Planar fault-tolerant circuits for non-Clifford gates on the 2D color code

Abstract

We introduce a family of scalable planar fault-tolerant circuits that implement logical non-Clifford operations on a 2D color code, such as a logical $T$ gate or a logical non-Pauli measurement that prepares a magic $|T⟩$ state. The circuits are relatively simple, consisting only of physical $T$ gates, $CX$ gates, and few-qubit measurements. They can be implemented with an array of qubits on a 2D chip with nearest-neighbor couplings, and no wire crossings. The construction is based on a spacetime path integral representation of a non-Abelian 2+1D topological phase, which is related to the 3D color code. We turn the path integral into a circuit by expressing it as a spacetime $ZX$ tensor network, and then traversing it in some chosen time direction. We describe in detail how fault tolerance is achieved using a "just-in-time" decoding strategy, for which we repurpose and extend state-of-the-art color-code matching decoders.

References in corpus (23)

• Logical quantum processor based on reconfigurable atom arrays
• Topological Quantum Distillation
• Quantum error correction below the surface code threshold
• Topological fault-tolerance in cluster state quantum computation
• Magic state distillation with low overhead
• Topological Computation without Braiding
• Dynamically Generated Logical Qubits
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Sparse Blossom: correcting a million errors per core second with minimum-weight matching
• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Performance of planar Floquet codes with Majorana-based qubits
• Scaling and logic in the color code on a superconducting quantum processor
• Unifying flavors of fault tolerance with the ZX calculus
• Twisted Quantum Double Model of Topological Orders with Boundaries
• Floquetifying the Colour Code
• A Pair Measurement Surface Code on Pentagons
• Topological error correcting processes from fixed-point path integrals
• XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime
• Low-overhead quantum computing with the color code
• Bulk-to-boundary anyon fusion from microscopic models
• Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases
• Magic Boundaries of 3D Color Codes