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The noisy intermediate-scale quantum devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the representation and generalization powers of VQC still require further investigation, particularly when the dimensionality of classical inputs is concerned. In this work, we first put forth an end-to-end QNN, TTN-VQC, which consists of a quantum tensor network based on a tensor-train network (TTN) for dimensionality reduction and a VQC for functional regression. Then, we aim at the error performance analysis for the TTN-VQC in terms of representation and generalization powers. We also characterize the optimization properties of TTN-VQC by leveraging the Polyak-Lojasiewicz condition. Moreover, we conduct the experiments of functional regression on a handwritten digit classification dataset to justify our theoretical analysis.

We introduce and analyze approximate quantum secret sharing in a formal cryptographic setting, wherein a dealer encodes and distributes a quantum secret to players such that authorized structures (sets of subsets of players) can approximately reconstruct the quantum secret and omnipotent adversarial agents controlling nonauthorized subsets of players are approximately denied the quantum secret. In particular, viewing the map encoding the quantum secret shares for players in an authorized structure as a quantum channel, we show that approximate reconstructability of the quantum secret by these players is possible if and only if the information leakage, given in terms of a certain entanglement-assisted capacity of the complementary quantum channel to the players outside the structure and the environment, is small.

Equivalence checking of quantum circuits is an essential element in quantum program compilation, in which a quantum program can be synthesized into different quantum circuits that may vary in the number of qubits, initialization requirements, and output states. Verifying the equivalences among the implementation variants requires proper generality. Although different notions of quantum circuit equivalence have been defined, prior methods cannot check observational equivalence between two quantum circuits whose qubits are partially initialized, which is referred to as partial equivalence. In this work, we prove a necessary and sufficient condition for two circuits to be partially equivalent. Based on the condition, we devise algorithms for checking quantum circuits whose partial equivalence cannot be verified by prior approaches. Experiment results confirm the generality and demonstrate the efficiency and effectiveness of our method. Our result may unleash the optimization power of quantum program compilation to take more aggressive steps.

The eligibility of various advanced quantum algorithms will be questioned if they can not guarantee privacy. To fill this knowledge gap, here we devise an efficient quantum differentially private (QDP) Lasso estimator to solve sparse regression tasks. Concretely, given $N~d$-dimensional data points with $N\ll d$ , we first prove that the optimal classical and quantum non-private Lasso requires $\Omega (N+d)$ and $\Omega (\sqrt {N}+\sqrt {d})$ runtime, respectively. We next prove that the runtime cost of QDP Lasso is dimension independent, i.e., $O(N^{5/2})$ , which implies that the QDP Lasso can be faster than both the optimal classical and quantum non-private Lasso. Last, we exhibit that the QDP Lasso attains a near-optimal utility bound $\tilde {O}(N^{-2/3})$ with privacy guarantees and discuss the chance to realize it on near-Term quantum chips with advantages.

We consider state redistribution of a "hybrid" information source that has both classical and quantum components. The sender transmits classical and quantum information at the same time to the receiver, in the presence of classical and quantum side information both at the sender and at the decoder. The available resources are shared entanglement, and noiseless classical and quantum communication channels. We derive one-shot direct and converse bounds for these three resources, represented in terms of the smooth conditional entropies of the source state. Various coding theorems for two-party source coding problems are systematically obtained by reduction from our results, including the ones that have not been addressed in previous literatures.

A locally testable code (LTC) is an error correcting code with a property tester. The tester tests if a word is a codeword by reading constant random bits and rejects the word with probability proportional to the distance from the word to the closest codeword. An important open question until recently is whether there exist c3-LTCs which are LTCs with a constant rate, constant relative distance, and constant locality. In this work, we construct a new LTC family using 1-sided lossless expanders and balanced products.

