A dynamic circuit for the honeycomb Floquet code

Abstract

In the typical implementation of a quantum error-correcting code, each stabilizer is measured by entangling one or more ancilla qubits with the data qubits and measuring the ancilla qubits to deduce the value of the stabilizer. Recently, the dynamic circuit approach has been introduced, in which stabilizers are measured without ancilla qubits. Here, we demonstrate that dynamic circuits are particularly useful for the Floquet code. Our dynamic circuit increases the timelike distance of the code, automatically removes leakage, and both significantly increases the threshold and lowers the logical error rate compared to the standard ancilla-based circuit. At a physical error rate of $10^{-3}$, we estimate a nearly $3\times$ reduction in the number of qubits required to reach a $10^{-12}$ logical error rate.

4 page main text, 1 page Appendix

References in corpus (29)

• Surface codes: Towards practical large-scale quantum computation
• Topological quantum memory
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological fault-tolerance in cluster state quantum computation
• Surface code quantum computing by lattice surgery
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• High threshold universal quantum computation on the surface code
• Stim: a fast stabilizer circuit simulator
• Stabilizer Formalism for Operator Quantum Error Correction
• Low-distance Surface Codes under Realistic Quantum Noise
• Dynamically Generated Logical Qubits
• Flag fault-tolerant error correction with arbitrary distance codes
• Sparse Blossom: correcting a million errors per core second with minimum-weight matching
• A Fault-Tolerant Honeycomb Memory
• Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes
• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Floquet codes without parent subsystem codes
• Boundaries for the Honeycomb Code
• Performance of planar Floquet codes with Majorana-based qubits
• Benchmarking the Planar Honeycomb Code
• Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
• Engineering 3D Floquet codes by rewinding
• Floquetifying the Colour Code
• Comparative study of quantum error correction strategies for the heavy-hexagonal lattice
• Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits
• Fault-tolerant hyperbolic Floquet quantum error correcting codes
• 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
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code