoku and
              Jorge A. Campos-Gonzalez-Angulo and Mohammad Ghazi Vakili and
              Haozhe Huang and Mohsen Bagherimehrab and Christoph Gorgulla and
              FuTe Wong and Alex McCaskey and Jin-Sung Kim and Thien Nguyen and
              Pooja Rao and Qi Gao and Michihiko Sugawara and Naoki Yamamoto and
              Alán Aspuru-Guzik},
    year = {2025},
    eprint = {2401.09253},
    archivePrefix = {arXiv},
    primaryClass = {quant-ph},
    url = {https://arxiv.org/abs/2401.09253},
}

@inproceedings{calibration-aware-transpilation,
    author = {Ji, Yanjun and Brandhofer, Sebastian and Polian, Ilia},
    booktitle = {2022 IEEE International Conference on Quantum Computing and
                 Engineering (QCE)},
    title = {Calibration-Aware Transpilation for Variational Quantum
             Optimization},
    year = {2022},
    volume = {},
    number = {},
    pages = {204-214},
    keywords = {Computers;Quantum computing;Quantum algorithm;Program
                processors;Error analysis;Logic
                gates;Calibration;Calibration-Aware;Transpilation;NISQ;QAOA;Benchmarking;Quantum
                Computing},
    doi = {10.1109/QCE53715.2022.00040},
}

@article{topology-driven-search,
    author = {Su, Junjian and Fan, Jiacheng and Wu, Shengyao and Li, Guanghui
              and Qin, Sujuan and Gao, Fei},
    title = {Topology-driven quantum architecture search framework},
    journal = {Science China Information Sciences},
    year = {2025},
    month = {Jul},
    day = {03},
    volume = {68},
    number = {8},
    pages = {180507},
    abstract = {The limitations of noisy intermediate-scale quantum (NISQ)
                devices have motivated the development of variational quantum
                algorithms (VQAs), which are designed to potentially achieve
                quantum advantage for specific tasks. Quantum architecture search
                (QAS) algorithms play a critical role in automating the design of
                high-performance parameterized quantum circuits (PQCs) for VQAs.
                However, existing QAS approaches struggle with large search
                spaces, leading to substantial computational overhead when
                optimizing large-scale quantum circuits. Extensive empirical
                analysis reveals that circuit topology has a greater impact on
                quantum circuit performance than gate types. Based on this
                insight, we propose the topology-driven quantum architecture
                search (TD-QAS) framework, which first identifies optimal circuit
                topologies and then fine-tunes the gate types. In the fine-tuning
                phase, the QAS inherits parameters from the topology search phase
                , eliminating the need for training from scratch. By decoupling
                the large search space into separate topology and gate-type
                components, TD-QAS avoids exploring gate configurations within
                low-performance topologies, thereby significantly reducing
                computational complexity. Numerical simulations across various
                tasks, under both noiseless and noisy conditions, validate the
                effectiveness of the TD-QAS framework. This framework advances
                standard QAS algorithms by enabling the identification of
                high-performance quantum circuits while minimizing computational
                demands. These findings indicate that TD-QAS deepens our
                understanding of VQAs and offers broad potential for the
                development of future QAS algorithms.},
    issn = {1869-1919},
    doi = {10.1007/s11432-024-4486-x},
    url = {https://doi.org/10.1007/s11432-024-4486-x},
}

@article{Hirsbrunner2024beyondmp,
    doi = {10.22331/q-2024-11-26-1538},
    url = {https://doi.org/10.22331/q-2024-11-26-1538},
    title = {Beyond {MP}2 initialization for unitary coupled cluster quantum
             circuits},
    author = {Hirsbrunner, Mark R. and Chamaki, Diana and Mullinax, J. Wayne and
              Tubman, Norm M.},
    journal = {{Quantum}},
    issn = {2521-327X},
    publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den
                 Quantenwissenschaften}},
    volume = {8},
    pages = {1538},
    month = nov,
    year = {2024},
}

@misc{liu2025haqgnnhardwareawarequantumkernel,
    title = {HaQGNN: Hardware-Aware Quantum Kernel Design Based on Graph Neural
             Networks},
    author = {Yuxiang Liu and Fanxu Meng and Lu Wang and Yi Hu and Sixuan Li and
              Xutao Yu and Zaichen Zhang},
    year = {2025},
    eprint = {2506.21161},
    archivePrefix = {arXiv},
    primaryClass = {quant-ph},
    url = {https://arxiv.org/abs/2506.21161},
}

