Unifying flavors of fault tolerance with the ZX calculus

Abstract

There are several models of quantum computation which exhibit shared fundamental fault-tolerance properties. This article makes commonalities explicit by presenting these different models in a unifying framework based on the ZX calculus. We focus on models of topological fault tolerance - specifically surface codes - including circuit-based, measurement-based and fusion-based quantum computation, as well as the recently introduced model of Floquet codes. We find that all of these models can be viewed as different flavors of the same underlying stabilizer fault-tolerance structure, and sustain this through a set of local equivalence transformations which allow mapping between flavors. We anticipate that this unifying perspective will pave the way to transferring progress among the different views of stabilizer fault-tolerance and help researchers familiar with one model easily understand others.

Accepted in Quantum, 16 pages, 13 figures, V2: updated bibliography links, minor corrections

References in corpus (16)

• Topological Quantum Distillation
• Quantum Low-Density Parity-Check Codes
• Dynamically Generated Logical Qubits
• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Floquet codes without parent subsystem codes
• Anyon condensation and the color code
• Logical blocks for fault-tolerant topological quantum computation
• Boundaries for the Honeycomb Code
• Performance of planar Floquet codes with Majorana-based qubits
• Equivalence Checking of Quantum Circuits with the ZX-Calculus
• Benchmarking the Planar Honeycomb Code
• Opportunities and Challenges in Fault-Tolerant Quantum Computation
• A Pair Measurement Surface Code on Pentagons
• Active volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections
• Modular decoding: parallelizable real-time decoding for quantum computers
• Graphical quantum Clifford-encoder compilers from the ZX calculus

Cited by in corpus (24)

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• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Perturbative stability and error correction thresholds of quantum codes
• Low-overhead quantum computing with the color code
• XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime
• Dynamical Logical Qubits in the Bacon-Shor Code
• Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes
• Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases
• Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma
• ZX-calculus is Complete for Finite-Dimensional Hilbert Spaces
• Contextuality of Quantum Error-Correcting Codes
• Low-density parity-check representation of fault-tolerant quantum circuits
• String Diagrams for Defect-Based Surface Code Computing
• Competing automorphisms and disordered Floquet codes
• A dataflow programming framework for linear optical distributed quantum computing
• Comparing Schemes for Creating Qudit Graph States from 16- & 128-dimensional Hilbert Space using Donors in Silicon
• Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
• Simulating plasma wave propagation on a superconducting quantum chip
• Increasing the distance of topological codes with time vortex defects
• Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases
• Planar fault-tolerant circuits for non-Clifford gates on the 2D color code
• Nonlinear photonic architecture for fault-tolerant quantum computing