add to tf-qas presentation

presentations/tf-qas.typ

@@ -0,0 +1,180 @@
+
+#import "@preview/touying:0.6.1": *
+#import "@preview/physica:0.9.5": *
+#import "@preview/cetz:0.3.4"
+#import "@preview/typsium:0.2.0": ce
+#import "@preview/numbly:0.1.0": numbly
+#import "./theme.typ": *
+
+#set heading(numbering: numbly("{1}.", default: "1.1"))
+#show ref: set text(size:0.5em, baseline: -0.75em)
+
+#let cetz-canvas = touying-reducer.with(reduce: cetz.canvas, cover: cetz.draw.hide.with(bounds: true))
+
+
+#show: university-theme.with(
+  config-info(
+    title: "Implementation Specific QAS", // Required
+    date: datetime.today().display(),
+    authors: ("Noa Aarts"),
+  
+    // Optional Styling (for more / explanation see in the typst universe)
+    // ignore how bad the images look i'll adjust it until Monday
+    title-color: blue.darken(10%),
+  ),
+  config-common(
+    // handout: true, // enable this for a version without animations
+  ),
+  aspect-ratio: "16-9",
+  config-colors(
+   primary: rgb("#00a6d6"),
+   secondary: rgb("#00b3dc"),
+   tertiary: rgb("#b8cbde"),
+   neutral-lightest: rgb("#ffffff"),
+   neutral-darkest: rgb("#000000"),
+ ),
+)
+
+#show outline.entry: it => link(
+  it.element.location(),
+   text(fill: rgb("#00b3dc"), size: 1.3em)[#it.indented(it.prefix(), it.body())],
+)
+
+
+#slide[
+- #text(fill: purple)[Purple text is a question I have]
+- #text(fill: red)[Red text is something I think they did not do well]
+- #text(fill: orange)[Orange text is something I would have preferred a reference for]
+]
+
+#title-slide()
+
+#outline(depth: 1, title: text(fill: rgb("#00a6d6"))[Content])
+
+= Introduction
+
+== Variational Quantum Algorithms
+ 
+- Classical optimisation
+
+- Parametrized Quantum Circuit
+
+- Very structure dependent
+
+== Quantum Architecture Search
+
+- Automated Design
+
+- New Problems
+  - Exponential search space
+  - Ranking circuits during search
+
+- Parallels with Neural Architecture Search
+  - Differentiable QAS
+  - Reinforcement-learning QAS
+  - Predictor-based QAS
+  - Weight-sharing QAS
+
+== Training Free Proxies
+
+- No need to train parametrized quantum circuit
+  \ $->$ Faster searching
+
+- No objective functions
+  - Possibility for easier transfer
+
+- Need to prove correlation with ground-truth
+  #text(fill: red)[- not done in paper]
+
+= Method
+
+== Overview
+
+#align(horizon)[
+1. Sample circuits from search space
+
+2. Filter using Path proxy
+
+3. Rank on Expressibility
+]
+
+== Search Space
+
+Following Neural Predictor based QAS@npqas
+- Native gate set ($cal(A) = {R_x, R_y, R_z, X X, Y Y, Z Z}$)
+- Layer based sampling
+  - Layers of $n/2$ gates
+- Gate based sampling
+  - placing 1 gate at a time
+
+- Why not fully random circuits?
+  - Mitigating barren plateaus
+  - Mitigating high circuit depth
+  #text(fill:purple)[- What is the difference with gate-based?]
+
+== Path Proxy
+
+#slide(composer: (auto, auto))[
+- 'zero-cost'
+  #text(fill:orange)[- best case: $O("Operations" times "Qubits"^2)$] 
+  // I think it'd scale like this, but am uncertain since they didn't explain it anywhere
+  - below $7.8 times 10^(-4)$s
+
+1. Represent as Directed acyclic graph
+
+2. Count distinct paths from input-to-output
+
+3. Top-R highest path count circuits
+][
+  #image("tf-qas/circuit.png", height: 40%)
+  #image("tf-qas/dag.png")
+  #text(size: 0.6em)[#align(right)[from Training-Free QAS@training-free]]
+]
+
+== Expressibility Proxy
+
+#text(fill: red)[- Performance hinges on Expressibility]
+- Particularly valueable without prior knowledge
+
+#block(fill: blue.lighten(85%), inset: 12pt, radius: 6pt, stroke: 2pt + blue)[
+  *Expressibility:* \ 
+  The capability to uniformly reach the entire Hilbert space.
+]
+
+1. Calculate expressibility:
+#align(center)[$cal(E)(cal(C)) = -D_"KL" (P(cal(C),F) || P_"Haar" (F)$]
+
+2. Top expressibility circuits
+
+= Results
+
+== Evaluation
+
+- Three variational quantum eigensolver tasks
+  - Transverse field Ising model
+  - Heisenberg model
+  - $"Be"space.hair"H"_2$ molecule
+
+- Compared to
+  - Network-Predictive QAS@npqas
+  #text(fill: red)[- Hardware-efficient ansatz@hea-kandala] // but like, which one
+  - Random sampling
+
+- Implementation details
+  - TensorCircuit python package@tensorcircuit
+  #text(fill: red)[- No code included anywhere]
+
+
+= Conclusion
+
+==
+
+- Combining proxies can improve on either
+
+
+
+#slide[
+  == References <touying:unoutlined>
+  #bibliography("references.bib", title: [])
+]
+

