Universal fault tolerant quantum computation in 2D without getting tied in knots

Abstract

We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a path integral framework which provides both a macroscopic picture for different logical gates as well as a way to derive the associated microscopic circuits. We also show an equivalence between our approach and prior proposals where a 2D array of qubits reproduces the action of a transversal gate in a 3D stabilizer code over time, thus, establishing a new connection between 3D codes and 2D non-Abelian topological phases. We prove a threshold theorem for our protocols under local stochastic circuit noise using a just-in-time decoder to correct the non-Abelian code.

62 pages, 35 figures; v2: minor edits

References in corpus (86)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Surface codes: Towards practical large-scale quantum computation
• Topological quantum memory
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• String-net condensation: A physical mechanism for topological phases
• Quantum Error Correction for Quantum Memories
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• Roads towards fault-tolerant universal quantum computation
• Surface code quantum computing by lattice surgery
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Models for gapped boundaries and domain walls
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Condensate induced transitions between topologically ordered phases
• Quantum Low-Density Parity-Check Codes
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• Topological Computation without Braiding
• Long-range quantum entanglement in noisy cluster states
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Fractal symmetries: Ungauging the cubic code
• Dynamically Generated Logical Qubits
• Single-shot fault-tolerant quantum error correction
• Topological phases with generalized global symmetries
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• Classification of topologically protected gates for local stabilizer codes
• Unfolding the color code
• Symmetry fractionalization and twist defects
• Universal transversal gates with color codes - a simplified approach
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Quantum computation with Turaev-Viro codes
• Reliable Cellular Automata with Self-Organization
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Encoding a magic state with beyond break-even fidelity
• Quantum Measurements and Gates by Code Deformation
• Fault-tolerant logical gates in quantum error-correcting codes
• Low-overhead fault-tolerant quantum computing using long-range connectivity
• Long-range entanglement from measuring symmetry-protected topological phases
• Universal Quantum Computation with Metaplectic Anyons
• Universal topological phase of 2D stabilizer codes
• Topological color code and symmetry-protected topological phases
• Fault-tolerant magic state preparation with flag qubits
• Topological Defect Networks for Fractons of all Types
• Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
• A fault-tolerant non-Clifford gate for the surface code in two dimensions
• Toward fault-tolerant quantum computation without concatenation
• Dynamically enriched topological orders in driven two-dimensional systems
• Gapped boundaries, group cohomology and fault-tolerant logical gates
• Anyon condensation and the color code
• Pauli stabilizer models of twisted quantum doubles
• Code Deformation and Lattice Surgery Are Gauge Fixing
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Universal Quantum Computation with Gapped Boundaries
• Decoding non-Abelian topological quantum memories
• Gauging permutation symmetries as a route to non-Abelian fractons
• Higher cup products on hypercubic lattices: application to lattice models of topological phases
• Quantum Circuits for Measuring Levin-Wen Operators
• Field Theories for Gauged Symmetry Protected Topological Phases: Abelian Gauge Theories with non-Abelian Quasiparticles
• Twisted Quantum Double Model of Topological Orders with Boundaries
• Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices
• Fault-Tolerant Quantum Error Correction for non-Abelian Anyons
• A Non-Commuting Stabilizer Formalism
• Type-II fractons from coupled spin chains and layers
• Quantum computation from dynamic automorphism codes
• Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
• Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code
• Computing data for Levin-Wen with defects
• Fusing Binary Interface Defects in Topological Phases: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ case
• Topological error correcting processes from fixed-point path integrals
• Universal quantum computation in the surface code using non-Abelian islands
• Transversal Diagonal Logical Operators for Stabiliser Codes
• Non-Pauli topological stabilizer codes from twisted quantum doubles
• Continuous error correction for Ising anyons
• Fault-tolerant logical measurements via homological measurement
• Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials
• Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
• Bulk-to-boundary anyon fusion from microscopic models
• Towards topological fixed-point models beyond gappable boundaries
• Computing Defects Associated to Bounded Domain Wall Structures: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ Case
• Protocols for Creating Anyons and Defects via Gauging
• Low-overhead fault-tolerant quantum computation by gauging logical operators
• Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases
• Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries