Error Correction for Reliable Quantum Computing
arXiv:2202.08599 · doi:10.15581/10171/63067
Abstract
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum paradigm and that renders quantum information useless when left unchecked. The science of quantum error correction, a discipline that seeks to combine and protect quantum information from the effects of decoherence using structures known as codes, has arisen to meet this challenge. Stabilizer codes, a particular subclass of quantum codes, have enabled fast progress in the field of quantum error correction by allowing parallels to be drawn with the widely studied field of classical error correction. This has resulted in the construction of the quantum counterparts of well-known capacity-approaching classical codes like sparse codes and quantum turbo codes. However, quantum codes obtained in this manner do not entirely evoke the stupendous error correcting abilities of their classical counterparts. This occurs because classical strategies ignore important differences between the quantum and classical paradigms, an issue that needs to be addressed if quantum error correction is to succeed in its battle with decoherence. In this dissertation we study a phenomenon exclusive to the quantum paradigm, known as degeneracy, and its effects on the performance of sparse quantum codes. Furthermore, we also analyze and present methods to improve the performance of a specific family of sparse quantum codes in various different scenarios.
arXiv commentPhD Dissertation. Defended on February 14 2022
References in corpus (63)
- Fault-tolerant quantum computation by anyons
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- Experimental quantum teleportation
- Mixed State Entanglement and Quantum Error Correction
- Quantum cryptography: Public key distribution and coin tossing
- Surface codes: Towards practical large-scale quantum computation
- Good Quantum Error-Correcting Codes Exist
- Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
- Decoherence, the measurement problem, and interpretations of quantum mechanics
- Multiple Particle Interference and Quantum Error Correction
- Beating the channel capacity limit for linear photonic superdense coding
- Stabilizer Codes and Quantum Error Correction
- Quantum key distribution in the Holevo limit
- Building logical qubits in a superconducting quantum computing system
- Correcting Quantum Errors with Entanglement
- Instantaneous non-local computation of low T-depth quantum circuits
- The Heisenberg Representation of Quantum Computers
- Quantum Decoherence
- Exponential suppression of bit or phase flip errors with repetitive error correction
- Sparse Graph Codes for Quantum Error-Correction
- Resilient Quantum Computation: Error Models and Thresholds
- Quantum channels and memory effects
- Design and Analysis of Nonbinary LDPC Codes for Arbitrary Discrete-Memoryless Channels
- Symmetrised Characterisation of Noisy Quantum Processes
- Quantum Channels with Memory
- Degenerate Quantum LDPC Codes With Good Finite Length Performance
- Correlating decoherence in transmon qubits: Low frequency noise by single fluctuators
- Decoding Across the Quantum LDPC Code Landscape
- Asymmetric quantum error correcting codes
- Coherence of qubits based on single Ca ions
- Quantum Graphical Models and Belief Propagation
- Degenerate Quantum Codes for Pauli Channels
- General entanglement-assisted quantum error-correcting codes
- Coherence of Spin Qubits in Silicon
- Trapped-ion quantum logic with global radiation fields
- Catalytic quantum error correction
- Description of a quantum convolutional code
- Quantum Belief Propagation
- Optimal and Efficient Decoding of Concatenated Quantum Block Codes
- Convolutional and tail-biting quantum error-correcting codes
- Surface code with decoherence: An analysis of three superconducting architectures
- Entanglement-Assisted Quantum Quasi-Cyclic Low-Density Parity-Check Codes
- Nondestructive detection of photonic qubits
- Quantum Quasi-Cyclic LDPC Codes
- NP-hardness of decoding quantum error-correction codes
- Experimentally scalable protocol for identification of correctable codes
- Asymmetric quantum error correction via code conversion
- Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes
- EXIT-Chart Aided Near-Capacity Quantum Turbo Code Design
- Error correction optimisation in the presence of X/Z asymmetry
- Constructions and performance of classes of quantum LDPC codes
- Quantum Error Correction beyond the Bounded Distance Decoding Limit
- Computing the distance between quantum channels: Usefulness of the Fano representation
- The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
- Modified belief propagation decoders for quantum low-density parity-check codes
- On the logical operators of quantum codes
- Depolarizing channel parameter estimation using noisy initial states
- Near-Hashing-Bound Multiple-Rate Quantum Turbo Short-Block Codes
- Short Codes for Quantum Channels with One Prevalent Pauli Error Type
- A characterization of entanglement-assisted quantum low-density parity-check codes
- Quantum outage probability for time-varying quantum channels
- Trellis Decoding For Qudit Stabilizer Codes And Its Application To Qubit Topological Codes
- Cramér-Rao bound and quantum parameter estimation with non-Hermitian systems