report/references.bib

@@ -1,6 +1,6 @@
 @article{quantum-advantage-bounds,
-	title = {Information-Theoretic Bounds on Quantum Advantage in Machine Learning
+    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},
@@ -28,35 +28,36 @@
     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
+                the physical world. An experiment that processes quantum data
-	            a quantum computer could have substantial advantages over
+                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,
+                physical systems, performing quantum principal component analysis
-	            and learning about physical dynamics. Furthermore, the quantum
+                , 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
+                superconducting qubits and 1300 quantum gates, we demonstrated
-	            a substantial quantum advantage is possible with today’s quantum
+                that a substantial quantum advantage is possible with today’s
-	            processors. There is considerable interest in extending the recent
+                quantum processors. There is considerable interest in extending
-	            success of quantum computers in outperforming their conventional
+                the recent success of quantum computers in outperforming their
-	            classical counterparts (quantum advantage) from some model
+                conventional classical counterparts (quantum advantage) from some
-	            mathematical problems to more meaningful tasks. Huang et al. show
+                model mathematical problems to more meaningful tasks. Huang et
-	            how manipulating multiple quantum states can provide an exponential
+                al. show how manipulating multiple quantum states can provide an
-	            advantage over classical processing of measurements of
+                exponential advantage over classical processing of measurements
-	            single-quantum states for certain learning tasks. These include
+                of single-quantum states for certain learning tasks. These
-	            predicting properties of physical systems, performing quantum
+                include predicting properties of physical systems, performing
-	            principal component analysis on noisy states, and learning
+                quantum principal component analysis on noisy states, and
-	            approximate models of physical dynamics (see the Perspective by
+                learning approximate models of physical dynamics (see the
-	            Dunjko). In their proof-of-principle experiments using up to 40
+                Perspective by Dunjko). In their proof-of-principle experiments
-	            qubits on a Google Sycamore quantum processor, the authors achieved
+                using up to 40 qubits on a Google Sycamore quantum processor, the
-	            almost four orders of magnitude of reduction in the required number
+                authors achieved almost four orders of magnitude of reduction in
-	            of experiments over the best-known classical lower bounds. —YS
+                the required number of experiments over the best-known classical
-	            Quantum-enhanced strategies can provide a dramatic performance
+                lower bounds. —YS Quantum-enhanced strategies can provide a
-	            boost in learning useful information from quantum experiments.},
+                dramatic performance boost in learning useful information from
+                quantum experiments.},
 }
 
