A proposal for a minimal surface code experiment

TL;DR

This paper proposes the smallest possible surface code experiment for quantum error correction, requiring 17 qubits and high gate fidelities, to demonstrate proof-of-principle fault-tolerance in quantum computing.

Contribution

It introduces a minimal surface code experiment design that can detect and correct errors with fewer qubits and shallower circuits than previous approaches.

Findings

Requires >99% fidelity for preparation, gates, and measurement

Uses 17 qubits and 16 entangling gates in the minimal setup

Provides noise thresholds for successful error correction

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 $99\%$.