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

2025/03/19 by Margarita Davydova, Andreas Bauer, Davydova, Margarita +9 · 2 voices · 13 citations
Computer Science · Physics and Astronomy · #quant-ph #cond-mat.str-el

paper · pdf · doi:10.1103/vrty-qs5h

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.

Citations

• Topological quantum memory
• Fault-tolerant quantum computation by anyons
• Non-Abelian anyons and topological quantum computation
• Planar Fault-Tolerant Circuits for Non-Clifford Gates on the 2D Color Code

Cited by

• Characterising the failure mechanisms of error-corrected quantum logic gates
• Quantum computing with anyons is fault tolerant
• Fast magic state preparation by gauging higher-form transversal gates in parallel
• Parsimonious Quantum Low-Density Parity-Check Code Surgery
• Constant depth magic state cultivation with Clifford measurements by gauging
• Universal Gates from Braiding and Fusing Anyons on Quantum Hardware
• Spacetime Spins: Statistical mechanics for error correction with stabilizer circuits
• Constant-Depth Clifford-Hierarchy Gates via Non-Abelian Surface Codes
• Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic
• Finding diagonal logical gates in CSS codes and circuits
• Dynamical quantum codes and logic gates on a lattice with sparse connectivity
• Hyperbolic Floquet code with graph-edge syndromes
• Graphical Calculus for Fermionic Tensors
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order

Discussions

• Logic gates can often be understood in terms of topological phases, so I often felt it was a shortcoming of my work on a 2D CCZ gate that I did not see the analogous physical picture. So I am pleased [bsky, 24 points, 2 comments]
• Are you a fan of fault-tolerant non-Clifford gates on the 2D surface code? Have you been wondering what was really going on in the protocols by Bombín and Brown? We have a new work for you: arxiv. [bsky, 23 points, 1 comments]

Related

• Doubled Color Codes
• How to fault-tolerantly realize any quantum circuit with local operations
• 2D quantum computation with 3D topological codes
• Fault-tolerant Quantum Computation without Distillation on a 2D Device
• A Topologically Fault-Tolerant Quantum Computer with Four Dimensional Geometric Codes