 @article{expressibility-and-entanglement,
@@ -69,42 +70,44 @@
     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
+    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
+                role in the performance of many variational quantum algorithms.
-	            challenge in implementing such algorithms is choosing an effective
+                One challenge in implementing such algorithms is choosing an
-	            circuit that well represents the solution space while maintaining a
+                effective circuit that well represents the solution space while
-	            low circuit depth and parameter count. To characterize and identify
+                maintaining a low circuit depth and parameter count. To
-	            expressible, yet compact, circuits, several descriptors are
+                characterize and identify expressible, yet compact, circuits,
-	            proposed, including expressibility and entangling capability, that
+                several descriptors are proposed, including expressibility and
-	            are statistically estimated from classical simulations. These
+                entangling capability, that are statistically estimated from
-	            descriptors are computed for different circuit structures, varying
+                classical simulations. These descriptors are computed for
-	            the qubit connectivity and selection of gates. From these
+                different circuit structures, varying the qubit connectivity and
-	            simulations, circuit fragments that perform well with respect to
+                selection of gates. From these simulations, circuit fragments
-	            the descriptors are identified. In particular, a substantial
+                that perform well with respect to the descriptors are identified.
-	            improvement in performance of two-qubit gates in a ring or
+                In particular, a substantial improvement in performance of
-	            all-to-all connected arrangement, compared to that of those on a
+                two-qubit gates in a ring or all-to-all connected arrangement,
-	            line, is observed. Furthermore, improvement in both descriptors is
+                compared to that of those on a line, is observed. Furthermore,
-	            achieved by sequences of controlled X-rotation gates compared to
+                improvement in both descriptors is achieved by sequences of
-	            sequences of controlled Z-rotation gates. In addition, it is
+                controlled X-rotation gates compared to sequences of controlled
-	            investigated how expressibility “saturates” with increased circuit
+                Z-rotation gates. In addition, it is investigated how
-	            depth, finding that the rate and saturated value appear to be
+                expressibility “saturates” with increased circuit depth, finding
-	            distinguishing features of a PQC. While the correlation between
+                that the rate and saturated value appear to be distinguishing
-	            each descriptor and algorithm performance remains to be
+                features of a PQC. While the correlation between each descriptor
-	            investigated, methods and results from this study can be useful for
+                and algorithm performance remains to be investigated, methods and
-	            algorithm development and design of experiments.},
+                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.
+    author = {Nielsen, Michael A. and Dawson, Christopher M. and Dodd, Jennifer
-	          and Gilchrist, Alexei and Mortimer, Duncan and Osborne, Tobias J. and
+              L. and Gilchrist, Alexei and Mortimer, Duncan and Osborne, Tobias
-	          Bremner, Michael J. and Harrow, Aram W. and Hines, Andrew},
+              J. and Bremner, Michael J. and Harrow, Aram W. and Hines, Andrew},
     journal = {Phys. Rev. A},
     volume = {67},
     issue = {5},
@@ -122,8 +125,8 @@
     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,
+    author = {Bravo-Prieto, Carlos and Lumbreras-Zarapico, Josep and Tagliacozzo
-	          Luca and Latorre, Jos{\'{e}} I.},
+              , Luca and Latorre, Jos{\'{e}} I.},
     journal = {{Quantum}},
     issn = {2521-327X},
     publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den
@@ -135,7 +138,8 @@
 }
 
 @misc{akash,
-      title={Reinforcement learning-assisted quantum architecture search for variational quantum algorithms}, 
+    title = {Reinforcement learning-assisted quantum architecture search for
+             variational quantum algorithms},
     author = {Akash Kundu},
     year = {2024},
     eprint = {2402.13754},
@@ -145,8 +149,8 @@
 }
 