Rényi and Augustin information are generalizations of mutual information defined via the Rényi divergence, playing a significant role in evaluating the performance of information processing tasks by virtue of its connection to the error exponent analysis. In quantum information theory, there are three generalizations of the classical Rényi divergence—the Petz’s, sandwiched, and log-Euclidean versions, that possess meaningful operational interpretation. However, the associated quantum Rényi and Augustin information are much less explored compared with their classical counterpart, and lacking crucial properties hinders applications of these quantities to error exponent analysis in the quantum regime. The goal of this paper is to analyze fundamental properties of the Rényi and Augustin information from a noncommutative measure-theoretic perspective. Firstly, we prove the uniform equicontinuity for all three quantum versions of Rényi and Augustin information, and it hence yields the joint continuity of these quantities in order and prior input distributions. Secondly, we establish the concavity of the scaled Rényi and Augustin information in the region of s∈ (- 1 , 0) for both Petz’s and the sandwiched versions. This completes the open questions raised by Holevo (IEEE Trans Inf Theory 46(6):2256–2261, 2000), and Mosonyi and Ogawa (Commun Math Phys 355(1):373–426, 2017). For the applications, we show that the strong converse exponent in classical-quantum channel coding satisfies a minimax identity, which means that the strong converse exponent can be attained by the best constant composition code. The established concavity is further employed to prove an entropic duality between classical data compression with quantum side information and classical-quantum channel coding, and a Fenchel duality in joint source-channel coding with quantum side information.

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.

PURPOSE: Today, male and female adult and pediatric cancer patients, individuals transitioning between gender identities, and other individuals facing health extending but fertility limiting treatments can look forward to a fertile future. This is, in part, due to the work of members associated with the Oncofertility Consortium. METHODS: The Oncofertility Consortium is an international, interdisciplinary initiative originally designed to explore the urgent unmet need associated with the reproductive future of cancer survivors. As the strategies for fertility management were invented, developed or applied, the individuals for who the program offered hope, similarly expanded. As a community of practice, Consortium participants share information in an open and rapid manner to addresses the complex health care and quality-of-life issues of cancer, transgender and other patients. To ensure that the organization remains contemporary to the needs of the community, the field designed a fully inclusive mechanism for strategic planning and here present the findings of this process. RESULTS: This interprofessional network of medical specialists, scientists, and scholars in the law, medical ethics, religious studies and other disciplines associated with human interventions, explore the relationships between health, disease, survivorship, treatment, gender and reproductive longevity. CONCLUSION: The goals are to continually integrate the best science in the service of the needs of patients and build a community of care that is ready for the challenges of the field in the future.

In classical machine learning, a set of weak classifiers can be adaptively combined for improving the overall performance, a technique called adaptive boosting (or AdaBoost). However, constructing a combined classifier for a large data set is typically resource consuming. Here we propose a quantum extension of AdaBoost, demonstrating a quantum algorithm that can output the optimal strong classifier with a quadratic speedup in the number of queries of the weak classifiers. Our results also include a generalization of the standard AdaBoost to the cases where the output of each classifier may be probabilistic. We prove that the query complexity of the non-deterministic classifiers is the same as those of deterministic classifiers, which may be of independent interest to the classical machine-learning community. Additionally, once the optimal classifier is determined by our quantum algorithm, no quantum resources are further required. This fact may lead to applications on near term quantum devices.

Quantum machine learning is expected to be one of the first practical applications of near-term quantum devices. Pioneer theoretical works suggest that quantum generative adversarial networks (GANs) may exhibit a potential exponential advantage over classical GANs, thus attracting widespread attention. However, it remains elusive whether quantum GANs implemented on near-term quantum devices can actually solve real-world learning tasks. Here, we devise a flexible quantum GAN scheme to narrow this knowledge gap. In principle, this scheme has the ability to complete image generation with high-dimensional features and could harness quantum superposition to train multiple examples in parallel. We experimentally achieve the learning and generating of real-world handwritten digit images on a superconducting quantum processor. Moreover, we utilize a gray-scale bar dataset to exhibit competitive performance between quantum GANs and the classical GANs based on multilayer perceptron and convolutional neural network architectures, respectively, benchmarked by the Fréchet distance score. Our work provides guidance for developing advanced quantum generative models on near-term quantum devices and opens up an avenue for exploring quantum advantages in various GAN-related learning tasks.

Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies. However, noise has often played beneficial roles, from enhancing weak signals in stochastic resonance to protecting the privacy of data in differential privacy. It is then natural to ask: Can we harness the power of quantum noise that is beneficial to quantum computing? An important current direction for quantum computing is its application to machine learning, such as classification problems. One outstanding problem in machine learning for classification is its sensitivity to adversarial examples. These are small, undetectable perturbations from the original data where the perturbed data is completely misclassified in otherwise extremely accurate classifiers. They can also be considered as worst-case perturbations by unknown noise sources. We show that by taking advantage of depolarization noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise. This robustness property is intimately connected with an important security concept called differential privacy, which can be extended to quantum differential privacy. For the protection of quantum data, this quantum protocol can be used against the most general adversaries. Furthermore, we show how the robustness in the classical case can be sensitive to the details of the classification model, but in the quantum case the details of the classification model are absent, thus also providing a potential quantum advantage for classical data. This opens the opportunity to explore other ways in which quantum noise can be used in our favor, as well as identifying other ways quantum algorithms can be helpful in a way which is distinct from quantum speedups.

Quantum neural network (QNN), or equivalently, the parameterized quantum circuit (PQC) with a gradient-based classical optimizer, has been broadly applied to many experimental proposals for noisy intermediate-scale quantum (NISQ) devices. However, the learning capability of QNN remains largely unknown due to the nonconvex optimization landscape, the measurement error, and the unavoidable gate noise introduced by NISQ machines. In this study, we theoretically explore the learnability of QNN in the view of the trainability and generalization. Particularly, we derive the convergence performance of QNN under the NISQ setting, and identify classes of computationally hard concepts that can be efficiently learned by QNN. Our results demonstrate that large gate noise, few quantum measurements, and deep circuit depth will lead to poor convergence rates of QNN towards the empirical risk minimization. Moreover, we prove that any concept class, which is efficiently learnable by a quantum statistical query (QSQ) learning model, can also be efficiently learned by PQCs. Since the QSQ learning model can tackle certain problems such as parity learning with a runtime speedup, our result suggests that PQCs established on NISQ devices will retain the quantum advantage measured by generalization ability. Our work provides theoretical guidance for developing advanced QNNs and opens up avenues for exploring quantum advantages beyond hybrid quantum-classical learning protocols in the NISQ era.

We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels (MACs) with an arbitrary number of senders. As an example, we consider the bosonic thermal-loss MAC and solve the one-shot capacity region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA capacity region is strictly larger than the capacity region without entanglement-assistance. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. Four practical receiver designs, based on optical parametric amplifiers, are given and analyzed. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates. Our work provides a unique and practical network communication scenario where entanglement can be beneficial.

Quantum resource theory under different classes of quantum operations advances multiperspective understandings of inherent quantum-mechanical properties, such as quantum coherence and quantum entanglement. We establish hierarchies of different operations for manipulating coherence and entanglement in distributed settings, where at least one of the two spatially separated parties are restricted from generating coherence. In these settings, we introduce new classes of operations and also characterize those maximal, i.e., the resource-non-generating operations, progressing beyond existing studies on incoherent versions of local operations and classical communication and those of separable operations. The maximal operations admit a semidefiniteprogramming formulation useful for numerical algorithms, whereas the existing operations not. To establish the hierarchies, we prove a sequence of inclusion relations among the operations by clarifying tasks where separation of the operations appears. We also demonstrate an asymptotically non-surviving separation of the operations in the hierarchy in terms of performance of the task of assisted coherence distillation, where a separation in a one-shot scenario vanishes in the asymptotic limit. Our results serve as fundamental analytical and numerical tools to investigate interplay between coherence and entanglement under different operations in the resource theory.

