arXiv subjects

Lorenzo Valentini

Publications and source records attributed to Lorenzo Valentini.

At least 19 recordsLinked to original sources

arXiv2026

Practical Low-Weight Codes for Energy-Efficient Bus Encoding

We consider the transmission of data encoded into binary messages, with the goal of minimizing the Hamming distance, i.e., the number of bit-flips, between consecutive messages. This problem is relevant for enhancing the longevity of Non-Volatile Memories and reducing transition-induced energy consumption in data buses. Known as Write-Efficient Memory coding in the literature, this challenge has traditionally been addressed using optimal but complex schemes. In low-power computer systems the same topic is known as bus encoding. In this paper, we derive closed-form expressions to evaluate the average number of bit-flips for practical, sub-optimal encoding schemes, and propose two new schemes assisted by predefined random codebooks. We demonstrate that low-complexity solutions achieve performance very close to the optimal schemes, making them attractive for implementation in energy-sensitive and memory-critical applications. For instance, by adding 8 extra bits to 64-bits data, sub-optimal schemes can achieve a bit-flip reduction (related to energy saving) of approximately 24.7%, compared to the 26.4% reduction offered by the significantly more complex optimal scheme.

cs.IT↗

arXiv2026

Performance Limits of Fault-Tolerant Quantum Error Correction Schemes

Quantum error correction (QEC) is essential for realizing scalable quantum computation. However, when evaluating its benefits, most analyses assume idealized components, overlooking the imperfections inherent in realistic fault-tolerant (FT) implementations. In this paper, we investigate the performance of QEC schemes taking into account that quantum gates and measurements are themselves error-prone. We derive bounds for the failure probability of Shor-style FT-QEC schemes using limited structural information, such as the number of flag qubits and quantum gates. Our analysis separates and quantifies two key contributors to the failure rate: decoding errors and residual errors arising from circuit-level faults. The derived bounds highlight fundamental limitations in Shor-style FT-QEC performance and quantify how circuit imperfections degrade error correction capabilities, under the assumption of depolarizing noise.

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arXiv2026

Fault-Tolerant Cut-Cat State Syndrome Extraction for Quantum Codes

Reliable quantum computation requires fault-tolerant protocols to prevent errors from propagating during syndrome extraction in quantum error correction. We present a novel fault-tolerant syndrome extraction technique for CSS codes, which we refer to as the cut-cat state scheme. While each ancilla qubit interacts non-fault-tolerantly with a pair of data qubits, we introduce additional cat stabilizer measurements to identify and correct the resulting hook errors. Our approach maintains the key benefit of cat-based extraction, i.e., parallelized data qubit interactions, while reducing the number of simultaneous qubits required by more than half. Compared to flag-based state-of-the-art protocols, the cut-cat scheme offers a notable advantage in terms of two-qubit gate count as the code distance increases.

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arXiv2026

Dimensioning of Quantum Memories for Distilled Quantum EPR Packets

The quantum Internet envisions a network where information is transmitted through entanglement, with Einstein-Podolsky-Rosen (EPR) pairs serving as one of the fundamental carriers. In this work, we propose a framework for dimensioning quantum memories capable of storing distilled EPR pairs useful to transmitting and manage quantum error correcting codes. Using a Markov chain model, we capture the stochastic evolution of stored entangled states in quantum memories, linking memory performance to system parameters such as technology characteristics and initial entanglement fidelity. Building on this framework, we provide analytical tools and design principles for optimizing memory architectures that preserve high-fidelity entanglement over time, ensuring the availability of encoded quantum resources necessary for several operations in future quantum Internet infrastructures transmitting EPR packets.

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arXiv2025

Restart Belief: A General Quantum LDPC Decoder

Hardware-friendly quantum low-density parity-check (QLDPC) decoders are commonly built upon belief propagation (BP) processing. Yet, quantum degeneracy often prevents BP from achieving reliable convergence. To overcome this fundamental limitation, we propose the restart belief (RB) decoder, an iterative BP-based algorithm inspired by branch-and-bound optimization principles. From our analysis we find that the RB decoder represents both the fastest and most accurate decoding algorithm applicable to QLDPC codes to date, conceived with the explicit goal of approaching error correction up to the code distance.

