arXiv subjects

Wooyeong Song

Publications and source records attributed to Wooyeong Song.

15 recordsLinked to original sources

arXiv2026

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis

Modular arithmetic is central to quantum algorithms for cryptographic problems, including Shor's algorithm and Grover-based cryptanalysis, with modular reduction contributing substantially to circuit cost. Pseudo-Mersenne moduli $q=2^n-c$ allow classical Crandall reduction to replace division with folding and constant arithmetic, providing a structural opportunity for more efficient quantum modular reduction than Barrett reduction. We translate this advantage into a reversible quantum setting by deriving explicit folding and normalization conditions for $2n$-bit inputs. To the best of our knowledge, this constitutes the first exact reversible quantum circuit formulation of Crandall reduction. Based on this formulation, we develop two variants: Crandall reduction-1 is designed to minimize execution cost through one-step normalization, whereas Crandall reduction-2 uses two-step normalization to support a wider range of $c$ with limited overhead. Logical resource estimates show that both variants require fewer qubits and lower T-count and T-depth than optimized folding Barrett reduction. At $n=10$, Crandall reduction-1 reduces both T-count and T-depth by approximately 46.9% relative to optimized folding Barrett reduction. Surface-code analysis further shows that, at $n=20$ under the Sparse Blossom decoder, the estimated runtimes of the two variants are 30.05 ms and 35.39 ms, respectively, compared with 53.77 ms for optimized folding Barrett reduction. These results demonstrate the practical value of exploiting modulus-specific arithmetic structure in fault-tolerant quantum circuit design.

quant-ph↗

arXiv2026

Syndrome-as-Header: A Quantum Label-Switching Architecture via Uncorrectable Error Injection

Scaling quantum networks beyond point-to-point links requires packet forwarding that can tolerate control-plane timing uncertainty. Existing optical-burst switching (OBS) and quantum-wrapper-based packet switching (QW) rely on external classical headers whose jitter-prone processing must remain aligned with in-flight quantum payloads, creating guard-window or fiber-delay-line budget failures. This paper proposes Syndrome-as-Header (SAH), a quantum label-switching architecture that embeds routing labels into the syndrome structure of an encoded payload. The proposed scheme uses Uncorrectable Error Injection (UEI) to map flow labels to reference syndromes and builds a syndrome-space header codebook whose decoding regions remain distinguishable under correctable channel-induced syndrome deviations. Core routers extract the syndrome header, suppress the correctable residual channel-error component, and swap labels without measuring or decoding the logical payload. SAH supports FAST forwarding and VERIFICATION mode, the latter providing end-to-end consistency checking while retaining swappable labels. In NSFNet timing benchmarks with common per-hop quantum error correction (QEC), SAH eliminates the external-header/payload alignment condition, so timing uncertainty appears as memory residence and delivered latency rather than alignment-budget drops. With a $T_2$-based memory-residence penalty, the advantage depends on router memory coherence; for sufficiently long coherence, SAH maintains higher acceptance and throughput than OBS+QEC and QW+QEC under high jitter.

quant-ph↗

arXiv2026

Asymmetry-aided measurement-based quantum repeaters and distributed quantum computing with a decoder-free client

Distributed quantum computation needs to move logical qubits across lossy optical links, yet this transmission layer is usually designed separately from the computation it serves. We treat the two together by recognizing that a measurement-based quantum repeater is a two-dimensional code foliated along the transmission axis, so that the dominant channel loss is concentrated on the transmitted sector while the locally measured qubits are largely spared. Matching a code's distance to this structural asymmetry, we show that a rectangular Bacon-Shor subsystem code transmits a logical qubit markedly more efficiently than transmission-unaware encodings. Over continental distances, its cost-optimal repeater density is about an order of magnitude lower than that of a recent $[[48,6,8]]$ benchmark at comparable transmission rate, and roughly half that of a symmetric code of equal size. Moreover, we extend the framework to a central-to-client round trip in which a code-level, distance-preserving code switch joins the transmission legs to the client's computation, and joint decoding of the heterogeneous syndrome record at the central node lets distributed quantum computation proceed with a decoder-free client.