@article{training-free,
    title = {Training-Free Quantum Architecture Search},
    volume = {38},
    url = {https://ojs.aaai.org/index.php/AAAI/article/view/29135},
    DOI = {10.1609/aaai.v38i11.29135},
    abstractNote = {Variational quantum algorithm (VQA) derives advantages from
                    its error resilience and high flexibility in quantum resource
                    requirements, rendering it broadly applicable in the noisy
                    intermediate-scale quantum era. As the performance of VQA
                    highly relies on the structure of the parameterized quantum
                    circuit, it is worthwhile to propose quantum architecture
                    search (QAS) algorithms to automatically search for
                    high-performance circuits. Nevertheless, existing QAS methods
                    are time-consuming, requiring circuit training to assess
                    circuit performance. This study pioneers training-free QAS by
                    utilizing two training-free proxies to rank quantum circuits,
                    in place of the expensive circuit training employed in
                    conventional QAS. Taking into account the precision and
                    computational overhead of the path-based and
                    expressibility-based proxies, we devise a two-stage
                    progressive training-free QAS (TF-QAS). Initially, directed
                    acyclic graphs (DAGs) are employed for circuit representation
                    , and a zero-cost proxy based on the number of paths in the
                    DAG is designed to filter out a substantial portion of
                    unpromising circuits. Subsequently, an expressibility-based
                    proxy, finely reflecting circuit performance, is employed to
                    identify high-performance circuits from the remaining
                    candidates. These proxies evaluate circuit performance
                    without circuit training, resulting in a remarkable reduction
                    in computational cost compared to current training-based QAS
                    methods. Simulations on three VQE tasks demonstrate that
                    TF-QAS achieves a substantial enhancement of sampling
                    efficiency ranging from 5 to 57 times compared to
                    state-of-the-art QAS, while also being 6 to 17 times faster.},
    number = {11},
    journal = {Proceedings of the AAAI Conference on Artificial Intelligence},
    author = {He, Zhimin and Deng, Maijie and Zheng, Shenggen and Li, Lvzhou and
              Situ, Haozhen},
    year = {2024},
    month = {Mar.},
    pages = {12430-12438},
}

@article{npqas,
    doi = {10.1088/2632-2153/ac28dd},
    url = {https://doi.org/10.1088/2632-2153/ac28dd},
    year = {2021},
    month = {oct},
    publisher = {IOP Publishing},
    volume = {2},
    number = {4},
    pages = {045027},
    author = {Zhang, Shi-Xin and Hsieh, Chang-Yu and Zhang, Shengyu and Yao,
              Hong},
    title = {Neural predictor based quantum architecture search},
    journal = {Machine Learning: Science and Technology},
    abstract = {Variational quantum algorithms (VQAs) are widely speculated to
                deliver quantum advantages for practical problems under the
                quantum–classical hybrid computational paradigm in the near term.
                Both theoretical and practical developments of VQAs share many
                similarities with those of deep learning. For instance, a key
                component of VQAs is the design of task-dependent parameterized
                quantum circuits (PQCs) as in the case of designing a good neural
                architecture in deep learning. Partly inspired by the recent
                success of AutoML and neural architecture search (NAS), quantum
                architecture search (QAS) is a collection of methods devised to
                engineer an optimal task-specific PQC. It has been proven that
                QAS-designed VQAs can outperform expert-crafted VQAs in various
                scenarios. In this work, we propose to use a neural network based
                predictor as the evaluation policy for QAS. We demonstrate a
                neural predictor guided QAS can discover powerful quantum circuit
                ansatz, yielding state-of-the-art results for various examples
                from quantum simulation and quantum machine learning. Notably,
                neural predictor guided QAS provides a better solution than that
                by the random-search baseline while using an order of magnitude
                less of circuit evaluations. Moreover, the predictor for QAS as
                well as the optimal ansatz found by QAS can both be transferred
                and generalized to address similar problems.},
}

@article{hea-kandala,
    author = {Kandala, Abhinav and Mezzacapo, Antonio and Temme, Kristan and
              Takita, Maika and Brink, Markus and Chow, Jerry M. and Gambetta,
              Jay M.},
    title = {Hardware-efficient variational quantum eigensolver for small
             molecules and quantum magnets},
    journal = {Nature},
    year = {2017},
    month = {Sep},
    day = {01},
    volume = {549},
    number = {7671},
    pages = {242-246},
    abstract = {The ground-state energy of small molecules is determined
                efficiently using six qubits of a superconducting quantum
                processor.},
    issn = {1476-4687},
    doi = {10.1038/nature23879},
    url = {https://doi.org/10.1038/nature23879},
}

