Creating entangled logical qubits in the heavy-hex lattice with topological codes

Creating entangled logical qubits in the heavy-hex lattice with topological codes

April 25, 2024 | Bence Hetényi and James R. Wootton
This paper presents a method to create entangled logical qubits in a heavy-hex lattice using topological codes. The authors demonstrate how to implement both the 3CX surface code and the Bacon-Shor code on a 133-qubit IBM Quantum device. By utilizing the unused qubits of one code to execute another, they enable the implementation of multiple codes on the same physical qubits, allowing for the application of fault-tolerant entangling gates and measurements. The authors show that this approach allows for entanglement between logical qubits with code distances up to d=4 and five rounds of stabilizer measurement cycles. They also demonstrate the violation of Bell's inequality for both d=2 and d=3 cases, with fidelities of 94% and 93.7%, respectively. The nonplanar coupling between the qubits allows for simultaneous measurement of the logical XX, YY, and ZZ observables. The paper also discusses the compatibility of the 3CX and Bacon-Shor codes, showing that their logical subspaces are compatible and that transversal CX gates can be used to entangle the two logical qubits. The authors also describe the use of lattice surgery to measure the logical observables and the importance of post-selection in improving the logical fidelity. The results show that the 3CX code has a threshold error rate of approximately 0.3% and the Bacon-Shor code has a pseudo-threshold of approximately 0.1%. The paper concludes that the implementation of multiple codes on the same physical qubits is a promising approach for quantum error correction in superconducting qubit platforms.This paper presents a method to create entangled logical qubits in a heavy-hex lattice using topological codes. The authors demonstrate how to implement both the 3CX surface code and the Bacon-Shor code on a 133-qubit IBM Quantum device. By utilizing the unused qubits of one code to execute another, they enable the implementation of multiple codes on the same physical qubits, allowing for the application of fault-tolerant entangling gates and measurements. The authors show that this approach allows for entanglement between logical qubits with code distances up to d=4 and five rounds of stabilizer measurement cycles. They also demonstrate the violation of Bell's inequality for both d=2 and d=3 cases, with fidelities of 94% and 93.7%, respectively. The nonplanar coupling between the qubits allows for simultaneous measurement of the logical XX, YY, and ZZ observables. The paper also discusses the compatibility of the 3CX and Bacon-Shor codes, showing that their logical subspaces are compatible and that transversal CX gates can be used to entangle the two logical qubits. The authors also describe the use of lattice surgery to measure the logical observables and the importance of post-selection in improving the logical fidelity. The results show that the 3CX code has a threshold error rate of approximately 0.3% and the Bacon-Shor code has a pseudo-threshold of approximately 0.1%. The paper concludes that the implementation of multiple codes on the same physical qubits is a promising approach for quantum error correction in superconducting qubit platforms.
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