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arXiv2025

Bubble Clustering Decoder for Quantum Topological Codes

Quantum computers are highly vulnerable to noise, necessitating the use of error-correcting codes to protect stored data. Errors must be continuously corrected over time to counteract decoherence using appropriate decoders. Therefore, fast decoding strategies capable of handling real-time syndrome extraction are crucial for achieving fault-tolerant quantum computing. In this paper, we introduce the bubble clustering (BC) decoder for quantum surface codes, which serves as a low-latency replacement for MWPM, achieving significantly faster execution at the cost of a slight performance degradation. This speed boost is obtained leveraging an efficient cluster generation based on bubbles centered on defects, and avoiding the computational overhead associated with cluster growth and merging phases, commonly adopted in traditional decoders. Our complexity analysis reveals that the proposed decoder operates with a complexity on the order of the square of the number of defects. For moderate physical error rates, this is equivalent to linear complexity in the number of data qubits.

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arXiv2025

Cylindrical and M\"obius Quantum Codes for Asymmetric Pauli Errors

In the implementation of quantum information systems, one type of Pauli error, such as phase-flip errors, may occur more frequently than others, like bit-flip errors. For this reason, quantum error-correcting codes that handle asymmetric errors are critical to mitigating the impact of such impairments. To this aim, several asymmetric quantum codes have been proposed. These include variants of surface codes like the XZZX and ZZZY surface codes, tailored to preserve quantum information in the presence of error asymmetries. In this work, we propose two classes of Calderbank, Shor and Steane (CSS) topological codes, referred to as cylindrical and M\"obius codes, particular cases of the fiber bundle family. Cylindrical codes maintain a fully planar structure, while M\"obius codes are quasi-planar, with minimal non-local qubit interactions. We construct these codes employing the algebraic chain complexes formalism, providing theoretical upper bounds for the logical error rate. Our results demonstrate that cylindrical and M\"obius codes outperform standard surface codes when using the minimum weight perfect matching (MWPM) decoder.

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arXiv2024

Quantum codes for asymmetric channels: ZZZY surface codes

We introduce surface ZZZY codes, a novel family of quantum error-correcting codes designed for asymmetric channels. Derived from standard surface codes through tailored modification of generators, ZZZY codes can be decoded by the minimum weight perfect matching (MWPM) algorithm with a suitable pre-processing phase. The resulting decoder exploits the information provided by the modified generators without introducing additional complexity. ZZZY codes demonstrate a significant performance advantage over surface codes when increasing the channel asymmetry, while maintaining the same correction capability over depolarizing channel.

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arXiv2024

Reliable Quantum Communications based on Asymmetry in Distillation and Coding

The reliable provision of entangled qubits is an essential precondition in a variety of schemes for distributed quantum computing. This is challenged by multiple nuisances, such as errors during the transmission over quantum links, but also due to degradation of the entanglement over time due to decoherence. The latter can be seen as a constraint on the latency of the quantum protocol, which brings the problem of quantum protocol design into the context of latency-reliability constraints. We address the problem through hybrid schemes that combine: (1) indirect transmission based on teleportation and distillation; (2) direct transmission, based on quantum error correction (QEC). The intuition is that, at present, the quantum hardware offers low fidelity, which demands distillation; on the other hand, low latency can be obtained by QEC techniques. It is shown that, in the proposed framework, the distillation protocol gives rise to asymmetries that can be exploited by asymmetric quantum error correcting code (QECC), which sets the basis for unique hybrid distillation and coding design. Our results show that ad-hoc asymmetric codes give, compared to conventional QEC, a performance boost and codeword size reduction both in a single link and in a quantum network scenario.

