arXiv subjects

Antonio deMarti iOlius

Publications and source records attributed to Antonio deMarti iOlius.

11 recordsLinked to original sources

arXiv2026

Patchwork: automated lattice surgery and space-time partitioning for real-time decoding

We introduce patchwork, a lattice-surgery compiler for arbitrary multi-qubit Pauli measurements on a prescribed narrow-corridor two-dimensional surface-code layout. Systematic geometric rules simplify stabilizer placement and gate scheduling, including for logical $Y$ measurements implemented using twist defects. We introduce measurement circuits and schedules that, together with protruding lobes of $Y$-extension patches, preserve the full effective code distance for all numerically tested code distances. To support parallel decoding, we develop a wavefront algorithm that partitions merged lattice-surgery patches into space-time commit, buffer, and cleanup regions. Simulations of three sequential multi-qubit Pauli measurements acting on ten logical qubits show that staged decoding achieves total failure probabilities close to those of monolithic decoding over the parameters tested. These methods provide an automated framework for fault-tolerant lattice surgery and a route toward scalable, real-time decoding.

quant-ph↗

arXiv2026

An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise

Fault-tolerant quantum computers must be designed in conjunction with classical co-processors that decode quantum error correction measurement information in real-time. In this work, we introduce the belief propagation plus ordered Tanner forest (BP+OTF) algorithm as an almost-linear time decoder for quantum low-density parity-check codes. The OTF post-processing stage removes qubits from the decoding graph until it has a tree-like structure. Provided that the resultant loop-free OTF graph supports a subset of qubits that can generate the syndrome, BP decoding is then guaranteed to converge. To enhance performance under circuit-level noise, we introduce a technique for sparsifying detector error models. This method uses a transfer matrix to map soft information from the full detector graph to the sparsified graph, preserving critical error propagation information from the syndrome extraction circuit. Our BP+OTF implementation first applies standard BP to the full detector graph, followed by BP+OTF post-processing on the sparsified graph. Numerical simulations show that the BP+OTF decoder achieves similar logical error suppression compared to state-of-the-art inversion-based and matching decoders for bivariate bicycle and surface codes, respectively, while maintaining almost-linear runtime complexity across all stages.

quant-ph↗

arXiv2024

Decoding algorithms for surface codes

Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build near term error corrected qubits given their two-dimensional architecture, the requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that they can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art decoding algorithms for surface codes is provided. The target audience of this work are both readers with an introductory understanding of the field as well as those seeking to further their knowledge of the decoding paradigm of surface codes. We describe the core principles of these decoding methods as well as existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface codes decoding is also provided.

quant-ph↗

arXiv2024

Quantum CSS Duadic and Triadic Codes: New Insights and Properties

In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum duadic codes. Furthermore, we present a technique for computing or bounding the minimum distances of quantum codes constructed through this approach. Additionally, we introduce quantum CSS triadic codes, a family of quantum codes with a rate of at least $\frac{1}{3}$.

cs.IT↗

arXiv2024

Cybersecurity in Critical Infrastructures: A Post-Quantum Cryptography Perspective

The machinery of industrial environments was connected to the Internet years ago with the scope of increasing their performance. However, this change made such environments vulnerable against cyber-attacks that can compromise their correct functioning resulting in economic or social problems. Moreover, implementing cryptosystems in the communications between operational technology (OT) devices is a more challenging task than for information technology (IT) environments since the OT networks are generally composed of legacy elements, characterized by low-computational capabilities. Consequently, implementing cryptosystems in industrial communication networks faces a trade-off between the security of the communications and the amortization of the industrial infrastructure. Critical Infrastructure (CI) refers to the industries which provide key resources for the daily social and economical development, e.g. electricity. Furthermore, a new threat to cybersecurity has arisen with the theoretical proposal of quantum computers, due to their potential ability of breaking state-of-the-art cryptography protocols, such as RSA or ECC. Many global agents have become aware that transitioning their secure communications to a quantum secure paradigm is a priority that should be established before the arrival of fault-tolerance. In this paper, we aim to describe the problematic of implementing post-quantum cryptography (PQC) to CI environments. For doing so, we describe the requirements for these scenarios and how they differ against IT. We also introduce classical cryptography and how quantum computers pose a threat to such security protocols. Furthermore, we introduce state-of-the-art proposals of PQC protocols and present their characteristics. We conclude by discussing the problematic of integrating PQC in industrial environments.

cs.CR↗

arXiv2024

An infinite class of quantum codes derived from duadic constacyclic codes

We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a square root bound. For each fixed dimension, this allows us to construct an infinite sequence of binary quantum codes with a growing minimum distance. Additionally, we prove that this family of quantum codes includes an infinite subclass of degenerate codes. We also introduce a technique for extending splittings of duadic constacyclic codes, providing new insights into the minimum distance and minimum odd-like weight of specific duadic constacyclic codes. Finally, we provide numerical examples of some quantum codes with short lengths within this family.

