Experimental Quantum Computations on a Topologically Encoded Qubit (1403.5426v1)

Abstract: The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant quantum computing (FTQC). Here we present a step towards this by implementing a quantum error correcting code, encoding one qubit in entangled states distributed over 7 trapped-ion qubits. We demonstrate the capability of the code to detect one bit flip, phase flip or a combined error of both, regardless on which of the qubits they occur. Furthermore, we apply combinations of the entire set of logical single-qubit Clifford gates on the encoded qubit to explore its computational capabilities. The implemented 7-qubit code is the first realization of a complete Calderbank-Shor-Steane (CSS) code and constitutes a central building block for FTQC schemes based on concatenated elementary quantum codes. It also represents the smallest fully functional instance of the color code, opening a route towards topological FTQC.

• The paper demonstrates the first complete realization of a CSS code using topologically encoded qubits in a trapped-ion system for single-qubit error correction.
• The study employs transversal operations to execute a complete set of single-qubit Clifford gates, effectively reducing error propagation.
• Experimental outcomes reveal an 88.8% fidelity in creating a four-qubit entangled state and a 32.7% fidelity in encoding the logical state, highlighting both achievements and challenges in FTQC.

Quantum Computations on Topologically Encoded Qubits

The paper presents a significant paper on the implementation of quantum error correcting codes using topologically encoded qubits with trapped ions. Using seven trapped-ion qubits, the research focuses on developing a foundational piece for fault-tolerant quantum computing (FTQC) by realizing a Calderbank-Shor-Steane (CSS) code. This work is particularly critical because it represents the first complete realization of a CSS code using a topological quantum error-correcting code, an approach that is key for robust quantum computation.

Overview of the Research

The researchers employed a topologically protected quantum error correction code that disperses one logical qubit over seven physical qubits. This code allows for the detection and correction of single-qubit errors, be they bit flip, phase flip, or a combination. The experimental results successfully demonstrated these capabilities, establishing error syndromes for correction with high fidelity to the logical qubit initialized state.

Specifically, the research involved manipulating the ion-trap system to perform logical qubits operations. These operations include the implementation of the entire set of logical single-qubit Clifford gates, showcasing the qubit's computational functionality. The implementation utilized transversal operations which minimize error propagation—a major consideration in quantum error correction necessary to meet the thresholds for fault tolerance.

Key Results and Numerical Outcomes

The results indicated a 88.8% fidelity in creating a four-qubit entangled state and a 32.7% overall fidelity in encoding the logical state, witnessing genuine six-qubit entanglement. These outcomes signify that while the project successfully implemented a logical gate set transversally and protected the logical state to a degree, it also delineates the technical challenges present at the intersection of quantum error correction and qubit operation fidelity.

Theoretical and Practical Implications

Theoretically, the work details a shift towards FTQC algorithms that involve encoding qubits in topologically robust structures. Practically, such an approach aligns with the current pathway for scaling quantum computers. The paper suggests that future implementations could incorporate additional error correction cycles and ancillary qubits to further robustness and move towards universal encoded quantum computation.

Additionally, this work opens avenues for adapting the methodology across other scalable quantum platforms such as ion-trap arrays and chip-based systems. Demonstrating fault tolerance in these systems is essential, as it dictates the scalability and practical use of quantum computers for solving complex problems beyond the reach of classical systems.

Prospective Developments

Looking forward, the research suggests further exploration of non-Clifford gate implementation and repeated error correction cycle incorporation. Additionally, expanding to larger code distances by integrating more physical qubits within the logical encoding could improve error thresholds crucial for FTQC.

Finally, this foundational research sets a precedent for developing measurement-based quantum error correction protocols that involve distributing qubits across multiple physical systems or integrating global measurement techniques in physical implementations.

In conclusion, this paper not only serves to confirm the viability of topologically encoded qubits for quantum error correction but also provides a stepping stone for future investigations aiming to bring FTQC schemes to practical fruition, exploring new realms in quantum computation's theoretical and application landscapes.