April 25, 2024 | Bence Hetényi* and James R. Wootton
This paper presents a method to implement two topological error-correcting codes, the 3CX surface code and the Bacon-Shor code, on a 133-qubit IBM Quantum device using the heavy-hex lattice architecture. The authors demonstrate that the unused qubits in the 3CX code can be utilized to execute the Bacon-Shor code, allowing for the simultaneous application of fault-tolerant entangling gates and measurements. By using transversal CX gates and lattice surgery, they achieve entanglement between logical qubits with code distances up to \(d = 4\) and five rounds of stabilizer measurement cycles. The non-planar coupling between the qubits enables simultaneous measurement of the logical \(XX\), \(YY\), and \(ZZ\) observables, allowing for the verification of Bell's inequality. The results show a fidelity of 94% for the \(d = 2\) case with post-selection and a violation of Bell's inequality for both the \(d = 2\) and \(d = 3\) cases. This work highlights the potential of using the unused qubits in one code to enhance the performance of another, demonstrating the feasibility of fault-tolerant quantum computing on the heavy-hex lattice.This paper presents a method to implement two topological error-correcting codes, the 3CX surface code and the Bacon-Shor code, on a 133-qubit IBM Quantum device using the heavy-hex lattice architecture. The authors demonstrate that the unused qubits in the 3CX code can be utilized to execute the Bacon-Shor code, allowing for the simultaneous application of fault-tolerant entangling gates and measurements. By using transversal CX gates and lattice surgery, they achieve entanglement between logical qubits with code distances up to \(d = 4\) and five rounds of stabilizer measurement cycles. The non-planar coupling between the qubits enables simultaneous measurement of the logical \(XX\), \(YY\), and \(ZZ\) observables, allowing for the verification of Bell's inequality. The results show a fidelity of 94% for the \(d = 2\) case with post-selection and a violation of Bell's inequality for both the \(d = 2\) and \(d = 3\) cases. This work highlights the potential of using the unused qubits in one code to enhance the performance of another, demonstrating the feasibility of fault-tolerant quantum computing on the heavy-hex lattice.