Fault-Tolerant Code-Switching Protocols for Near-Term Quantum Processors
2024-05-29 08:48
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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 nondeterministic 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 nondeterministic 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 Vasmer and Kubica [PRX Quantum 3, 030319
(2022)], we reduce the logical failure rates by 2 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.
Article: https://doi.org/10.1103/PRXQuantum.5.020345