The hybrid quantum-classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example toward this goal is the quantum neural network (QNN), which has been developed to accomplish various supervised learning tasks such as classification and regression. However, there are two central issues that remain obscure when QNN is exploited to accomplish classification tasks. First, a quantum classifier that can well balance the computational cost such as the number of measurements and the learning performance is unexplored. Second, it is unclear whether quantum classifiers can be applied to solve certain problems that outperform their classical counterparts. Here we devise a Grover-search based quantum learning scheme (GBLS) to address the above two issues. Notably, most existing QNN-based quantum classifiers can be seamlessly embedded into the proposed scheme. The key insight behind our proposal is reformulating the classification tasks as the search problem. Numerical simulations exhibit that GBLS can achieve comparable performance with other quantum classifiers under various noise settings, while the required number of measurements is dramatically reduced. We further demonstrate a potential quantum advantage of GBLS over classical classifiers in the measure of query complexity. Our work provides guidance to develop advanced quantum classifiers on near-term quantum devices and opens up an avenue to explore potential quantum advantages in various classification tasks.

© 1963-2012 IEEE. We study the communication capabilities of a quantum channel under the most general channel model known as the one-shot model. Unlike classical channels that can only be used to transmit classical information (bits), a quantum channel can be used for transmission of classical information, quantum information (qubits) and simultaneous transmission of classical and quantum information. In this work, we investigate the one-shot capabilities of a quantum channel for simultaneously transmitting bits and qubits. This problem was studied in the asymptotic regime for a memoryless channel where a regularized characterization of the capacity region was reported. It is known that the transmission of private classical information is closely related to the problem of quantum information transmission. We resort to this idea and find achievable and converse bounds on the simultaneous transmission of the public and private classical information. Then shifting the classical private rate to the quantum information rate leads to a rate region for simultaneous transmission of classical and quantum information. In the case of asymptotic i.i.d. setting, our one-shot result is evaluated to the known results in the literature. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.

© 1963-2012 IEEE. In this paper, we study tail inequalities of the largest eigenvalue of a matrix infinitely divisible (i.d.) series, which is a finite sum of fixed matrices weighted by i.d. random variables. We obtain several types of tail inequalities, including Bennett-type and Bernstein-type inequalities. This allows us to further bound the expectation of the spectral norm of a matrix i.d. series. Moreover, by developing a new lower-bound function for Q(s)=(s+1)\log (s+1)-s that appears in the Bennett-type inequality, we derive a tighter tail inequality of the largest eigenvalue of the matrix i.d. series than the Bernstein-type inequality when the matrix dimension is high. The resulting lower-bound function is of independent interest and can improve any Bennett-type concentration inequality that involves the function Q(s). The class of i.d. probability distributions is large and includes Gaussian and Poisson distributions, among many others. Therefore, our results encompass the existing work on matrix Gaussian series as a special case. Lastly, we show that the tail inequalities of a matrix i.d. series have applications in several optimization problems including the chance constrained optimization problem and the quadratic optimization problem with orthogonality constraints. In addition, we also use the resulting tail bounds to show that random matrices constructed from i.d. random variables satisfy the restricted isometry property (RIP) when it acts as a measurement matrix in compressed sensing.

© 1963-2012 IEEE. In this paper, we investigate the additivity phenomenon in the quantum dynamic capacity region of a quantum channel for trading the resources of classical communication, quantum communication, and entanglement. Understanding such an additivity property is important if we want to optimally use a quantum channel for general communication purposes. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity region, and it is largely unknown if this could lead to a strictly superadditive double or triple resource capacity region, respectively. For example, if a channel has additive classical and quantum capacities, can the classical-quantum capacity region be strictly superadditive? In this paper, we answer such questions affirmatively. We give proof-of-principle requirements for these channels to exist. In most cases, we can provide an explicit construction of these quantum channels. The existence of these superadditive phenomena is surprising in contrast to the result that the additivity of both classical-entanglement and classical-quantum capacity regions imply the additivity of the triple resource capacity region for a given channel.

