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

Abstract

Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also further restrict the connectivity, resulting in a relatively sparse graph such as the heavy-hex architecture of current IBM Quantum devices. In such cases it is hard to use all qubits to their full potential. Instead, in order to emulate the denser connectivity required to implement well-known quantum error correcting codes, many qubits remain effectively unused. In this work we show how this bug can be turned into a feature. By using the unused qubits of one code to execute another, two codes can be implemented on top of each other, allowing easy application of fault-tolerant entangling gates and measurements. We demonstrate this by realizing a surface code and a Bacon-Shor code on a 133 qubit IBM Quantum device. Using transversal CX gates and lattice surgery we demonstrate entanglement between these logical qubits with code distance up to $d=4$ and five rounds of stabilizer measurement cycles. The nonplanar coupling between the qubits allows us to simultaneously measure the logical $XX$, $YY$, and $ZZ$ observables. With this we verify the violation of Bell's inequality for both the $d=2$ case with post selection featuring a fidelity of $94\%$, and the $d=3$ instance using only quantum error correction.

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• Error correction of transversal CNOT gates for scalable surface code computation
• Realizing Lattice Surgery on Two Distance-Three Repetition Codes with Superconducting Qubits
• Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning
• Effectiveness of the syndrome extraction circuit with flag qubits on IBM quantum hardware
• Characterization of errors in a CNOT between surface code patches
• A Simple and Efficient Joint Measurement Strategy for Estimating Fermionic Observables and Hamiltonians
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code
• Lattice surgery-based logical state teleportation via noisy links
• Fundamental thresholds for computational and erasure errors via the coherent information
• Feasibility of Logical Bell State Generation in Memory Assisted Quantum Networks
• Magic State Injection on IBM Quantum Processors Above the Distillation Threshold
• Transversal CNOT gate with multi-cycle error correction
• Demonstration of High-Fidelity Entangled Logical Qubits using Transmons
• Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
• Coarse-grained dynamics in quantum many-body systems using the maximum entropy principle
• Optimal number of stabilizer measurement rounds in an idling surface code patch