Quantum Error Correction: New Circuit Halves Gate Count for Encoding States

A new unitary circuit encodes surface code states with half the gate count of existing methods. Simulations demonstrate improved performance in preparing Pauli Y-eigenstates under realistic noise conditions, particularly benefiting quantum computing platforms utilising non-local interactions like neutral atoms and trapped ions. Conventional decoders remain effective.

Quantum error correction represents a critical challenge in realising practical quantum computation. Surface codes, favoured for their relatively high fault tolerance threshold and amenability to implementation on various hardware platforms, require efficient methods for state preparation – a process known as encoding. Researchers at Yale University have developed a novel encoding circuit for surface codes that reduces the number of quantum gates required compared to existing methods. This advance potentially simplifies implementation and improves performance, particularly on architectures supporting non-local interactions, such as those utilising neutral atoms or trapped ions. The work, detailed in a paper titled ‘A Unitary Encoder for Surface Codes’, is authored by Pei-Kai Tsai and Shruti Puri, both affiliated with the Department of Applied Physics and the Yale Quantum Institute.

Efficient Encoding for Topological Quantum Error Correction

Protecting quantum information requires robust error correction, and topological codes, such as the surface code, represent a leading approach. Current research focuses on both theoretical refinements to error correction and practical implementations on diverse hardware, including neutral atoms and trapped ions, to realise functional quantum computers. A key area of investigation centres on optimising the preparation of quantum states essential for universal quantum computation, particularly the generation of ‘magic states’ – states that enable operations beyond those achievable with purely stabiliser-based quantum gates – with improved fidelity and reduced resource demands.

Recent work details a novel unitary circuit designed for encoding surface code states. This circuit halves the gate count required compared with previous methods, offering a significant practical advantage for quantum systems capable of performing non-local interactions – operations where qubits interact directly without needing intermediary qubits. The circuit achieves this efficiency through a code conversion between rotated and regular surface codes, streamlining the encoding process and enabling the efficient generation of specific surface code eigenstates.

Crucially, the circuit prepares the Pauli Y-eigenstate and Clifford eigenstates. These states are difficult to access using only transversal operations – gates that act on qubits in a geometrically local manner – and their efficient preparation expands the range of possible quantum computations.

Given the non-local nature of the new circuit, researchers investigated whether this would introduce increased complexity in the decoding process – the task of identifying and correcting errors that have occurred during computation. Surprisingly, simulations demonstrate that conventional matching decoders – algorithms that identify error patterns by matching syndromes, or error indicators – perform effectively. This result dispels concerns about significantly harder decoding challenges and confirms the practicality of the approach.

Performance benchmarks directly compare the new encoder against both a local unitary encoder and the standard stabiliser-measurement based encoder when preparing the Pauli Y-eigenstate. The results reveal a clear advantage for the new circuit.

This work highlights the practical benefits of the encoder for quantum platforms supporting non-local interactions, notably neutral atoms and trapped ions. The circuit design leverages the inherent capabilities of these platforms to achieve efficient state preparation, contributing to the ongoing effort to build practical, fault-tolerant quantum computers by offering a more efficient method for encoding quantum information and improving overall performance.