Experimental implementation of encoded logical qubit operations in a perfect quantum error correcting code

TL;DR

This paper demonstrates the experimental implementation of logical qubit operations, including NOT and Hadamard gates, within a five-qubit quantum error correcting code, crucial for reliable large-scale quantum computing.

Contribution

It presents the first experimental realization of nontrivial logical gates in a five-qubit quantum error correcting code with process tomography and error correction validation.

Findings

Successful implementation of logical NOT and Hadamard gates

Demonstration of correction for all single qubit errors

Measured fidelities of logical gate operations

Abstract

Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single qubit errors. We perform quantum process tomography of the encoded gate operations, demonstrate the successful correction of all possible single qubit errors and measure the fidelity of the encoded logical gate operations.