© 1963-2012 IEEE. We study lower bounds on the optimal error probability in classical coding over classical-quantum channels at rates below the capacity, commonly termed quantum sphere-packing bounds. Winter and Dalai have derived such bounds for classical-quantum channels; however, the exponents in their bounds only coincide when the channel is classical. In this paper, we show that these two exponents admit a variational representation and are related by the Golden-Thompson inequality, reaffirming that Dalai's expression is stronger in general classical-quantum channels. Second, we establish a finite blocklength sphere-packing bound for classical-quantum channels, which significantly improves Dalai's prefactor from the order of subexponential to polynomial. Furthermore, the gap between the obtained error exponent for constant composition codes and the best known classical random coding exponent vanishes in the order of $o(\log n / n)$ , indicating our sphere-packing bound is almost exact in the high rate regime. Finally, for a special class of symmetric classical-quantum channels, we can completely characterize its optimal error probability without the constant composition code assumption. The main technical contributions are two converse Hoeffding bounds for quantum hypothesis testing and the saddle-point properties of error exponent functions.

© 2019 IEEE. The 2-receiver broadcast channel with primary and third-party receivers is studied. The messages are classified into public, private and confidential. The messages in the public class are messages intended for both receivers. The private messages are intended for the primary receiver with no secrecy requirements imposed upon them. And the confidential messages are aimed exclusively to the primary receiver such that they must not be accessible to the other receiver. The encoder performs the necessary encryption by virtue of local randomness whose rate is assumed to be limited. We find an achievability region on the trade-off between the rates of the three messages and the source of randomness in the one-shot regime of a quantum broadcast channel.

© 2019 IEEE. In this paper, we establish an interesting duality between two different quantum information-processing tasks, namely, classical source coding with quantum side information, and channel coding over classical-quantum channels. The duality relates the optimal error exponents of these two tasks, generalizing the classical results of Ahlswede and Dueck. We establish duality both at the operational level and at the level of the entropic quantities characterizing these exponents. For the latter, the duality is given by an exact relation, whereas for the former, duality manifests itself in the following sense: an optimal coding strategy for one task can be used to construct an optimal coding strategy for the other task. Along the way, we derive a bound on the error exponent for classical-quantum channel coding with constant composition codes which might be of independent interest.

In spite of the extensive contribution of intestinal pathology to the pathophysiology of schistosomiasis, little is known of the impact of schistosome infection on the composition of the gut microbiota of its mammalian host. Here, we characterised the fluctuations in the composition of the gut microbial flora of the small and large intestine, as well as the changes in abundance of individual microbial species, of mice experimentally infected with Schistosoma mansoni with the goal of identifying microbial taxa with potential roles in the pathophysiology of infection and disease. Bioinformatic analyses of bacterial 16S rRNA gene data revealed an overall reduction in gut microbial alpha diversity, alongside a significant increase in microbial beta diversity characterised by expanded populations of Akkermansia muciniphila (phylum Verrucomicrobia) and lactobacilli, in the gut microbiota of S. mansoni-infected mice when compared to uninfected control animals. These data support a role of the mammalian gut microbiota in the pathogenesis of hepato-intestinal schistosomiasis and serves as a foundation for the design of mechanistic studies to unravel the complex relationships amongst parasitic helminths, gut microbiota, pathophysiology of infection and host immunity.

© 1963-2012 IEEE. In this paper, we study the tradeoffs between the error probabilities of classical-quantum channels and the blocklength n when the transmission rates approach the channel capacity at a rate lower than 1 {n} , a research topic known as moderate deviation analysis. We show that the optimal error probability vanishes under this rate convergence. Our main technical contributions are a tight quantum sphere-packing bound, obtained via Chaganty and Sethuraman's concentration inequality in strong large deviation theory, and asymptotic expansions of error-exponent functions. Moderate deviation analysis for quantum hypothesis testing is also established. The converse directly follows from our channel coding result, while the achievability relies on a martingale inequality.

