arXiv subjects

Alexis Schotte

Publications and source records attributed to Alexis Schotte.

4 recordsLinked to original sources

arXiv2025

Computing Efficiently in QLDPC Codes

It is the prevailing belief that quantum error correcting techniques will be required to build a utility-scale quantum computer able to perform computations that are out of reach of classical computers. The QECCs that have been most extensively studied and therefore highly optimized, surface codes, are extremely resource intensive in terms of the number of physical qubits needed. A promising alternative, QLDPC codes, has been proposed more recently. These codes are much less resource intensive, requiring significantly fewer physical qubits per logical qubit than practical surface code implementations. A successful application of QLDPC codes would therefore drastically reduce the timeline to reaching quantum computers that can run algorithms with proven exponential speedups like Shor's algorithm and QPE. However to date QLDPC codes have been predominantly studied in the context of quantum memories; there has been no known method for implementing arbitrary logical Clifford operators in a QLDPC code proven efficient in terms of circuit depth. In combination with known methods for implementing T gates, an efficient implementation of the Clifford group unlocks resource-efficient universal quantum computation. In this paper, we introduce a new family of QLDPC codes that enable efficient compilation of the full Clifford group via transversal operations. Our construction executes any m-qubit Clifford operation in at most O(m) syndrome extraction rounds, significantly surpassing state-of-the-art lattice surgery methods. We run circuit-level simulations of depth-126 logical circuits to show that logical operations in our QLDPC codes attains near-memory performance. These results demonstrate that QLDPC codes are a viable means to reduce the resources required to implement all logical quantum algorithms, thereby unlocking a reduced timeline to commercially valuable quantum computing.

quant-ph↗

arXiv2022

Fault-tolerant error correction for a universal non-Abelian topological quantum computer at finite temperature

We study fault-tolerant error correction in a quantum memory constructed as a two-dimensional model of Fibonacci anyons on a torus, in the presence of thermal noise represented by pair-creation processes and measurement errors. The correction procedure is based on the cellular automaton decoders originating in the works of Gács and Harrington. Through numerical simulations, we observe that this code behaves fault-tolerantly and that threshold behavior is likely present. Hence, we provide strong evidence for the existence of a fault-tolerant universal non-Abelian topological quantum computer.

quant-ph↗

arXiv2021

Quantum error correction thresholds for the universal Fibonacci Turaev-Viro code

We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonaccistring-net code, and devise strategies for error correction when those qubits are subjected to depolarizing noise.Building on the concept of tube algebras, we construct a set of measurements and of quantum gates whichmap arbitrary qubit errors to the string-net subspace and allow for the characterization of the resulting errorsyndrome in terms of doubled Fibonacci anyons. Tensor network techniques then allow to quantitatively studythe action of Pauli noise on the string-net subspace. We perform Monte Carlo simulations of error correctionin this Fibonacci code, and compare the performance of several decoders. For the case of a fixed-rate samplingdepolarizing noise model, we find an error correction threshold of 4.7% using a clustering decoder. To the bestof our knowledge, this is the first time that a threshold has been estimated for a two-dimensional error correctingcode for which universal quantum computation can be performed within its code space via braiding anyons

quant-ph↗

arXiv2019

Tensor-network approach to phase transitions in string-net models

We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops expectation values, and a natural order parameter detecting the breakdown of the topological phase. In the presence of a string tension, a quantum phase transition occurs between the topological phase and a trivial phase. We benchmark our approach for $\mathbb{Z}_2$ string nets and capture the second-order phase transition which is well known from the exact mapping onto the transverse-field Ising model. More interestingly, for Fibonacci string nets, we obtain first-order transitions in contrast with previous studies but in qualitative agreement with mean-field results.

cond-mat.str-el↗