arXiv subjects

Seok-Hyung Lee

Publications and source records attributed to Seok-Hyung Lee.

16 recordsLinked to original sources

arXiv2026

Error correction on an array of superconducting qubits with defective components

A solid-state quantum-computing architecture will require the fabrication of arrays of many coupled qubits. It is inevitable that this process will produce qubits and couplers with varying performance, with some components underperforming due to imperfect fabrication. Quantum error-correction requires high-performing components and hence these defects must be dealt with, either by adapting the code to exclude the defects, or by informing the decoder to accommodate defects in post-processing. Here we implement and compare strategies to operate distance-5 surface codes on a quantum processor consisting of a square-lattice array of 120 superconducting qubits. We demonstrate a dramatic reduction in the probability of a logical error in a memory experiment by excluding underperforming components, compared with both a standard approach of ignoring defects, and a defect-aware decoding approach. We observe up to 2.8X improvement in logical errors per round when excluding defects compared with the standard defect-ignorant approach (1.62% compared to 4.49%). In contrast, defect-aware decoding gives only modest gains. Defects are also expected to be particularly harmful for measurement-based logical operations. Using a stability experiment we show that excluding defects resurrects measurement-based logic gate performance, observing a 6.3% per-round suppression of failure rate when excluding defects, compared to zero suppression otherwise. Furthermore, we show a further substantial decrease in logical errors when using leakage post-selection in combination with our defect exclusion strategies, resulting in a distance-5 code outperforming the best distance-3 in one basis. Our experiments therefore give a proof-of-principle demonstration of the essential utility of defect exclusion methods in the scale-up of solid-state quantum computing approaches.

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arXiv2026

Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons

Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. We here introduce a fault-tolerant hybrid quantum computation by building on the advantages of both discrete-variable (DV) and continuous-variable (CV) systems. Particularly, we define a CV-DV hybrid qubit with bosonic cat-code and single photon, which is implementable in current photonic platforms. By the cat-code encoded in the CV part, the dominant loss errors are readily correctable without multi-qubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error correction code such as topological codes, exploring their potential merits in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource-efficient over all previous proposals in photonic platforms, allowing us to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss its realization not only in all-photonic platforms but also in other hybrid platforms including superconducting and trapped-ion systems, which allows us to find various efficient routes towards fault-tolerant quantum computing.

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arXiv2026

Scalable quantum error correction tailored for a heavy-hex qubit array

To produce an operable quantum computer that is made with imperfect hardware, we must design and test scalable quantum error correcting codes that are suited for the devices we can build and, in unison, develop decoding strategies that accommodate device-specific noise characteristics. Here, we introduce the \emph{dynamic compass code}, a subsystem code with a novel syndrome extraction cycle, that has a competitive threshold while making efficient use of qubits arranged on a heavy-hex lattice. We use a superconducting qubit array to implement a distance-5 instance of this code, and demonstrate how detailed noise characterisation can boost decoder performance to yield significant improvements in logical error rates. We perform averaged circuit eigenvalue sampling (ACES) to acquire detailed context-dependent error information on all elements of the syndrome extraction process. Furthermore, we leverage soft information produced from measurement devices to augment the decoder with measurement error information and detect leakage errors for exclusion through post-selection. Our noise-informed approach yields up to 38.3\% improvement in the logical error rate of a distance-5 implementation of the dynamic compass code in experiment.

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arXiv2026

Low-valency scalable quantum error correction with a dynamic compass code

The ongoing development of hardware that is capable of reliably executing general quantum algorithms requires quantum error-correcting codes that are both practical for realisation and rapidly reduce logical error rates as they are scaled up. Here we introduce the dynamic compass code, a code that can be implemented with a modest footprint on the heavy-hex lattice while also demonstrating a threshold. The dynamic code is obtained by choosing a novel measurement schedule for the syndrome extraction circuit of the heavy-hex subsystem code. We numerically evaluate its performance and observe that different choices of schedule can provide a trade-off in protection against logical errors in the $X$ vs $Z$ basis. We also demonstrate that this new measurement schedule provides the code with a threshold for stability experiments. We finally show how the dynamic compass code could be used for fault-tolerant logic by illustrating lattice surgery between code patches.