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arXiv2024

Spanning Tree Matching Decoder for Quantum Surface Codes

We introduce the spanning tree matching (STM) decoder for surface codes, which guarantees the error correction capability up to the code's designed distance by first employing an instance of the minimum spanning tree on a subset of ancilla qubits within the lattice. Then, a perfect matching graph is simply obtained, by selecting the edges more likely to be faulty. A comparative analysis reveals that the STM decoder, at the cost of a slight performance degradation, provides a substantial advantage in decoding time compared to the minimum weight perfect matching (MWPM) decoder. Finally, we propose an even more simplified and faster algorithm, the Rapid-Fire (RFire) decoder, designed for scenarios where decoding speed is a critical requirement.

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arXiv2024

An Implementation of the Optimal Scheme for Energy Efficient Bus Encoding

In computer system buses, most of the energy is spent to change the voltage of each line from high to low or vice versa. Bus encoding schemes aim to improve energy efficiency by limiting the number of transitions between successive uses of the bus. We propose an implementation of the optimal code with reduced number of clock cycles.

cs.IT↗

arXiv2023

Logical Error Rates of XZZX and Rotated Quantum Surface Codes

Surface codes are versatile quantum error-correcting codes known for their planar geometry, making them ideal for practical implementations. While the original proposal used Pauli $X$ or Pauli $Z$ operators in a square structure, these codes can be improved by rotating the lattice or incorporating a mix of generators in the XZZX variant. However, a comprehensive theoretical analysis of the logical error rate for these variants has been lacking. To address this gap, we present theoretical formulas based on recent advancements in understanding the weight distribution of stabilizer codes. For example, over an asymmetric channel with asymmetry $A=10$ and a physical error rate $p \to 0$, we observe that the logical error rate asymptotically approaches $p_\mathrm{L} \to 10 p^2$ for the rotated $[[9,1,3]]$ XZZX code and $p_\mathrm{L} \to 18.3 p^2$ for the $[[13,1,3]]$ surface code. Additionally, we observe a particular behavior regarding rectangular lattices in the presence of asymmetric channels. Our findings demonstrate that implementing both rotation and XZZX modifications simultaneously can lead to suboptimal performance. Thus, in scenarios involving a rectangular lattice, it is advisable to avoid using both modifications simultaneously. This research enhances our theoretical understanding of the logical error rates for XZZX and rotated surface codes, providing valuable insights into their performance under different conditions.

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arXiv2023

Exploiting Pilot Mixtures in Coded Random Access

The construction of preamble sequences for channel estimation by superposition of orthogonal pilots can improve performance of massive grant-free uplink from machine-type devices. In this letter, a technique is proposed to obtain full benefit from these "pilot mixtures" in presence of a base station with a massive number of antennas. The proposed technique consists of combining pilot mixtures with an intra-slot successive interference cancellation (SIC) algorithm, referred to as inner SIC, to increase the number of decoded messages per slot. In framed systems, the synergic effect of inner SIC and of an outer SIC algorithm across slots, typical of coded random access protocols, allows achieving a very high reliability with a low number of packet replicas per active user.

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arXiv2023

Heterogeneous radio access with multiple latency targets

Since the advent of ultra-reliable and low-latency communications (URLLC), the requirements of low-latency applications tend to be completely characterized by a single pre-defined latency-reliability target. That is, operation is optimal whenever the pre-defined latency threshold is met but the system is assumed to be in error when the latency threshold is violated. This vision is severely limited and does not capture the real requirements of most applications, where multiple latency thresholds can be defined, together with incentives or rewards associated with meeting each of them. Such formulation is a generalization of the single-threshold case popularized by URLLC and, in the asymptotic case, approximates to defining a cost for each point in the support of the latency distribution. In this paper, we explore the implications of defining multiple latency targets on the design of access protocols and on the optimization of repetition-based access strategies in orthogonal and non-orthogonal multiple access scenarios with users that present heterogeneous traffic characteristics and requirements. We observe that the access strategies of the users can be effectively adapted to the requirements of the application by carefully defining the latency targets and the associated rewards.