 @article{architecture-search,
-	author = {Du, Yuxuan and Huang, Tao and You, Shan and Hsieh, Min-Hsiu and Tao,
+    author = {Du, Yuxuan and Huang, Tao and You, Shan and Hsieh, Min-Hsiu and
-	          Dacheng},
+              Tao, Dacheng},
     title = {Quantum circuit architecture search for variational quantum
              algorithms},
     journal = {npj Quantum Information},
@@ -156,24 +160,25 @@
     volume = {8},
     number = {1},
     pages = {62},
-	abstract = {Variational quantum algorithms (VQAs) are expected to be a path to
+    abstract = {Variational quantum algorithms (VQAs) are expected to be a path
-	            quantum advantages on noisy intermediate-scale quantum devices.
+                to quantum advantages on noisy intermediate-scale quantum
-	            However, both empirical and theoretical results exhibit that the
+                devices. However, both empirical and theoretical results exhibit
-	            deployed ansatz heavily affects the performance of VQAs such that
+                that the deployed ansatz heavily affects the performance of VQAs
-	            an ansatz with a larger number of quantum gates enables a stronger
+                such that an ansatz with a larger number of quantum gates enables
-	            expressivity, while the accumulated noise may render a poor
+                a stronger expressivity, while the accumulated noise may render a
-	            trainability. To maximally improve the robustness and trainability
+                poor trainability. To maximally improve the robustness and
-	            of VQAs, here we devise a resource and runtime efficient scheme
+                trainability of VQAs, here we devise a resource and runtime
-	            termed quantum architecture search (QAS). In particular, given a
+                efficient scheme termed quantum architecture search (QAS). In
-	            learning task, QAS automatically seeks a near-optimal ansatz (i.e.,
+                particular, given a learning task, QAS automatically seeks a
-	            circuit architecture) to balance benefits and side-effects brought
+                near-optimal ansatz (i.e., circuit architecture) to balance
-	            by adding more noisy quantum gates to achieve a good performance.
+                benefits and side-effects brought by adding more noisy quantum
-	            We implement QAS on both the numerical simulator and real quantum
+                gates to achieve a good performance. We implement QAS on both the
-	            hardware, via the IBM cloud, to accomplish data classification and
+                numerical simulator and real quantum hardware, via the IBM cloud,
-	            quantum chemistry tasks. In the problems studied, numerical and
+                to accomplish data classification and quantum chemistry tasks. In
-	            experimental results show that QAS cannot only alleviate the
+                the problems studied, numerical and experimental results show
-	            influence of quantum noise and barren plateaus but also outperforms
+                that QAS cannot only alleviate the influence of quantum noise and
-	            VQAs with pre-selected ansatze.},
+                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},
@@ -203,13 +208,13 @@
                 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
+                algorithm with quantum-specific configurations to perform
-	            searching of optimal PQC architectures. Experimental results show
+                efficient searching of optimal PQC architectures. Experimental
-	            that our method can find architectures that have superior learning
+                results show that our method can find architectures that have
-	            performance on three benchmark RL tasks, and are also optimized for
+                superior learning performance on three benchmark RL tasks, and
-	            additional objectives including reductions in quantum noise and
+                are also optimized for additional objectives including reductions
-	            model size. Further analysis of patterns and probability
+                in quantum noise and model size. Further analysis of patterns and
-	            distributions of quantum operations helps identify
+                probability distributions of quantum operations helps identify
                 performance-critical design choices of hybrid quantum-classical
                 learning systems.},
     DOI = {10.3390/e25010093},
@@ -218,11 +223,12 @@
 @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
+    author = {Kouhei Nakaji and Lasse Bjørn Kristensen and Ryota Kemmoku and
-	          A. Campos-Gonzalez-Angulo and Mohammad Ghazi Vakili and Haozhe Huang
+              Jorge A. Campos-Gonzalez-Angulo and Mohammad Ghazi Vakili and
-	          and Mohsen Bagherimehrab and Christoph Gorgulla and FuTe Wong and
+              Haozhe Huang and Mohsen Bagherimehrab and Christoph Gorgulla and
-	          Alex McCaskey and Jin-Sung Kim and Thien Nguyen and Pooja Rao and Qi
+              FuTe Wong and Alex McCaskey and Jin-Sung Kim and Thien Nguyen and
-	          Gao and Michihiko Sugawara and Naoki Yamamoto and Alán Aspuru-Guzik},
+              Pooja Rao and Qi Gao and Michihiko Sugawara and Naoki Yamamoto and
+              Alán Aspuru-Guzik},
     year = {2025},
     eprint = {2401.09253},
     archivePrefix = {arXiv},
@@ -234,7 +240,8 @@
     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},
+    title = {Calibration-Aware Transpilation for Variational Quantum
+             Optimization},
     year = {2022},
     volume = {},
     number = {},
@@ -247,8 +254,8 @@
 }
 