© 2018 IOP Publishing Ltd. We find one-shot bounds for concentration of maximally coherent states in the so called assisted scenario. In this setting, Bob is restricted to performing incoherent operations on his quantum system, however he is assisted by Alice, who holds a purification of Bob's state and can send classical data to him. We further show that in the asymptotic limit our one-shot bounds recover the previously computed rate of asymptotic assisted concentration.

© 2018 IEEE. We aim to study the optimal rates of transmission of public and private classical information over a quantum channel in the most general channel model. To this end, we discuss a scenario in which a quantum channel is being used only once, i.e., one-shot regime is considered. A quantum channel can be used to send classical information (bits) either publicly or privately and for either case, one-shot bounds have been reported in the literature. This paper investigates the one-shot capacity capabilities of a quantum channel for simultaneous transmission of public and private information. We derive an achievable rate region in the form of a tradeoff between public and private rates. We also provide converse bounds assessing the " of our achievable rates. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.

© 2018 American Physical Society. A question that is commonly asked in all areas of physics is how a certain property of a physical system can be used to achieve useful tasks and how to quantify the amount of such a property in a meaningful way. We answer this question by showing that, in a general resource-theoretic framework that allows the use of free states as catalysts, the amount of "resources" contained in a given state, in the asymptotic scenario, is equal to the regularized relative entropy of a resource of that state. While we need to place a few assumptions on our resource-theoretical framework, it is still sufficiently general, and its special cases include quantum resource theories of entanglement, coherence, asymmetry, athermality, nonuniformity, and purity. As a by-product, our result also implies that the amount of noise one has to inject locally to erase all the entanglement contained in an entangled state is equal to the regularized relative entropy of entanglement.

© 2018 IEEE. In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat such error patterns in the quantum regime. Our contributions are as follows. Firstly, we derive an upper bound for the correctable burst errors of QBECCs, the quantum Reiger bound (QRB). Secondly, we propose two constructions of QBECCs: one by heuristic computer search and the other by concatenating two quantum tensor product codes (QTPCs). We obtain several new QBECCs with better parameters than existing codes with the same coding length. Moreover, some of the constructed codes can saturate the quantum Reiger bounds. Finally, we perform numerical experiments for our constructed codes over Markovian correlated depolarizing quantum memory channels, and show that QBECCs indeed outperform standard QECCs in this scenario.

© 2017 The Author(s). In distributed quantum and classical information processing, spatially separated parties operate locally on their respective subsystems, but coordinate their actions through multiple exchanges of public communication. With interaction, the parties can perform more tasks. But how the exact number and order of exchanges enhances their operational capabilities is not well understood. Here we consider the minimum number of communication rounds needed to perform the locality-constrained tasks of entanglement transformation and its classical analog of secrecy manipulation. We provide an explicit construction of both quantum and classical state transformations which, for any given r, can be achieved using r rounds of classical communication exchanges, but no fewer. To show this, we build on the common structure underlying both resource theories of quantum entanglement and classical secret key. Our results reveal that highly complex communication protocols are indeed necessary to fully harness the information-theoretic resources contained in general quantum and classical states.

© 2017 IEEE. 'To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award.' We study the asymptotic behavior of the type-I error in quantum hypothesis testing when the exponent of the type-II error approaches the quantum relative entropy sufficiently slowly. Our result shows that the moderate deviation principle holds for the testing problem if the quantum relative variance is positive. Our proof strategy employs strong large deviation theory and a martingale inequality.

© 2017 IEEE. "To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award." We provide a sphere-packing lower bound for the optimal error probability in finite blocklengths when coding over a symmetric classical-quantum channel. Our result shows that the pre-factor can be significantly improved from the order of the subexponential to the polynomial, This established pre-factor is arguably optimal because it matches the best known random coding upper bound in the classical case. Our approaches rely on a sharp concentration inequality in strong large deviation theory and crucial properties of the error-exponent function.