Single-Step Parity Check Gate Set for Quantum Error Correction

Abstract

A key requirement for an effective Quantum Error Correction (QEC) scheme is that the physical qubits have error rates below a certain threshold. The value of this threshold depends on the details of the specific QEC scheme, and its hardware-level implementation. This is especially important with parity-check circuits, which are the fundamental building blocks of QEC codes. The standard way of constructing the parity check circuit is using a universal set of gates, namely sequential CNOT gates, single-qubit rotations and measurements. We exploit the insight that a QEC code does not require universal logic gates, but can be simplified to perform the sole task of error detection and correction. By building gates that are fundamental to QEC, we can boost the threshold and ease the experimental demands on the physical hardware. We present a rigorous formalism for constructing and verifying the error behavior of these gates, linking the physical measurement of a process matrix to the abstract error models commonly used in QEC analysis. This allows experimentalists to directly map the gates used in their systems to thresholds derived for a broad-class of QEC codes. We give an example of these new constructions using the model system of two nuclear spins, coupled to an electron spin, showing the potential benefits of redesigning fundamental gate sets using QEC primitives, rather than traditional gate sets reliant on simple single and two-qubit gates.

Updated the arXiv version. Minor edits to Appendices 2, 3, 4 and 7

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• Scalable entanglement of nuclear spins mediated by electron exchange
• Single-step high-fidelity three-qubit gates by anisotropic chiral interactions
• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates
• Superconducting qubits in the millions: the potential and limitations of modularity
• Multiqubit Rydberg Gates for Quantum Error Correction
• Maximizing the nondemolition nature of a quantum measurement via an adaptive readout protocol