quant-ph↗

arXiv2026

Learning with Active Quantum Subspaces: Scalable Hybrid Advantage without Full Quantum Data-Encoding

We study whether quantum learning advantage can persist without fully embedding a large classical input into a highly superposed quantum state. To address this question, we introduce active quantum subspace data-encoding, in which only an information-bearing subset of the input is lifted to a quantum representation while the remaining variables stay classical. For this model, we define a projected hybrid readout and prove three structural results. First, the projected hybrid kernel is positive semidefinite and its sample regularized dimension is bounded by the number of projected observables, so the dimension blow-up of naive global kernels is avoided. Second, we give a necessary and sufficient criterion for improvement over a purely classical predictor in squared loss: the projected quantum sector must contain a direction that lies outside the classical feature span and correlates with the classical residual. Third, in a realizable noisy-oracle setting, we derive a PAC sample-complexity bound proportional to the inverse square of the oracle reliability. We then show, for a canonical Clifford active-subspace family under local dephasing noise, that this reliability can remain inverse-polynomial even when the encoding gate complexity grows polynomially with system size. Hence, the polynomial encoding cost does not by itself destroy the hybrid learning advantage. A sixty-four-qubit family and a synthetic contextual classification task illustrate how one projected quantum feature can compress a useful high-order interaction into a low-dimensional hybrid model. Our results generalize QRAM-free hybrid learning and provide a scalable route toward NISQ-compatible quantum advantage without full quantum data-encoding.

quant-ph↗

arXiv2025

Structural encoding with classical codes for computational-basis bit-flip correction in the early fault-tolerant regime

Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the functionality of classical error correction. In this approach, quantum computation is performed within the codeword subspace defined by a classical error correction code. The correction of various types of errors that manifest as bit flips is carried out based on the final measurement outcomes. The approach leverages the asymmetric structure of many key algorithms, where problem-defining diagonal operators (e.g., oracles) are paired with fixed non-diagonal operators (e.g., diffusion operators). The proposed encoding maps computational basis states to classical codewords. This approach commutes with diagonal operators, obviating their overhead and confining the main computational cost to simpler non-diagonal components. Noisy simulations corroborate this analysis, demonstrating that the proposed scheme serves as a viable protocol-level layer for enhancing performance in the early fault-tolerant regime.

quant-ph↗

arXiv2025

Enhanced Extrapolation-Based Quantum Error Mitigation Using Repetitive Structure in Quantum Algorithms

Quantum error mitigation is a crucial technique for suppressing errors especially in noisy intermediate-scale quantum devices, enabling more reliable quantum computation without the overhead of full error correction. Zero-Noise Extrapolation (ZNE), which we mainly consider in this work, is one of prominent quantum error mitigation methods. For algorithms with deep circuits - such as iterative quantum algorithms involving multiple oracle calls - ZNE's effectiveness is significantly degraded under high noise. Extrapolation based on such low-fidelity data often yields inaccurate estimates and requires substantial overhead. In this study, we propose a lightweight, extrapolation-based error mitigation framework tailored for structured quantum algorithms composed of repeating operational blocks. The proposed method characterizes the error of the repeated core operational block, rather than the full algorithm, using shallow circuits. Extrapolation is used to estimate the block fidelity, followed by a reconstruction of the mitigated success probability. We validate our method via simulations of the 6-qubit Grover's algorithm on IBM's Aer simulator, then further evaluating it on the real 127-qubit IBM Quantum system based on Eagle r3 under a physical noise environment. Our results, particularly those from Aer simulator, demonstrate that the core block's error follows a highly consistent exponential decay. This allows our technique to achieve robust error mitigation, overcoming the limitations of conventional ZNE which is often compromised by statistically unreliable data from near-random behavior under heavy noise. In low-noise conditions, our method approaches theoretical success probability, outperforms ZNE. In high-noise conditions, ZNE fails to mitigate errors due to overfitting of its extrapolation data, whereas our method achieves over a 20% higher success probability.