 @article{topology-driven-search,
-	author = {Su, Junjian and Fan, Jiacheng and Wu, Shengyao and Li, Guanghui and
+    author = {Su, Junjian and Fan, Jiacheng and Wu, Shengyao and Li, Guanghui
-	          Qin, Sujuan and Gao, Fei},
+              and Qin, Sujuan and Gao, Fei},
     title = {Topology-driven quantum architecture search framework},
     journal = {Science China Information Sciences},
     year = {2025},
@@ -257,32 +264,33 @@
     volume = {68},
     number = {8},
     pages = {180507},
-	abstract = {The limitations of noisy intermediate-scale quantum (NISQ) devices
+    abstract = {The limitations of noisy intermediate-scale quantum (NISQ)
-	            have motivated the development of variational quantum algorithms
+                devices have motivated the development of variational quantum
-	            (VQAs), which are designed to potentially achieve quantum advantage
+                algorithms (VQAs), which are designed to potentially achieve
-	            for specific tasks. Quantum architecture search (QAS) algorithms
+                quantum advantage for specific tasks. Quantum architecture search
-	            play a critical role in automating the design of high-performance
+                (QAS) algorithms play a critical role in automating the design of
-	            parameterized quantum circuits (PQCs) for VQAs. However, existing
+                high-performance parameterized quantum circuits (PQCs) for VQAs.
-	            QAS approaches struggle with large search spaces, leading to
+                However, existing QAS approaches struggle with large search
-	            substantial computational overhead when optimizing large-scale
+                spaces, leading to substantial computational overhead when
-	            quantum circuits. Extensive empirical analysis reveals that circuit
+                optimizing large-scale quantum circuits. Extensive empirical
-	            topology has a greater impact on quantum circuit performance than
+                analysis reveals that circuit topology has a greater impact on
-	            gate types. Based on this insight, we propose the topology-driven
+                quantum circuit performance than gate types. Based on this
-	            quantum architecture search (TD-QAS) framework, which first
+                insight, we propose the topology-driven quantum architecture
-	            identifies optimal circuit topologies and then fine-tunes the gate
+                search (TD-QAS) framework, which first identifies optimal circuit
-	            types. In the fine-tuning phase, the QAS inherits parameters from
+                topologies and then fine-tunes the gate types. In the fine-tuning
-	            the topology search phase, eliminating the need for training from
+                phase, the QAS inherits parameters from the topology search phase
-	            scratch. By decoupling the large search space into separate
+                , eliminating the need for training from scratch. By decoupling
-	            topology and gate-type components, TD-QAS avoids exploring gate
+                the large search space into separate topology and gate-type
-	            configurations within low-performance topologies, thereby
+                components, TD-QAS avoids exploring gate configurations within
-	            significantly reducing computational complexity. Numerical
+                low-performance topologies, thereby significantly reducing
-	            simulations across various tasks, under both noiseless and noisy
+                computational complexity. Numerical simulations across various
-	            conditions, validate the effectiveness of the TD-QAS framework.
+                tasks, under both noiseless and noisy conditions, validate the
-	            This framework advances standard QAS algorithms by enabling the
+                effectiveness of the TD-QAS framework. This framework advances
-	            identification of high-performance quantum circuits while
+                standard QAS algorithms by enabling the identification of
-	            minimizing computational demands. These findings indicate that
+                high-performance quantum circuits while minimizing computational
-	            TD-QAS deepens our understanding of VQAs and offers broad potential
+                demands. These findings indicate that TD-QAS deepens our
-	            for the development of future QAS algorithms.},
+                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},
@@ -291,20 +299,25 @@
 @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},
+    title = {Beyond {MP}2 initialization for unitary coupled cluster quantum
-  author = {Hirsbrunner, Mark R. and Chamaki, Diana and Mullinax, J. Wayne and Tubman, Norm M.},
+             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}},
+    publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den
+                 Quantenwissenschaften}},
     volume = {8},
     pages = {1538},
     month = nov,
-  year = {2024}
+    year = {2024},
 }
 
 @misc{liu2025haqgnnhardwareawarequantumkernel,
-      title={HaQGNN: Hardware-Aware Quantum Kernel Design Based on Graph Neural Networks}, 
+    title = {HaQGNN: Hardware-Aware Quantum Kernel Design Based on Graph Neural
-      author={Yuxiang Liu and Fanxu Meng and Lu Wang and Yi Hu and Sixuan Li and Xutao Yu and Zaichen Zhang},
+             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},
@@ -317,11 +330,129 @@
     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.}, 
+    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}, 
+    author = {He, Zhimin and Deng, Maijie and Zheng, Shenggen and Li, Lvzhou and
+              Situ, Haozhen},
     year = {2024},
     month = {Mar.},
-    pages={12430-12438} 
+    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},
 }