March 21, 2024 | Ivan Pogorelov, Friederike Butt, Lukas Postler, Christian D. Marciniak, Philipp Schindler, Markus Müller, Thomas Monz
This paper presents the first experimental implementation of fault-tolerant code switching between two error-correcting codes: the seven-qubit color code and the 10-qubit code. The seven-qubit color code supports fault-tolerant CNOT and Hadamard gates, while the 10-qubit code enables fault-tolerant T-gate implementation. By switching between these codes, a complementary universal gate set is formed, allowing for the preparation of 12 different logical states that cannot be achieved using a single code. The authors demonstrate the switching procedure, which involves measuring stabilizers and applying local Pauli operations to preserve encoded information. They also show how to entangle two logical qubits using the full universal gate set in a single logical quantum circuit. The results open a new route for deterministic control over logical qubits with low auxiliary qubit overhead, independent of probabilistic resource state preparation. The experimental setup uses a 16-ion chain of $^{40}$Ca$^+$ ions trapped in a linear Paul trap, with optical qubits encoded in Zeeman sub-levels. The paper includes detailed characterizations of the essential building blocks for implementing the universal gate set, including initialization, logical gates, and switching operations. The authors discuss the advantages and limitations of fault-tolerant code switching, noting that it can significantly improve fidelities in certain situations compared to non-fault-tolerant methods, but current bottlenecks in circuit depth and mid-circuit measurements limit its effectiveness. Future work will focus on extending the approach to larger-distance codes and more complex circuits.This paper presents the first experimental implementation of fault-tolerant code switching between two error-correcting codes: the seven-qubit color code and the 10-qubit code. The seven-qubit color code supports fault-tolerant CNOT and Hadamard gates, while the 10-qubit code enables fault-tolerant T-gate implementation. By switching between these codes, a complementary universal gate set is formed, allowing for the preparation of 12 different logical states that cannot be achieved using a single code. The authors demonstrate the switching procedure, which involves measuring stabilizers and applying local Pauli operations to preserve encoded information. They also show how to entangle two logical qubits using the full universal gate set in a single logical quantum circuit. The results open a new route for deterministic control over logical qubits with low auxiliary qubit overhead, independent of probabilistic resource state preparation. The experimental setup uses a 16-ion chain of $^{40}$Ca$^+$ ions trapped in a linear Paul trap, with optical qubits encoded in Zeeman sub-levels. The paper includes detailed characterizations of the essential building blocks for implementing the universal gate set, including initialization, logical gates, and switching operations. The authors discuss the advantages and limitations of fault-tolerant code switching, noting that it can significantly improve fidelities in certain situations compared to non-fault-tolerant methods, but current bottlenecks in circuit depth and mid-circuit measurements limit its effectiveness. Future work will focus on extending the approach to larger-distance codes and more complex circuits.