Low-overhead magic state distillation with color codes

Abstract

Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but requires significant resources. Hence, it is crucial to tailor and optimize magic state distillation for specific codes from both logical- and physical-level perspectives. In this work, we perform such optimization for two-dimensional color codes, which are promising due to their higher encoding rates compared to surface codes, transversal implementation of Clifford gates, and efficient lattice surgery. We propose two carefully designed distillation schemes based on the 15-to-1 distillation circuit and lattice surgery, differing in their methods for handling faulty rotations. Our first scheme employs faulty T-measurement, achieving infidelities of $O(p^3)$ for physical noise strength $p$. To achieve lower infidelities, our second scheme integrates distillation with 'cultivation' (a distillation-free approach to fault-tolerantly prepare magic states through transversal Clifford measurements). Our second scheme achieves significantly lower infidelities (e.g., $\sim 2\times 10^{-16}$ at $p=10^{-3}$), surpassing the capabilities of both cultivation and single-level distillation. Notably, to reach a given target infidelity, our schemes require approximately two orders of magnitude fewer resources than the previous best magic state distillation schemes for color codes.

50 pages, 26 figures, 4 tables; v5 (final) - Updated Fig. 12 with additional data points for cultivation and added Appendix K on integrated cultivation + growing simulations; v3,v4 - Reconstructed combined MSD scheme by integrating cultivation and analysis on the required improvements for color code decoders; v2 - Updated combined MSD scheme thanks to Sam Roberts's suggestion

References in corpus (40)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Surface codes: Towards practical large-scale quantum computation
• Topological quantum memory
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Quantum Computing with Very Noisy Devices
• Logical quantum processor based on reconfigurable atom arrays
• Topological Quantum Distillation
• High threshold universal quantum computation on the surface code
• Models for gapped boundaries and domain walls
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Stim: a fast stabilizer circuit simulator
• Magic state distillation with low overhead
• Demonstration of fault-tolerant universal quantum gate operations
• Magic State Distillation: Not as Costly as You Think
• Quantum computation with realistic magic state factories
• Improved magic states distillation for quantum universality
• Universal transversal gates with color codes - a simplified approach
• Fault-tolerant thresholds for quantum error correction with the surface code
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Decoding color codes by projection onto surface codes
• Triangular color codes on trivalent graphs with flag qubits
• Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes
• The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
• Fault-tolerant magic state preparation with flag qubits
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes
• Advantages of versatile neural-network decoding for topological codes
• Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
• Anyon condensation and the color code
• Demonstration of fault-tolerant Steane quantum error correction
• 2-D color code quantum computation
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Efficient Decoding of Topological Color Codes
• Efficient color code decoders in $d\ge 2$ dimensions from toric code decoders
• Efficient Magic State Distillation by Zero-Level Distillation
• Fault-tolerant Post-Selection for Low Overhead Magic State Preparation
• Color code decoder with improved scaling for correcting circuit-level noise
• Decoding quantum color codes with MaxSAT
• Mitigating errors in logical qubits
• Ising model formulation for highly accurate topological color codes decoding
• Low-overhead quantum computing with the color code

Cited by in corpus (2)

• Unfolded distillation: very low-cost magic state preparation for biased-noise qubits
• Color code with a logical control-$S$ gate using transversal $T$ rotations