@article{tensorcircuit,
    doi = {10.22331/q-2023-02-02-912},
    url = {https://doi.org/10.22331/q-2023-02-02-912},
    title = {Tensor{C}ircuit: a {Q}uantum {S}oftware {F}ramework for the {NISQ}
             {E}ra},
    author = {Zhang, Shi-Xin and Allcock, Jonathan and Wan, Zhou-Quan and Liu,
              Shuo and Sun, Jiace and Yu, Hao and Yang, Xing-Han and Qiu,
              Jiezhong and Ye, Zhaofeng and Chen, Yu-Qin and Lee, Chee-Kong and
              Zheng, Yi-Cong and Jian, Shao-Kai and Yao, Hong and Hsieh, Chang-Yu
              and Zhang, Shengyu},
    journal = {{Quantum}},
    issn = {2521-327X},
    publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den
                 Quantenwissenschaften}},
    volume = {7},
    pages = {912},
    month = feb,
    year = {2023},
}

@misc{genetic-expressibility,
    title = {Genetic optimization of ansatz expressibility for enhanced
             variational quantum algorithm performance},
    author = {Manish Mallapur and Ronit Raj and Ankur Raina},
    year = {2025},
    eprint = {2509.05804},
    archivePrefix = {arXiv},
    primaryClass = {quant-ph},
    url = {https://arxiv.org/abs/2509.05804},
}

@article{Zhang_2022,
    doi = {10.1088/2058-9565/ac87cd},
    url = {https://doi.org/10.1088/2058-9565/ac87cd},
    year = {2022},
    month = {aug},
    publisher = {IOP Publishing},
    volume = {7},
    number = {4},
    pages = {045023},
    author = {Zhang, Shi-Xin and Hsieh, Chang-Yu and Zhang, Shengyu and Yao,
              Hong},
    title = {Differentiable quantum architecture search},
    journal = {Quantum Science and Technology},
    abstract = {Quantum architecture search (QAS) is the process of automating
                architecture engineering of quantum circuits. It has been desired
                to construct a powerful and general QAS platform which can
                significantly accelerate current efforts to identify quantum
                advantages of error-prone and depth-limited quantum circuits in
                the NISQ era. Hereby, we propose a general framework of
                differentiable quantum architecture search (DQAS), which enables
                automated designs of quantum circuits in an end-to-end
                differentiable fashion. We present several examples of circuit
                design problems to demonstrate the power of DQAS. For instance,
                unitary operations are decomposed into quantum gates, noisy
                circuits are re-designed to improve accuracy, and circuit layouts
                for quantum approximation optimization algorithm are
                automatically discovered and upgraded for combinatorial
                optimization problems. These results not only manifest the vast
                potential of DQAS being an essential tool for the NISQ
                application developments, but also present an interesting
                research topic from the theoretical perspective as it draws
                inspirations from the newly emerging interdisciplinary paradigms
                of differentiable programming, probabilistic programming, and
                quantum programming.},
}

@article{qdea,
    title = {A survey on Quality-Diversity optimization: Approaches,
             applications, and challenges},
    journal = {Swarm and Evolutionary Computation},
    volume = {100},
    pages = {102240},
    year = {2026},
    issn = {2210-6502},
    doi = {https://doi.org/10.1016/j.swevo.2025.102240},
    url = {https://www.sciencedirect.com/science/article/pii/S2210650225003979},
    author = {Haoxiang Qin and Yi Xiang and Hainan Zhang and Yuyan Han and
              Yuting Wang and Xinrui Tao and Yiping Liu},
    keywords = {Quality-Diversity optimization, Evolutionary computation,
                Feature space, MAP-Elites},
    abstract = {Quality-Diversity (QD) optimization is a paradigm of
                evolutionary computation (EC) that extends the classic approaches
                , aiming to generate a collection of solutions that are both
                diverse and high-performing. Unlike traditional evolutionary
                algorithms (EAs), QD methods emphasize the illumination (or
                coverage) of a user-defined feature space, while simultaneously
                aiming for local optimization within each discovered region of
                the feature space. Over the past decade, QD has rapidly developed
                and proven effective in areas such as evolutionary robotics and
                video games. However, a systematic review of this growing field
                remains lacking. To date, the most recent review article on QD
                was published in 2021. Therefore, to offer a more comprehensive
                overview of the latest QD research, this paper provides a
                thorough survey of QD optimization, covering its foundational
                principles and representative algorithmic frameworks such as
                Novelty Search with Local Competition (NSLC), MAP-Elites, the
                unified modular QD framework, and RIBS. In addition, we divide
                the algorithm improvement part into three modules for discussion:
                containers, selection, and mutation. Then, the evaluation metrics
                widely used in QD optimization are listed for researchers. We
                further explore its diverse applications across domains such as
                evolutionary robotics, video games, scheduling, software testing,
                and engineering design. Finally, we discuss the current
                challenges in the field and outline promising directions for
                future research.},
}