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arXiv2026

Efficient Post-Selection for General Quantum LDPC Codes

Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline resource state generation and other moderate-depth fault-tolerant circuits. Prior work has primarily relied on the "logical gap" metric with the minimum-weight perfect matching decoder, but this approach faces fundamental limitations including computational overhead that scales exponentially with the number of logical qubits and poor generalizability to arbitrary codes beyond surface codes. We develop post-selection strategies based on computationally efficient heuristic confidence metrics that leverage error cluster statistics (specifically, aggregated cluster sizes and log-likelihood ratios) from clustering-based decoders, which are applicable to arbitrary quantum low-density parity check (QLDPC) codes. We validate our method through extensive numerical simulations on surface codes, bivariate bicycle codes, and hypergraph product codes, demonstrating orders of magnitude reductions in logical error rates with moderate abort rates. For instance, applying our strategy to the [[144, 12, 12]] bivariate bicycle code achieves approximately three orders of magnitude reduction in the logical error rate with an abort rate of only 1% (19%) at a physical error rate of 0.1% (0.3%). Additionally, we integrate our approach with the sliding-window framework for real-time decoding, featuring early mid-circuit abort decisions that eliminate unnecessary overheads. Notably, its performance matches or even surpasses the original strategy for global decoding, while exhibiting favorable scaling in the number of rounds. Our approach provides a practical foundation for efficient post-selection in fault-tolerant quantum computing with QLDPC codes.

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arXiv2025

SDQC: Distributed Quantum Computing Architecture Utilizing Entangled Ion Qubit Shuttling

We propose Shuttling-based Distributed Quantum Computing (SDQC), a hybrid architecture that combines the strengths of physical qubit shuttling and distributed quantum computing to enable scalable trapped-ion quantum computing. SDQC performs non-local quantum operations by distributing entangled ion qubits via deterministic shuttling, combining the high-fidelity and deterministic operations of shuttling-based architectures with the parallelism and pipelining advantages of distributed quantum computing. We present (1) a practical architecture incorporating quantum error correction (QEC), (2) pipelining strategies to exploit parallelism in entanglement distribution and measurement, and (3) a performance evaluation in terms of logical error rate and clock speed. For a 256-bit elliptic-curve discrete logarithm problem (ECDLP) instance, which requires 2,871 logical qubits at code distance 13, SDQC achieves a logical error rate which is $1.20^{+0.94}_{-0.45}\times10^{-8}$ of Photonic DQC error rate and $3.79^{+5.09}_{-2.84}\times10^{-3}$ of Quantum Charge-Coupled Device (QCCD) error rate, while providing 2.82 times faster logical clock speed than QCCD.

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arXiv2025

Photonic Hybrid Quantum Computing

Photons are a ubiquitous carrier of quantum information: they are fast, suffer minimal decoherence, and do not require huge cryogenic facilities. Nevertheless, their intrinsically weak photon-photon interactions remain a key obstacle to scalable quantum computing. This review surveys hybrid photonic quantum computing, which exploits multiple photonic degrees of freedom to combine the complementary strengths of discrete and bosonic encodings, thereby significantly mitigating the challenge of weak photon-photon interactions. We first outline the basic principles of discrete-variable, native continuous-variable, and bosonic-encoding paradigms. We then summarise recent theoretical advances and state-of-the-art experimental demonstrations with particular emphasis on the hybrid approach. Its unique advantages, such as efficient generation of resource states and nearly ballistic (active-feedforward-free) operations, are highlighted alongside remaining technical challenges. To facilitate a clear comparison, we explicitly present the error thresholds and resource overheads required for fault-tolerant quantum computing. Our work offers a focused overview that clarifies how the hybrid approach enables scalable and compatible architectures for quantum computing.

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arXiv2025

Low-overhead magic state distillation with color codes

Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but requires significant resources. Hence, it is crucial to tailor and optimize magic state distillation for specific codes from both logical- and physical-level perspectives. In this work, we perform such optimization for two-dimensional color codes, which are promising due to their higher encoding rates compared to surface codes, transversal implementation of Clifford gates, and efficient lattice surgery. We propose two carefully designed distillation schemes based on the 15-to-1 distillation circuit and lattice surgery, differing in their methods for handling faulty rotations. Our first scheme employs faulty T-measurement, achieving infidelities of $O(p^3)$ for physical noise strength $p$. To achieve lower infidelities, our second scheme integrates distillation with 'cultivation' (a distillation-free approach to fault-tolerantly prepare magic states through transversal Clifford measurements). Our second scheme achieves significantly lower infidelities (e.g., $\sim 2 \times 10^{-16}$ at $p = 10^{-3}$), surpassing the capabilities of both cultivation and single-level distillation. Notably, to reach a given target infidelity, our schemes require approximately two orders of magnitude fewer resources than the previous best magic state distillation schemes for color codes.

