A proposal for a minimal surface code experiment

Abstract

Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be the first major step towards fault-tolerant quantum computation. Here we propose a surface code based experiment that is the smallest, both in terms of code size and circuit depth, that would allow errors to be detected and corrected for both the $X$ and $Z$ basis of a qubit. This requires $17$ physical qubits initially prepared in a product state, on which $16$ two-qubit entangling gates are applied before a final measurement of all qubits. A platform agnostic error model is applied to give some idea of the noise levels required for success. It is found that a true demonstration of quantum error correction will require fidelities for the preparation and measurement of qubits and the entangling gates to be above $99\%$.

Additional author and numerics for v3

References in corpus (7)

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Cited by in corpus (8)

• Digitization of Scalar Fields for Quantum Computing
• Machine-learning-assisted correction of correlated qubit errors in a topological code
• A repetition code of 15 qubits
• A logical qubit in a linear array of semiconductor quantum dots
• Benchmarking near-term devices with quantum error correction
• Quantum error correction in crossbar architectures
• Measurement-free implementations of small-scale surface codes for quantum dot qubits
• An integrity measure to benchmark quantum error correcting memories