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arXiv2023

Quantum Two-Way Protocol Beyond Superdense Coding: Joint Transfer of Data and Entanglement

In this article, we introduce a generalization of one-way superdense coding to two-way communication protocols for transmitting classical bits by using entangled quantum pairs. The proposed protocol jointly addresses the provision of entangled pairs and superdense coding, introducing an integrated approach for managing entanglement within the communication protocol. To assess the performance of the proposed protocol, we consider its data rate and resource usage, and we analyze this both in an ideal setting with no decoherence and in a more realistic setting where decoherence must be taken into account. In the ideal case, the proposal offers a 50% increase in both data rate and resource usage efficiency compared to conventional protocols. Even when decoherence is taken into consideration, the quantum protocol performs better as long as the decoherence time is not extremely short. Finally, we present the results of implementing the protocol in a computer simulation based on the NetSquid framework. We compare the simulation results with the theoretical values.

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arXiv2023

Interference Cancellation Algorithms for Grant-Free Multiple Access with Massive MIMO

In next generation Internet-of-Things, the overhead introduced by grant-based multiple access protocols may engulf the access network as a consequence of the unprecedented number of connected devices. Grant-free access protocols are therefore gaining an increasing interest to support massive access from machine-type devices with intermittent activity. In this paper, coded random access (CRA) with massive multiple input multiple output (MIMO) is investigated as a solution to design highly-scalable massive multiple access protocols, taking into account stringent requirements on latency and reliability. With a focus on signal processing aspects at the physical layer and their impact on the overall system performance, critical issues of successive interference cancellation (SIC) over fading channels are first analyzed. Then, SIC algorithms and a scheduler are proposed that can overcome some of the limitations of the current access protocols. The effectiveness of the proposed processing algorithms is validated by Monte Carlo simulation, for different CRA protocols and by comparisons with developed benchmarks.

eess.SP↗

arXiv2023

Performance Analysis of Quantum CSS Error-Correcting Codes via MacWilliams Identities

We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the undetectable errors based on the quantum MacWilliams identities. The WE is then used to evaluate tight upper bounds on the error rate of CSS quantum codes with \acl{MW} decoding. For surface codes we also derive a simple closed form expression of the bounds over the depolarizing channel. We introduce a novel approach that combines the knowledge of WE with a logical operator analysis, allowing the derivation of the exact asymptotic error rate for short codes. For example, on a depolarizing channel with physical error rate $\rho \to 0$, the logical error rate $\rho_\mathrm{L}$ is asymptotically $\rho_\mathrm{L} \approx 16 \rho^2$ for the $[[9,1,3]]$ Shor code, $\rho_\mathrm{L} \approx 16.3 \rho^2$ for the $[[7,1,3]]$ Steane code, $\rho_\mathrm{L} \approx 18.7 \rho^2$ for the $[[13,1,3]]$ surface code, and $\rho_\mathrm{L} \approx 149.3 \rho^3$ for the $[[41,1,5]]$ surface code. For larger codes our bound provides $\rho_\mathrm{L} \approx 1215 \rho^4$ and $\rho_\mathrm{L} \approx 663 \rho^5$ for the $[[85,1,7]]$ and the $[[181,1,10]]$ surface codes, respectively. Finally, we extend our analysis to include realistic, noisy syndrome extraction circuits by modeling error propagation throughout gadgets. This enables estimation of logical error rates under faulty measurements. The performance analysis serves as a design tool for developing fault-tolerant quantum systems by guiding the selection of quantum codes based on their error correction capability. Additionally, it offers a novel perspective on quantum degeneracy, showing it represents the fraction of non-correctable error patterns shared by multiple logical operators.

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arXiv2023

Performance Analysis of Quantum Error-Correcting Surface Codes over Asymmetric Channels

One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing and quantum Internet. We here analyze the performance of surface codes, one of the most important class for practical implementations, on both symmetric and asymmetric quantum channels. We derive approximate expressions, confirmed by simulations, to evaluate the performance of surface codes and of XZZX codes, and provide a metric to assess the advantage of codes with respect to uncoded systems. Our findings allow to characterize the performance by means of analytical formulas of surface codes, like, for example, the [[13, 1, 3]], the [[23, 1, 3/5]], the [[33, 1, 3/7]], and the [[41, 1, 5]] surface codes.

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