Fault-Tolerant Code Switching Protocols for Near-Term Quantum Processors

TL;DR

This paper develops resource-efficient fault-tolerant code switching protocols between 2D and 3D topological color codes, enabling universal quantum gates and improved magic state preparation on near-term quantum processors.

Contribution

It introduces deterministic and non-deterministic code switching protocols using flag-qubits, enhancing fault-tolerance and practicality for near-term quantum computing.

Findings

Achieves a 3% logical failure rate for deterministic gates.

Reduces failure rates by two orders of magnitude using morphed codes.

Demonstrates code switching enables universal fault-tolerant quantum computation.

Abstract

Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the T-gate missing in the two-dimensional and the H-gate in the three-dimensional case. These complementary shortcomings of the isolated topologies may be overcome in a combined approach, by switching between a two- and a three-dimensional code while maintaining the logical state. In this work, we construct resource-optimized deterministic and non-deterministic code switching protocols for two- and three-dimensional distance-three color codes using fault-tolerant quantum circuits based on flag-qubits. Deterministic protocols allow for the fault-tolerant implementation of logical gates on an encoded quantum state, while non-deterministic protocols may be used for the fault-tolerant preparation of magic states. Taking the error rates of state-of-the-art trapped-ion quantum processors as a reference, we find a logical failure probability of $3\%$ for deterministic logical gates, which cannot be realized transversally in the respective code. By replacing the three-dimensional distance-three color code in the protocol for magic state preparation with the morphed code introduced in [1], we reduce the logical failure rates by two orders of magnitude, thus rendering it a viable method for magic state preparation on near-term quantum processors. Our results demonstrate that code switching enables the fault-tolerant and deterministic implementation of a universal gate set under realistic conditions, and thereby provide a practical avenue to advance universal, fault-tolerant quantum computing and enable quantum algorithms on first, error-corrected logical qubits.