Implementing fault-tolerant non-Clifford gates using the [[8,3,2]] color code

TL;DR

This paper demonstrates that the [[8,3,2]] color code can improve the fault-tolerance of non-Clifford gates, like the control-control Z gate, on near-term quantum hardware such as trapped-ion and superconducting systems.

Contribution

It provides experimental evidence that codes with transversal gates enhance the fault-tolerance of non-Clifford gates in practical quantum computing hardware.

Findings

Improved performance of encoded non-Clifford gates on hardware

Successful implementation of control-control Z gate with error mitigation

Potential for near-term quantum algorithms using transversal codes

Abstract

Quantum computers promise to solve problems that are intractable for classical computers, but qubits are vulnerable to many sources of error, limiting the depth of the circuits that can be reliably executed on today's quantum hardware. Quantum error correction has been proposed as a solution to this problem, whereby quantum information is protected by encoding it into a quantum error-correcting code. But protecting quantum information is not enough, we must also process the information using logic gates that are robust to faults that occur during their execution. One method for processing information fault-tolerantly is to use quantum error-correcting codes that have logical gates with a tensor product structure (transversal gates), making them naturally fault-tolerant. Here, we test the performance of a code with such transversal gates, the [[8,3,2]] color code, using trapped-ion and superconducting hardware. We observe improved performance (compared to no encoding) for encoded circuits implementing non-Clifford gates, a class of gates that are essential for achieving universal quantum computing. In particular, we find improved performance for an encoded circuit implementing the control-control $Z$ gate, a key gate in Shor's algorithm. Our results illustrate the potential of using codes with transversal gates to implement non-trivial algorithms on near-term quantum hardware.