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arXiv2025

Color code decoder with improved scaling for correcting circuit-level noise

Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes. However, decoding color codes presents a significant challenge due to their structure, where elementary errors violate three checks instead of just two (a key feature in surface code decoding), and the complexity of extracting syndrome is greater. We introduce an efficient color-code decoder that tackles these issues by combining two matching decoders for each color, generalized to handle circuit-level noise by employing detector error models. We provide comprehensive analyses of the decoder, covering its threshold and sub-threshold scaling both for bit-flip noise with ideal measurements and for circuit-level noise. Our simulations reveal that this decoding strategy nearly reaches the best possible scaling of logical failure ($p_\mathrm{fail} \sim p^{d/2}$) for both noise models, where $p$ is the noise strength, in the regime of interest for fault-tolerant quantum computing. While its noise thresholds are comparable with other matching-based decoders for color codes ($8.2\%$ for bit-flip noise and $0.46\%$ for circuit-level noise), the scaling of logical failure rates below threshold significantly outperforms the best matching-based decoders.

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arXiv2023

Graph-theoretical optimization of fusion-based graph state generation

Graph states are versatile resources for various quantum information processing tasks, including measurement-based quantum computing and quantum repeaters. Although the type-II fusion gate enables all-optical generation of graph states by combining small graph states, its non-deterministic nature hinders the efficient generation of large graph states. In this work, we present a graph-theoretical strategy to effectively optimize fusion-based generation of any given graph state, along with a Python package OptGraphState. Our strategy comprises three stages: simplifying the target graph state, building a fusion network, and determining the order of fusions. Utilizing this proposed method, we evaluate the resource overheads of random graphs and various well-known graphs. Additionally, we investigate the success probability of graph state generation given a restricted number of available resource states. We expect that our strategy and software will assist researchers in developing and assessing experimentally viable schemes that use photonic graph states.

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arXiv2022

Parity-encoding-based quantum computing with Bayesian error tracking

Measurement-based quantum computing (MBQC) in linear optical systems is promising for near-future quantum computing architecture. However, the nondeterministic nature of entangling operations and photon losses hinder the large-scale generation of graph states and introduce logical errors. In this work, we propose a linear optical topological MBQC protocol employing multiphoton qubits based on the parity encoding, which turns out to be highly photon-loss tolerant and resource-efficient even under the effects of nonideal entangling operations that unavoidably corrupt nearby qubits. For the realistic error analysis, we introduce a Bayesian methodology, in conjunction with the stabilizer formalism, to track errors caused by such detrimental effects. We additionally suggest a graph-theoretical optimization scheme for the process of constructing an arbitrary graph state, which greatly reduces its resource overhead. Notably, we show that our protocol is advantageous over several other existing approaches in terms of fault-tolerance, resource overhead, or feasibility of basic elements.

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arXiv2022

Virtual distillation with noise dilution

Virtual distillation is an error-mitigation technique that reduces quantum-computation errors without assuming the noise type. In scenarios where the user of a quantum circuit is required to additionally employ peripherals, such as delay lines, that introduce excess noise, we find that the error-mitigation performance can be improved if the peripheral, whenever possible, is split across the entire circuit; that is, when the noise channel is uniformly distributed in layers within the circuit. We show that under the multiqubit loss and Pauli noise channels respectively, for a given overall error rate, the average mitigation performance improves monotonically as the noisy peripheral is split~(diluted) into more layers, with each layer sandwiched between subcircuits that are sufficiently deep to behave as two-designs. For both channels, analytical and numerical evidence show that second-order distillation is generally sufficient for (near-)optimal mitigation. We propose an application of these findings in designing a quantum-computing cluster that houses realistic noisy intermediate-scale quantum circuits that may be shallow in depth, where measurement detectors are limited and delay lines are necessary to queue output qubits from multiple circuits.

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arXiv2022

All-photonic architectural roadmap for scalable quantum computing using Greenberger-Horne-Zeilinger states

Linear optical quantum computing is beset by the lack of deterministic entangling operations besides photon loss. Motivated by advancements at the experimental front in deterministic generation of various kinds of multiphoton entangled states, we propose an architecture for linear-optical quantum computing that harnesses the availability of three-photon Greenberger-Horne-Zeilinger (GHZ) states. Our architecture and its subvariants use polarized photons in GHZ states, polarization beam splitters, delay lines, optical switches and on-off detectors. We concatenate topological quantum error correction code with three-qubit repetition codes and estimate that our architecture can tolerate remarkably high photon-loss rate of $11.5 \%$; this makes a drastic change that is at least an order higher than those of known proposals. Further, considering three-photon GHZ states as resources, we estimate the resource overheads to perform gate operations with an accuracy of $10^{-6}~(10^{-15})$ to be $2.0\times10^6~(5.6\times10^7)$. Compared to other all-photonic schemes, our architecture is also resource-efficient. In addition, the resource overhead can be even further improved if larger GHZ states are available. Given its striking enhancement in the photon loss threshold and the recent progress in generating multiphoton entanglement, our scheme will make scalable photonic quantum computing a step closer to reality.

