Demonstration of fault-tolerant universal quantum gate operations

TL;DR

This paper demonstrates a fault-tolerant universal set of quantum gates on logical qubits in a trapped-ion system, showcasing error correction techniques that are crucial for scalable quantum computing.

Contribution

It introduces the use of flag fault tolerance for implementing universal quantum gates on logical qubits in a trapped-ion quantum computer.

Findings

Successful implementation of a fault-tolerant logical CNOT gate

Fault-tolerant preparation of a logical magic state

Enhanced performance over non-fault-tolerant methods

Abstract

Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a fault-tolerant circuit design which, in general, increases the complexity of the implementation. Here, we demonstrate a fault-tolerant universal set of gates on two logical qubits in a trapped-ion quantum computer. In particular, we make use of the recently introduced paradigm of flag fault tolerance, where the absence or presence of dangerous errors is heralded by usage of few ancillary 'flag' qubits. We perform a logical two-qubit CNOT-gate between two instances of the seven qubit color code, and we also fault-tolerantly prepare a logical magic state. We then realize a fault-tolerant logical T-gate by injecting the magic state via teleportation from one logical qubit onto the other. We observe the hallmark feature of fault tolerance, a superior performance compared to a non-fault-tolerant implementation. In combination with recently demonstrated repeated quantum error correction cycles these results open the door to error-corrected universal quantum computation.