A Theory of Fault-Tolerant Quantum Computation

Abstract

In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant operations based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a given code. I demonstrate that fault-tolerant universal computation is possible for any stabilizer code. I discuss a number of examples in more detail, including the five-qubit code.

30 pages, REVTeX, universal swapping operation added to allow universal computation on any stabilizer code

References in corpus (1)

• Fault-tolerant quantum computation

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• An Upper Bound to the Number of Gates on Single Qubit within One Error-Correction Period of Quantum Computation
• QUITS: A modular Qldpc code circUIT Simulator
• A decompositional framework for process theories in spacetime
• Clifford Gates in the Holant Framework
• Minimal degenerate CSS quantum code with low cost circuit
• NMR Quantum Information Processing and Entanglement
• Circuit-level fault tolerance of cat codes
• Simplifying errors by symmetry and randomisation
• Quantum Monte Carlo and Stabilizer States
• Transversal AND in Quantum Codes
• CQM: Cyclic Qubit Mappings
• Operator delocalization in disordered spin chains via exact MPO marginals
• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
• Performance and Error Analysis of Knill's Postselection Scheme in a Two-Dimensional Architecture
• Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions
• Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach
• Entanglemons: Cross-platform protected qubits from entanglement
• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions
• Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes
• Classical representation of local Clifford operators
• Syndrome Measurement Order for the [[7,1,3]] Quantum Error Correction Code
• iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures
• On the Construction for Quantum Code ((n,K, d))p via Logic Function over Fp
• Symmetry boosts quantum computer performance
• A Study on Stabilizer Rényi Entropy Estimation using Machine Learning
• Simple procedure for classical signal-procession in cluster-state quantum computation
• Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory
• Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems
• Ion-Trap Chip Architecture Optimized for Implementation of Quantum Error-Correcting Code
• The Contextual Heisenberg Microscope
• Monte Carlo studies of modified scalable designs for quantum computation
• Fault-tolerant fidelity based on few-qubit codes: Parity-check circuits for biased error channels
• Twisted Fourier analysis and pseudo-probability distributions
• Use of Electron Paramagnetic resonance (EPR) technique to build quantum computers: n-qubit (n=1,2,3,4) Toffoli Gates
• Programming quantum computers using 3-D puzzles, coffee cups, and doughnuts
• Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters
• Four qubits generated by Clifford gates
• Conjugate Logic