quant-ph↗

arXiv2025

Ensuring superior learning outcomes and data security for authorized learner

The learner's ability to generate a hypothesis that closely approximates the target function is crucial in machine learning. Achieving this requires sufficient data; however, unauthorized access by an eavesdropping learner can lead to security risks. Thus, it is important to ensure the performance of the "authorized" learner by limiting the quality of the training data accessible to eavesdroppers. Unlike previous studies focusing on encryption or access controls, we provide a theorem to ensure superior learning outcomes exclusively for the authorized learner with quantum label encoding. In this context, we use the probably-approximately-correct (PAC) learning framework and introduce the concept of learning probability to quantitatively assess learner performance. Our theorem allows the condition that, given a training dataset, an authorized learner is guaranteed to achieve a certain quality of learning outcome, while eavesdroppers are not. Notably, this condition can be constructed based only on the authorized-learning-only measurable quantities of the training data, i.e., its size and noise degree. We validate our theoretical proofs and predictions through convolutional neural networks (CNNs) image classification learning.

stat.ML↗

arXiv2024

Fault-tolerant and secure long-distance quantum communication via uncorrectable-error-injection

Quantum networks aim to facilitate the fault-tolerant and secure transmission of quantum states across distant devices. The widely adopted quantum teleportation scheme requires multiple rounds of entanglement swapping and purification, leading to significant resource overhead and operational complexity. In this study, we propose a novel fault-tolerant and secure quantum communication scheme based on uncorrectable error injection. Our method exploits a quantum state encoding scheme based on quantum error correction codes, which strategically introduces uncorrectable errors to enhance security. It eliminates the need for entanglement distribution while reducing resource requirements. The injected errors protect against eavesdropping by preventing unauthorized parties from retrieving meaningful information. Security analysis shows that as the data length and encoded message size increase, information leakage becomes negligible relative to the size of the total message. Comparative performance analysis with existing approaches indicates that our method reduces transmission overhead while maintaining comparable fidelity in low-error regimes. These findings suggest that the proposed method offers a scalable and practical alternative for secure long-distance quantum communication, distributed quantum computing, and future quantum internet applications.

quant-ph↗

arXiv2024

Encoded-Fusion-Based Quantum Computation for High Thresholds with Linear Optics

We propose a fault-tolerant quantum computation scheme in a measurement-based manner with finite-sized entangled resource states and encoded fusion scheme with linear optics. The encoded-fusion is an entangled measurement devised to enhance the fusion success probability in the presence of losses and errors based on a quantum error-correcting code. We apply an encoded-fusion scheme, which can be performed with linear optics and active feedforwards to implement the generalized Shor code, to construct a fault-tolerant network configuration in a three-dimensional Raussendorf-Harrington-Goyal lattice based on the surface code. Numerical simulations show that our scheme allows us to achieve up to 10 times higher loss thresholds than nonencoded fusion approaches with limited numbers of photons used in fusion. Our scheme paves an efficient route toward fault-tolerant quantum computing with finite-sized entangled resource states and linear optics.

quant-ph↗

arXiv2024

Nondestructive discrimination of Bell states between distant parties

Identifying Bell states without destroying it is frequently dealt with in nowadays quantum technologies such as quantum communication and quantum computing. In practice, quantum entangled states are often distributed among distant parties, and it might be required to determine them separately at each location, without inline communication between parties. We present a scheme for discriminating an arbitrary Bell state distributed to two distant parties without destroying it. The scheme requires two entangled states that are pre-shared between the parties, and we show that without these ancillary resources, the probability of non-destructively discriminating the Bell state is bounded by 1/4, which is the same as random guessing. Furthermore, we demonstrate a proof-of-principle experiment through an IonQ quantum computer that our scheme can surpass classical bounds when applied to practical quantum processor.

quant-ph↗

arXiv2024

Photonic variational quantum eigensolver using entanglement measurements

Variational quantum eigensolver (VQE), which combines quantum systems with classical computational power, has been arisen as a promising candidate for near-term quantum computing applications. However, the experimental resources such as the number of measurements to implement VQE rapidly increases as the Hamiltonian problem size grows. Applying entanglement measurements to reduce the number of measurement setups has been proposed to address this issue, however, entanglement measurements themselves can introduce additional resource demands. Here, we apply entanglement measurements to the photonic VQE utilizing polarization and path degrees of freedom of a single-photon. In our photonic VQE, entanglement measurements can be deterministically implemented using linear optics, so it takes full advantage of introducing entanglement measurements without additional experimental demands. Moreover, we show that such a setup can mitigate errors in measurement apparatus for a certain Hamiltonian.

