Demonstration of fault-tolerant universal quantum gate operations (2111.12654v3)

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.

Fault-Tolerant Quantum Gate Operations

The paper "Demonstration of fault-tolerant universal quantum gate operations" addresses the implementation of fault-tolerant quantum computation on a trapped-ion system. Specifically, it details the experimental realization of a fault-tolerant universal gate set on two logical qubits encoded in a 7-qubit color code. The work leverages the advancements in fault-tolerant quantum computing—a critical requirement to mitigate errors in quantum operations that arise due to inherent noise in quantum systems.

Main Contributions and Techniques Employed

The authors demonstrate several key components for fault-tolerant quantum computation using a combination of techniques:

1. Fault-Tolerant Initialization: The work introduces a verification step during the initialization phase to ensure that logical states, such as the logical zero state ($\ket{0}_L$), are prepared fault-tolerantly. This is achieved using an additional ancillary 'flag' qubit that indicates the presence of dangerous errors, thus safeguarding the initialized state.
2. Transversal Clifford Group: The implementation of the Clifford group, including transversal logical operations such as the \mbox{CNOT-gate}, is performed. This is possible because the color code allows for transversal implementation of these operations, inherently supporting fault tolerance. The logical \mbox{CNOT-gate} between two logical qubits is implemented with a significant suppression of logical errors compared to non-fault-tolerant circuits.
3. Magic State Preparation: The work extends to the preparation of a logical magic state, which is crucial for implementing the non-Clifford \mbox{T-gate}. This preparation utilizes a novel fault-tolerant protocol involving flag qubits, further supporting the error-tolerant goals of the paper.
4. Universal Set of Gates: The research advances by demonstrating the realization of a fault-tolerant universal gate set, comprising the Clifford group and the \mbox{T-gate}. The \mbox{T-gate} is implemented through magic state injection, ensuring that any quantum operation can be synthesized fault-tolerantly utilizing this complete gate set.

Results and Implications

• Performance Metrics: The experimental results exhibit haLLMark features of fault-tolerance where logical infidelities are sharply reduced when flag qubits are deployed. There is a marked improvement in the fidelity of logical states post-error correction and fault-tolerant circuit design.
• Scalability and Resource Concerns: While the paper demonstrates significant steps towards error-corrected quantum computation, it underscores the overhead associated with fault-tolerant procedures. Each additional layer of fault-tolerance incurs resource costs in terms of ancillary qubits and complexity in gate operations. This highlights the ongoing challenges in balancing fault tolerance with quantum hardware constraints.

Future Directions

The results pave the way for further integration of fault-tolerant measures with complex quantum circuits. Future studies could explore extending these techniques to quantum systems with greater numbers of qubits and to more intricate QEC codes beyond the color code framework. This is especially pertinent for the development of large-scale quantum computing devices that require robust error management.

Overall, the paper contributes significantly to the body of work in fault-tolerant quantum computing, showcasing experimentally viable solutions to long-standing challenges related to error correction and management in quantum information processing. The insights into flag-based error detection and transversal gate operations are valuable for ongoing research in scalable quantum architectures.