cs.IT↗

arXiv2024

The closed-branch decoder for quantum LDPC codes

Quantum error correction is the building block for constructing fault-tolerant quantum processors that can operate reliably even if its constituting elements are corrupted by decoherence. In this context, real-time decoding is a necessity for implementing arbitrary quantum computations on the logical level. In this work, we present a new decoder for Quantum Low Density Parity Check (QLDPC) codes, named the closed-branch decoder, with a worst-case complexity loosely upper bounded by $\mathcal{O}(n\text{max}_{\text{gr}}\text{max}_{\text{br}})$, where $\text{max}_{\text{gr}}$ and $\text{max}_{\text{br}}$ are tunable parameters that pose the accuracy versus speed trade-off of decoding algorithms. For the best precision, the $\text{max}_{\text{gr}}\text{max}_{\text{br}}$ product increases exponentially as $\propto dj^d$, where $d$ indicates the distance of the code and $j$ indicates the average row weight of its parity check matrix. Nevertheless, we numerically show that considering small values that are polynomials of the code distance are enough for good error correction performance. The decoder is described to great extent and compared with the Belief Propagation Ordered Statistics Decoder (BPOSD) operating over data qubit, phenomenological and circuit-level noise models for the class of Bivariate Bicycle (BB) codes. The results showcase a promising performance of the decoder, obtaining similar results with much lower complexity than BPOSD when considering the smallest distance codes, but experiencing some logical error probability degradation for the larger ones. Ultimately, the performance and complexity of the decoder depends on the product $\text{max}_{\text{gr}}\text{max}_{\text{br}}$, which can be considered taking into account benefiting one of the two aspects at the expense of the other.

quant-ph↗

arXiv2023

The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels

Quantum channel capacity is a fundamental quantity in order to understand how good can quantum information be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities, since the quantum channel coherent information is not additive for all channels, implying that it must be maximized over an unbounded number of channel uses. This leads to the phenomenon known as superadditivity, which refers to the fact that the regularized coherent information of $n$ channel uses exceeds one-shot coherent information. In this article, we study how the gain in quantum capacity of qudit depolarizing channels relates to the dimension of the systems considered. We make use of an argument based on the no-cloning bound in order to proof that the possible superadditive effects decrease as a function of the dimension for such family of channels. In addition, we prove that the capacity of the qudit depolarizing channel coincides with the coherent information when $d\rightarrow\infty$. We also discuss the private classical capacity and obain similar results. We conclude that when high dimensional qudits experiencing depolarizing noise are considered, the coherent information of the channel is not only an achievable rate but essentially the maximum possible rate for any quantum block code.

quant-ph↗

arXiv2023

Performance enhancement of surface codes via recursive MWPM decoding

The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or non-identical quantum noise. In this work, we modify the conventional MWPM decoder so that it considers the biases, the non-uniformities and the relationship between $X$, $Y$ and $Z$ errors of the constituent qubits of a given surface code. Our modified approach, which we refer to as the recursive MWPM decoder, obtains an $18\%$ improvement in the probability threshold $p_{th}$ under depolarizing noise. We also obtain significant performance improvements when considering biased noise and independent non-identically distributed (i.ni.d.) error models derived from measurements performed on state-of-the-art quantum processors. In fact, when subjected to i.ni.d. noise, the recursive MWPM decoder yields a performance improvement of $105.5\%$ over the conventional MWPM strategy and, in some cases, it even surpasses the performance obtained over the well-known depolarizing channel.

quant-ph↗

arXiv2022

Multi-qubit time-varying quantum channels for NISQ-era superconducting quantum processors

Recent experimental studies have shown that the relaxation time ($T_1$) and the dephasing time ($T_2$) of superconducting qubits fluctuate considerably over time. To appropriately consider this time-varying nature of the $T_1$ and $T_2$ parameters, a new class of quantum channels, known as Time-Varying Quantum Channels (TVQCs), has been proposed. In previous works, realizations of multi-qubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of $T_1$ and $T_2$ are block-to-block uncorrelated, but qubit-wise perfectly correlated for the same block. Physically, the fluctuations of these decoherence parameters are explained by the incoherent coupling of the qubits with unstable near-resonant two-level-systems (TLS), which indicates that such variations may be local to each of the qubits of the system. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of multi-qubit quantum processors ibmq\_quito, ibmq\_belem, ibmq\_lima, ibmq\_santiago and ibmq\_bogota. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multi-qubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the Fast Time-Varying Quantum Channel (FTVQC). Furthermore, we lower bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes (QECC) when they operate over FTVQCs.

quant-ph↗

arXiv2022

Performance of surface codes in realistic quantum hardware

Surface codes are generally studied based on the assumption that each of the qubits that make up the surface code lattice suffers noise that is independent and identically distributed (i.i.d.). However, real benchmarks of the individual relaxation ($T_1$) and dephasing ($T_2$) times of the constituent qubits of state-of-the-art quantum processors have recently shown that the decoherence effects suffered by each particular qubit actually vary in intensity. In consequence, in this article we introduce the independent non-identically distributed (i.ni.d.) noise model, a decoherence model that accounts for the non-uniform behaviour of the docoherence parameters of qubits. Additionally, we use the i.ni.d model to study how it affects the performance of a specific family of Quantum Error Correction (QEC) codes known as planar codes. For this purpose we employ data from four state-of-the-art superconducting processors: ibmq\_brooklyn, ibm\_washington, Zuchongzhi and Rigetti Aspen-M-1. Our results show that the i.i.d. noise assumption overestimates the performance of surface codes, which can suffer up to $95\%$ performance decrements in terms of the code pseudo-threshold when they are subjected to the i.ni.d. noise model. Furthermore, we consider and describe two methods which enhance the performance of planar codes under i.ni.d. noise. The first method involves a so-called re-weighting process of the conventional minimum weight perfect matching (MWPM) decoder, while the second one exploits the relationship that exists between code performance and qubit arrangement in the surface code lattice. The optimum qubit configuration derived through the combination of the previous two methods can yield planar code pseudo-threshold values that are up to $650\%$ higher than for the traditional MWPM decoder under i.ni.d. noise.

quant-ph↗