arXiv subjects

Francisco Revson F. Pereira

Publications and source records attributed to Francisco Revson F. Pereira.

10 recordsLinked to original sources

arXiv2024

Pruning qLDPC codes: Towards bivariate bicycle codes with open boundary conditions

Quantum low-density parity-check codes are promising candidates for quantum error correcting codes as they might offer more resource-efficient alternatives to surface code architectures. In particular, bivariate bicycle codes have recently gained attention due to their 2D-local structure, high encoding rate, and promising performance under simulation. In this work, we will explore how one can transform bivariate bicycle codes defined on lattices with periodic boundary conditions to codes with the same locality properties on a 2D lattice with open boundary conditions. For this, we introduce the concept of pruning quantum codes. We explain how pruning bivariate bicycle codes is always possible when the codes are hypergraph products of two classical cyclic codes. We also indicate that this might be possible for more general bivariate bicycle codes by constructing explicit examples. Finally, we investigate fault-tolerant quantum computation using the constructed pruned codes by describing fold-transversal gates.

quant-ph↗

arXiv2024

Low-Weight High-Distance Error Correcting Fermionic Encodings

We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high minimum distance, low-weight fermionic logical operators, a small qubit to fermionic mode ratio and a simple qubit connectivity graph including ancilla qubits for the measurement of stabilizers. Our strategy consists of a three-step procedure in which we: first generate encodings with code distances up to $d\leq4$ by a brute-force enumeration technique; subsequently, we use these encodings as starting points and apply Clifford deformations to them which allows us to identify higher-distance codes with $d\leq7$; finally, we optimize the hardware connectivity graphs of resulting encodings in terms of the graph thickness and the number of connections per qubit. We report multiple promising high-distance encodings which significantly improve the weights of stabilizers and logical operators compared to previously reported alternatives.

quant-ph↗

arXiv2024

Near-optimal decoding algorithm for color codes using Population Annealing

The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a recovery operation with a high success rate. In this work, we implement a decoder that finds the recovery operation with the highest success probability by mapping the decoding problem to a spin system and using Population Annealing to estimate the free energy of the different error classes. We study the decoder performance on a 4.8.8 color code lattice under different noise models, including code capacity with bit-flip and depolarizing noise, and phenomenological noise, which considers noisy measurements, with performance reaching near-optimal thresholds. This decoding algorithm can be applied to a wide variety of stabilizer codes, including surface codes and quantum low-density parity-check (qLDPC) codes.

quant-ph↗

arXiv2023

Stabilizer codes for Open Quantum Systems

The Lindblad master equation describes the evolution of a large variety of open quantum systems. An important property of some open quantum systems is the existence of decoherence-free subspaces. A quantum state from a decoherence-free subspace will evolve unitarily. However, there is no procedural and optimal method for constructing a decoherence-free subspace. In this paper, we develop tools for constructing decoherence-free stabilizer codes for open quantum systems governed by Lindblad master equation. This is done by pursuing an extension of the stabilizer formalism beyond the celebrated group structure of Pauli error operators. We then show how to utilize decoherence-free stabilizer codes in quantum metrology in order to attain the Heisenberg limit scaling with low computational complexity.

quant-ph↗

arXiv2022

An Algorithmic Approach to Entanglement-Assisted Quantum Error-Correcting Codes from the Hermitian Curve

We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is $c$, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing $c$ for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.

cs.IT↗

arXiv2020

Polar Codes for Quantum Reading

Quantum reading provides a general framework where to formulate the statistical discrimination of quantum channels. Several paths have been taken for such a problem. However, there is much to be done in the avenue of optimizing channel discrimination using classical codes. At least two open questions can be pointed to: how to construct low complexity encoding schemes that are interesting for channel discrimination and, more importantly, how to develop capacity-achieving protocols. The aim of this paper is to present a solution to these questions using polar codes. Firstly, we characterize the rate and reliability of the channels under polar encoding. We also show that the error probability of the scheme proposed decays exponentially with respect to the code length. Lastly, an analysis of the optimal quantum states to be used as probes is given.

cs.IT↗

arXiv2019

Entanglement-assisted Quantum Codes from Cyclic Codes

Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional stabilizer formalism. In this paper, it is shown a general method to construct QUENTA codes from cyclic codes. Afterwards, the method is applied to Reed-Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of QUENTA codes. Two families of QUENTA codes are maximal distance separable (MDS), and one is almost MDS or almost near MDS. The comparison of the codes in this paper is mostly based on the quantum Singleton bound.

cs.IT↗

arXiv2019

Entanglement-assisted Quantum Codes from Algebraic Geometry Codes

Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via the traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct several families of QUENTA codes via the Euclidean and the Hermitian construction. Two of the families created have maximal entanglement and have quantum Singleton defect equal to zero or one. Comparing the other families with the codes with the respective quantum Gilbert-Varshamov bound, we show that our codes have a rate that surpasses that bound. At the end, asymptotically good towers of linear complementary dual codes are used to obtain asymptotically good families of maximal entanglement QUENTA codes. Furthermore, a simple comparison with the quantum Gilbert-Varshamov bound demonstrates that using our construction it is possible to create an asymptotically family of QUENTA codes that exceeds this bound.

cs.IT↗

arXiv2017

Good and asymptotically good quantum codes derived from algebraic geometry codes

In this paper we construct several new families of quantum codes with good and asymptotically good parameters. These new quantum codes are derived from (classical) algebraic geometry (AG) codes by applying the Calderbank-Shor-Steane (CSS) construction. Many of these codes have large minimum distances when compared with its code length and they have relatively small Singleton defect. For example, we construct a family [[46; 2(t_2 - t1); d]]_25 of quantum codes, where t_1, t_2 are positive integers such that 1 < t_1 < t_2 < 23 and d >= min {46 - 2t_2, 2t_1-2}, of length n = 46, with minimum distance in the range 2 =< d =< 20, having Singleton defect four. Additionally, by utilizing t-point AG codes, with t >= 2, we show how to obtain sequences of asymptotically good quantum codes.

quant-ph↗

arXiv2016

New Convolutional Codes Derived from Algebraic Geometry Codes

In this paper, we construct new families of convolutional codes. Such codes are obtained by means of algebraic geometry codes. Additionally, more families of convolutional codes are constructed by means of puncturing, extending, expanding and by the direct product code construction applied to algebraic geometry codes. The parameters of the new convolutional codes are better than or comparable to the ones available in literature. In particular, a family of almost near MDS codes is presented.

cs.IT↗