Decoherence and Quantum Error Correction for Quantum Computing and Communications
arXiv:2202.08600 · doi:10.15581/10171/63013
Abstract
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.
arXiv commentPhD dissertation by Josu Etxezarreta Martinez defended on 15th february 2022
References in corpus (78)
- Quantum Computing in the NISQ era and beyond
- Mixed State Entanglement and Quantum Error Correction
- Charge insensitive qubit design derived from the Cooper pair box
- Good Quantum Error-Correcting Codes Exist
- Simulated Quantum Computation of Molecular Energies
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- An addressable quantum dot qubit with fault-tolerant control fidelity
- Quantum Error Correction and Orthogonal Geometry
- Towards Quantum Chemistry on a Quantum Computer
- Coherent Josephson qubit suitable for scalable quantum integrated circuits
- Elucidating Reaction Mechanisms on Quantum Computers
- Stabilizer Codes and Quantum Error Correction
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- Benchmarking an 11-qubit quantum computer
- Correcting Quantum Errors with Entanglement
- From Classical to Quantum Shannon Theory
- Instantaneous non-local computation of low T-depth quantum circuits
- The Heisenberg Representation of Quantum Computers
- Quantum Process Tomography: Resource Analysis of Different Strategies
- Experimental Quantum Key Distribution with Decoy States
- Sparse Graph Codes for Quantum Error-Correction
- Codes for the Quantum Erasure Channel
- Capacities of Quantum Erasure Channels
- Quantum channels and memory effects
- Fluctuations of Energy-Relaxation Times in Superconducting Qubits
- Entanglement enhanced information transmission over a quantum channel with correlated noise
- Symmetrised Characterisation of Noisy Quantum Processes
- Reducing decoherence in quantum computer memory with all quantum bits coupling to the same environment
- Randomized benchmarking and process tomography for gate errors in a solid-state qubit
- Fast Decoders for Topological Quantum Codes
- Quantum Channels with Memory
- Degenerate Quantum LDPC Codes With Good Finite Length Performance
- Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
- Correlating decoherence in transmon qubits: Low frequency noise by single fluctuators
- Fisher information in quantum statistics
- Decoding Across the Quantum LDPC Code Landscape
- A Quantum solution to the Byzantine agreement problem
- Degenerate Quantum Codes for Pauli Channels
- Machine-learning-assisted correction of correlated qubit errors in a topological code
- Decoding Small Surface Codes with Feedforward Neural Networks
- Catalytic quantum error correction
- Description of a quantum convolutional code
- Cavity Attenuators for Superconducting Qubits
- Optimal and Efficient Decoding of Concatenated Quantum Block Codes
- Entanglement-assisted quantum turbo codes
- Quantum Capacities of Channels with small Environment
- Quantum channels with a finite memory
- NP-hardness of decoding quantum error-correction codes
- Experimentally scalable protocol for identification of correctable codes
- Exploiting entanglement in communication channels with correlated noise
- EXIT-Chart Aided Near-Capacity Quantum Turbo Code Design
- Bounds on classical information capacities for a class of quantum memory channels
- Multi-path Summation for Decoding 2D Topological Codes
- Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions
- Semidefinite programs for completely bounded norms
- Entanglement-enhanced classical capacity of two-qubit quantum channels with memory: the exact solution
- Computing the distance between quantum channels: Usefulness of the Fano representation
- Capacities of lossy bosonic memory channels
- The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
- Modified belief propagation decoders for quantum low-density parity-check codes
- Framework for classifying logical operators in stabilizer codes
- Ancilla-Assisted Enhancement of Channel Estimation for Low-Noise Parameters
- Quantum Accelerators for High-Performance Computing Systems
- Belief Propagation with Quantum Messages for Quantum-Enhanced Classical Communications
- A Quantum von Neumann Architecture for Large-Scale Quantum Computing
- Short Codes for Quantum Channels with One Prevalent Pauli Error Type
- Near-Hashing-Bound Multiple-Rate Quantum Turbo Short-Block Codes
- Bounds on amplitude damping channel discrimination
- Depolarizing channel parameter estimation using noisy initial states
- Memory effects in attenuation and amplification quantum processes
- Always On Non-Nearest-Neighbor Coupling in Scalable Quantum Computing
- Entanglement and optimal strings of qubits for memory channels
- Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels
- Quantum outage probability for time-varying quantum channels
- Decoherence-free subspaces and subsystems for a collectively depolarizing bosonic channel
- Entanglement creation and distribution on a graph of exchange-coupled qutrits
- Quantum Insertion-Deletion Channels
- Effects of imperfect noise correlations on decoherence-free subsystems: SU(2) diffusion model