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arXiv2021

Universal resource-efficient topological measurement-based quantum computation via color-code-based cluster states

Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit Pauli measurements with a family of large entangled states called cluster states as resources. Raussendorf's three-dimensional cluster states (RTCSs) based on the surface codes are mainly considered for topological MBQC. In such schemes, however, the fault-tolerant implementation of the logical Hadamard, phase ($Z^{1/2}$), and $T$ ($Z^{1/4}$) gates which are essential for building up arbitrary logical gates has not been achieved to date without using state distillation, while the controlled-NOT (CNOT) gate does not require it, to best of our knowledge. State distillation generally consumes many ancillary logical qubits, thus it is a severe obstacle against practical quantum computing. To solve this problem, we suggest an MBQC scheme via a family of cluster states called color-code-based cluster states (CCCSs) based on the two-dimensional color codes instead of the surface codes. We define logical qubits, construct elementary logical gates, and describe error correction schemes. We show that all the logical Clifford gates including the CNOT, Hadamard, and phase gates can be implemented fault-tolerantly without state distillation, although the fault-tolerant $T$ gate still requires it. We further prove that the minimal number of physical qubits per logical qubit in a CCCS is at most approximately 1.8 times smaller than the case of an RTCS. We lastly show that the error threshold of MBQC via CCCSs for logical-$Z$ errors is 2.7-2.8%, which is comparable to the value for RTCSs, assuming a simple error model where physical qubits have $X$-measurement or $Z$ errors independently with the same probability.

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arXiv2021

Loss-tolerant concatenated Bell-state measurement with encoded coherent-state qubits for long-range quantum communication

The coherent-state qubit is a promising candidate for optical quantum information processing due to its nearly-deterministic nature of the Bell-state measurement (BSM). However, its non-orthogonality incurs difficulties such as failure of the BSM. One may use a large amplitude ($α$) for the coherent state to minimize the failure probability, but the qubit then becomes more vulnerable to dephasing by photon loss. We propose a hardware-efficient concatenated BSM (CBSM) scheme with modified parity encoding using coherent states with reasonably small amplitudes ($|α| \lessapprox 2$), which simultaneously suppresses both failures and dephasing in the BSM procedure. We numerically show that the CBSM scheme achieves a success probability arbitrarily close to unity for appropriate values of $α$ and sufficiently low photon loss rates (e.g., $\lessapprox 5\%$). Furthermore, we verify that the quantum repeater scheme exploiting the CBSM scheme for quantum error correction enables one to carry out efficient long-range quantum communication over 1000 km. We show that the performance is comparable to those of other up-to-date methods or even outperforms them for some cases. Finally, we present methods to prepare logical qubits under modified parity encoding and implement elementary logical operations, which consist of several physical-level ingredients such as generation of Schrödinger's cat state and elementary gates under coherent-state basis. Our work demonstrates that the encoded coherent-state qubits in free-propagating fields provide an alternative route to fault-tolerant information processing, especially long-range quantum communication.

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arXiv2020

Loss-tolerant transmission of multiphoton-qubit information via hybrid entanglement

It was shown that using multiphoton qubits, a nearly deterministic Bell-state measurement can be performed with linear optics and on-off photodetectors [Phys. Rev. Lett. 114, 113603 (2015)]. However, multiphoton qubits are generally more fragile than single-photon qubits under a lossy environment. In this paper, we propose and analyze a scheme to teleport multiphoton-qubit information using hybrid entanglement with a loss-tolerant carrier qubit. We consider three candidates for the carrier qubit: a coherent-state qubit, a single-photon polarization qubit, and a vacuum-and-single-photon qubit. We find that teleportation with the vacuum-and-single-photon qubit tolerates about 10 times greater photon losses than with the multiphoton qubit of the photon number $N \geq 4$ in the high fidelity regime ($F\geq 90\%$). The coherent-state qubit encoding may be even better than the vacuum-and-single-photon qubit as the carrier when its amplitude is as small as $α<0.78$. We further point out that the fidelity of the teleported state by our scheme is determined by loss in the carrier qubit while the success probability depends on loss only in the multiphoton qubit to be teleported. Our study implies that the hybrid architecture may complement the weaknesses of each qubit encoding.

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