arXiv subjects

Josu Etxezarreta Martinez

Publications and source records attributed to Josu Etxezarreta Martinez.

27 records · Page 2Linked to original sources

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↗

arXiv2022

On the logical error rate of sparse quantum codes

The quantum paradigm presents a phenomenon known as degeneracy that should improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse quantum codes and the logical error rate is not always correctly reported. In this paper, we discuss previously existing methods to compute the logical error rate and we present an efficient coset-based method inspired by classical coding strategies to estimate degenerate errors. Additionally, we show that the proposed method presents a computational advantage for the family of Calderbank-Shor-Steane codes. We use this method to prove that degenerate errors are frequent in a specific family of sparse quantum codes, which stresses the importance of accurately reporting their performance. Our results also reveal that the modified decoding strategies proposed in the literature are an important tool to improve the performance of sparse quantum codes.

quant-ph↗

arXiv2022

Decoherence and Quantum Error Correction for Quantum Computing and Communications

Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such capability to solve certain problems that are not classically tractable, quantum machines have the potential revolutionize the modern world via applications such as drug design, process optimization, unbreakable communications or machine learning. However, quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. In this thesis, the nature of decoherence is studied and mathematically modelled; and QECCs are designed and optimized so that they exhibit better error correction capabilities.

quant-ph↗

arXiv2021

Quantum outage probability for time-varying quantum channels

Recent experimental studies have shown that the relaxation time, $T_1$, and the dephasing time, $T_2$, of superconducting qubits fluctuate considerably over time. Time-varying quantum channel (TVQC) models have been proposed in order to consider the time varying nature of the parameters that define qubit decoherence. This dynamic nature of quantum channels causes a degradation of the performance of quantum error correction codes (QECC) that is portrayed as a flattening of their error rate curves. In this article, we introduce the concepts of quantum outage probability and quantum hashing outage probability as asymptotically achievable error rates by a QECC with quantum rate $R_Q$ operating over a TVQC. We derive closed-form expressions for the family of time-varying amplitude damping channels (TVAD) and study their behaviour for different scenarios. We quantify the impact of time-variation as a function of the relative variation of $T_1$ around its mean. We conclude that the performance of QECCs is limited in many cases by the inherent fluctuations of their decoherence parameters and corroborate that parameter stability is crucial to maintain the excellent performance observed over static quantum channels.

quant-ph↗