quant-ph↗

arXiv2022

Polynomial T-depth Quantum Solvability of Noisy Binary Linear Problem: From Quantum-Sample Preparation to Main Computation

The noisy binary linear problem (NBLP) is known as a computationally hard problem, and therefore, it offers primitives for post-quantum cryptography. An efficient quantum NBLP algorithm that exhibits a polynomial quantum sample and time complexities has recently been proposed. However, the algorithm requires a large number of samples to be loaded in a highly entangled state and it is unclear whether such a precondition on the quantum speedup can be obtained efficiently. Here, we present a complete analysis of the quantum solvability of the NBLP by considering the entire algorithm process, namely from the preparation of the quantum sample to the main computation. By assuming that the algorithm runs on "fault-tolerant" quantum circuitry, we introduce a reasonable measure of the computational time cost. The measure is defined in terms of the overall number of T gate layers, referred to as T-depth complexity. We show that the cost of solving the NBLP can be polynomial in the problem size, at the expense of an exponentially increasing logical qubits.

quant-ph↗

arXiv2022

Quantum solvability of noisy linear problems by divide-and-conquer strategy

Noisy linear problems have been studied in various science and engineering disciplines. A class of "hard" noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector $\mathbf{b}$ constructed using a finite set of samples, a hidden vector or structure involved in $\mathbf{b}$ is obtained by solving a noise-corrupted linear equation $\hat{A}\mathbf{x} \approx \mathbf{b} + \boldsymbolη$, where $\boldsymbolη$ is a noise vector that cannot be identified. For solving such a noisy linear problem, we consider a quantum algorithm based on a divide-and-conquer strategy, wherein a large core process is divided into smaller subprocesses. The algorithm appropriately reduces both the computational complexities and size of a quantum sample. More specifically, if a quantum computer can access a particular reduced form of the quantum samples, polynomial quantum-sample and time complexities are achieved in the main computation. The size of a quantum sample and its executing system can be reduced, e.g., from exponential to sub-exponential with respect to the problem length, which is better than other results we are aware. We analyse the noise model conditions for such a quantum advantage, and show when the divide-and-conquer strategy can be beneficial for quantum noisy linear problems.

quant-ph↗

arXiv2021

Tangible reduction in learning sample complexity with large classical samples and small quantum system

Quantum computation requires large classical datasets to be embedded into quantum states in order to exploit quantum parallelism. However, this embedding requires considerable resources. It would therefore be desirable to avoid it, if possible, for noisy intermediate-scale quantum (NISQ) implementation. Accordingly, we consider a classical-quantum hybrid architecture, which allows large classical input data, with a relatively small-scale quantum system. This hybrid architecture is used to implement an oracle. It is shown that in the presence of noise in the hybrid oracle, the effects of internal noise can cancel each other out and thereby improve the query success rate. It is also shown that such an immunity of the hybrid oracle to noise directly and tangibly reduces the sample complexity in the probably-approximately-correct learning framework. This NISQ-compatible learning advantage is attributed to the oracle's ability to handle large input features.

quant-ph↗

arXiv2021

Quantum secure learning with classical samples

Studies addressing the question "Can a learner complete the learning securely?" have recently been spurred from the standpoints of fundamental theory and potential applications. In the relevant context of this question, we present a classical-quantum hybrid sampling protocol and define a security condition that allows only legitimate learners to prepare a finite set of samples that guarantees the success of the learning; the security condition excludes intruders. We do this by combining our security concept with the bound of the so-called probably approximately correct (PAC) learning. We show that while the lower bound on the learning samples guarantees PAC learning, an upper bound can be derived to rule out adversarial learners. Such a secure learning condition is appealing, because it is defined only by the size of samples required for the successful learning and is independent of the algorithm employed. Notably, the security stems from the fundamental quantum no-broadcasting principle. No such condition can thus occur in any classical regime, where learning samples can be copied. Owing to the hybrid architecture, our scheme also offers a practical advantage for implementation in noisy intermediate-scale quantum devices.

quant-ph↗