Logical blocks for fault-tolerant topological quantum computation
arXiv:2112.12160 · doi:10.1103/PRXQuantum.4.020303
Abstract
Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and resource overheads of universal logical gate sets have so far been limited. In this paper, we present a comprehensive framework for universal fault-tolerant logic motivated by the combined need for platform-independent logical gate definitions, flexible and scalable tools for numerical analysis, and exploration of novel schemes for universal logic that improve resource overheads. Central to our framework is the description of logical gates holistically in a way which treats space and time on a similar footing. Focusing on schemes based on surface codes, we introduce explicit, but platform-independent representations of topological logic gates -- called logical blocks -- and generate new, overhead-efficient methods for universal quantum computation. As a specific example, we propose fault-tolerant schemes based on surface codes concatenated with more general low-density parity check (LDPC) codes. The logical blocks framework enables a convenient mapping from an abstract description of the logical gate to a precise set of physical instructions for both circuit-based and fusion-based quantum computation (FBQC). Using this, we numerically simulate a surface-code-based universal gate set implemented with FBQC, and verify that their thresholds are consistent with the bulk memory threshold. We find that boundaries, defects, and twists can significantly impact the logical error rate scaling, with periodic boundary conditions potentially halving the resource requirements. Motivated by the favorable logical error rates for boundaryless computation, we introduce a novel computational scheme based on the teleportation of twists that may offer further resource reductions.
arXiv comment39 pages, 32 figures, comments welcome, v2: published version
References in corpus (79)
- Fault-tolerant quantum computation by anyons
- Anyons in an exactly solved model and beyond
- Surface codes: Towards practical large-scale quantum computation
- Good Quantum Error-Correcting Codes Exist
- Topological quantum memory
- Generalized Global Symmetries
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Improved Simulation of Stabilizer Circuits
- Quantum Error Correction for Quantum Memories
- Multiple Particle Interference and Quantum Error Correction
- Multi-party entanglement in graph states
- Fault-tolerant quantum computation with high threshold in two dimensions
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Resource-efficient linear optical quantum computation
- Topological Quantum Distillation
- Topological fault-tolerance in cluster state quantum computation
- Surface code quantum computing by lattice surgery
- Braiding statistics approach to symmetry-protected topological phases
- Symmetry Fractionalization, Defects, and Gauging of Topological Phases
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Models for gapped boundaries and domain walls
- Quantum orders in an exact soluble model
- A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
- Topological Order with a Twist: Ising Anyons from an Abelian Model
- Magic state distillation with low overhead
- Stabilizer Formalism for Operator Quantum Error Correction
- Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
- Quantum Low-Density Parity-Check Codes
- A symmetry principle for Topological Quantum Order
- Low-distance Surface Codes under Realistic Quantum Noise
- Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
- Genons, twist defects, and projective non-Abelian braiding statistics
- Fast Decoders for Topological Quantum Codes
- Universal fault-tolerant quantum computation with only transversal gates and error correction
- Protected edge modes without symmetry
- From three-photon GHZ states to ballistic universal quantum computation
- Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
- Magic State Distillation: Not as Costly as You Think
- Tradeoffs for reliable quantum information storage in 2D systems
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Dynamically Generated Logical Qubits
- Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
- Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
- Thresholds for topological codes in the presence of loss
- Strong Resilience of Topological Codes to Depolarization
- Unfolding the color code
- Classification of Topological Defects in Abelian Topological States
- Balanced Product Quantum Codes
- Poking holes and cutting corners to achieve Clifford gates with the surface code
- Foliated Quantum Codes
- Quantum Measurements and Gates by Code Deformation
- Universal topological phase of 2D stabilizer codes
- The surface code with a twist
- A magic state's fidelity can be superior to the operations that created it
- Tensor-Network Simulations of the Surface Code under Realistic Noise
- Topological color code and symmetry-protected topological phases
- The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
- The ZX calculus is a language for surface code lattice surgery
- Symmetry protected topological order at nonzero temperature
- Boundary-Induced Phase Transitions in Equilibrium and Non-Equilibrium Systems
- Gapped boundaries, group cohomology and fault-tolerant logical gates
- Protected gates for topological quantum field theories
- Simulation of rare events in quantum error correction
- Transversal Clifford gates on folded surface codes
- Universal fault-tolerant measurement-based quantum computation
- Fault-Tolerant Quantum Gates with Defects in Topological Stabiliser Codes
- Topological Quantum Error Correction with Optimal Encoding Rate
- Symmetry-protected self-correcting quantum memories
- Fault-tolerant gates on hypergraph product codes
- Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
- Logical Error Rate Scaling of the Toric Code
- Quons: A 3D Language for Quantum Information
- Topological wormholes
- Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
- Generating Fault-Tolerant Cluster States from Crystal Structures
- Effective Compression of Quantum Braided Circuits Aided by ZX-Calculus
- The role of entropy in topological quantum error correction
- Accurate simulations of planar topological codes cannot use cyclic boundaries
- A Hierarchy of Anyon Models Realised by Twists in Stacked Surface Codes
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- Unifying flavors of fault tolerance with the ZX calculus
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- Machine-learning-inspired quantum control in many-body dynamics
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- Comparing Schemes for Creating Qudit Graph States from 16- & 128-dimensional Hilbert Space using Donors in Silicon
- On the learning abilities of photonic continuous-variable Born machines
- Tessellation codes: encoded quantum gates by geometric rotation
- Effective Distance of Higher Dimensional HGPs and Weight-Reduced Quantum LDPC Codes
- Optimal number of stabilizer measurement rounds in an idling surface code patch
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