Researchers Generate Logical Genuine Multipartite Entanglement for Universal Quantum Computation

This work extends a benchmark for multi-qubit quantum devices to the logical level by creating and verifying entanglement between three logical qubits.

This was achieved by combining two distinct quantum error-correction techniques using lattice surgery, a method of joining codes to enable more complex operations. They generated both standard and more complex entangled states, demonstrating a key step towards building more reliable quantum computers. Alex Steiner of the University of Innsbruck and colleagues from University of Vienna have, for the first time, generated and verified genuine multipartite entanglement between three logical qubits.

This protection is crucial as quantum states are susceptible to decoherence and other environmental disturbances. This achievement relied on combining two distinct quantum error-correction techniques, a surface code and a 3D colour code, using lattice surgery, a technique akin to connecting different computer chips to create a more powerful system, but applied to quantum codes to enhance error correction. The team used twelve physical qubits to demonstrate this process, creating both standard and more complex entangled states. The surface code is particularly well-suited for implementing transversal gates, where operations are performed directly on the encoded logical qubits without needing to decode them, simplifying the error correction process. The 3D colour code, while more complex, offers advantages in terms of its error correction capabilities and the types of gates it can support.

Combining surface and colour codes unlocks universal fault-tolerant quantum gates

A genuine multipartite entanglement with a logical fidelity of 83.0(1.1)% has been generated for the first time, representing a substantial improvement over previous attempts. Earlier efforts were limited to bipartite entanglement or lacked verified logical state fidelity. Bipartite entanglement, involving only two qubits, is insufficient for demonstrating the full capabilities of a quantum computer, while verifying the fidelity of the logical state ensures that the error correction is functioning as intended. By joining a surface code and a 3D colour code using lattice surgery, this breakthrough surpasses the limitations of single quantum error-correction codes, which cannot natively support a universal set of fault-tolerant gates. A universal gate set comprises a set of quantum gates that can be combined to approximate any quantum operation, essential for performing arbitrary quantum computations.

These codes, when combined, created a transversally implemented universal logical gate set, enabling complex operations on logical qubits, akin to bits in conventional computing but protected from errors, and paving the way for more robust quantum computations. The capability was demonstrated with a Hadamard gate on a four-qubit surface code and a doubly controlled Pauli-Z gate on an eight-qubit 3D colour code, accessing the universal logical gate set via lattice surgery. Stabiliser and non-stabiliser states of three logical qubits were generated to verify this, confirming genuine multipartite entanglement, a strong form of correlation, across all possible divisions of the qubits. Genuine multipartite entanglement signifies that the entanglement cannot be reduced to a simpler form involving only pairs of qubits, indicating a higher degree of quantum correlation. Arbitrary rotations on single logical qubits were also performed using a resource gadget based on the doubly controlled Pauli-Z gate, resulting in a logical Greenberger-Horne-Zeilinger state achieving a fidelity of 81.0(1.7)% with flags, which increased to 83.0(1.1)% with the inclusion of flag qubits for error detection. The Greenberger-Horne-Zeilinger state is a specific-entangled state used to demonstrate non-classical correlations, and the use of ‘flag’ qubits provides an additional layer of error detection and correction.

Combining surface and colour codes presents both advances and scaling limitations for

Lattice surgery offers a promising route towards scalable, fault-tolerant quantum computation, sidestepping the limitations of relying on a single error-correction strategy. The ability to combine different codes allows for the implementation of a wider range of gates and potentially more efficient error correction schemes. The current implementation, however, hinges on a specific transversal CCZ gate, a building block for universal computation, which does not scale easily. This reliance on a non-distance-growing code for this important gate introduces a potential bottleneck, as increasing qubit numbers would demand exponentially more physical qubits to maintain acceptable error rates. Non-distance-growing codes, conversely, exhibit a less favourable scaling behaviour.

Despite these scaling challenges, this demonstration remains significant. A functional architecture for building complex logical qubits has been successfully demonstrated, extending benchmarks for multi-qubit quantum devices into the area of error-corrected logic. This hybrid methodology, combining a surface code and a 3D colour code using a technique for joining quantum codes to enhance error correction, represents a key step towards building more robust and flexible quantum computers. Further optimisation of individual components is needed, and the work opens questions regarding scalable non-Clifford gate implementation. Non-Clifford gates are essential for universal quantum computation but are more difficult to implement efficiently in many quantum error correction schemes. Future research will likely focus on developing more scalable methods for implementing these gates and exploring alternative code combinations to overcome the current limitations. The successful demonstration of logical entanglement and universal gate sets represents a crucial advancement in the pursuit of practical, fault-tolerant quantum computers.

Researchers successfully generated and verified genuine multipartite entanglement using logical qubits in a trapped-ion quantum processor. This achievement demonstrates a functional architecture for building complex, error-corrected logical qubits by combining a four-qubit surface code and an eight-qubit 3D colour code via lattice surgery. The ability to implement a universal set of logical gates, including Hadamard and doubly controlled Pauli-Z gates, represents a key step towards more robust quantum computation. The authors suggest further optimisation of components and exploration of scalable non-Clifford gate implementation will be important areas for future work.