Quantum error correction (QEC) is the linchpin holding the promise of fault-tolerant quantum computing together. In our recent paper, "Scalable Decoding Protocols for Fast Transversal Logic in the Surface Code," we explore a novel approach to tackling QEC challenges in atomic, molecular, and optical (AMO) quantum computing platforms.
Today’s AMO platforms provide impressive connectivity and long coherence times. Their potential in terms of scalability has also been demonstrated by groups such as those at Quantinuum and Harvard University.
However, AMO platforms also lag in QEC cycle speeds compared to superconducting hardware. This speed disparity presents a significant hurdle that we aim to address by enabling more efficient logical operations.
Our work introduces the "ghost protocol", a decoding protocol designed to enable scalable decoding in the context of fast transversal logic, which is a decoding problem that previously relied on unscalable decoders requiring error information from across the whole system.
With our new protocols, we can enable more than a 10x speed up for AMO qubits.
What is transversal logic?
Transversal logic enables fault tolerant logical gates to be implemented with low circuit depth. In this approach, logical two-qubit gates can be performed by physically shifting two logical qubit patches so that their constituent qubits align pairwise, enabling a physical CNOT gate between each pairing of data qubits.
In this case, entanglement is created through standard gates applied directly on data qubits.
Transversal logic plays a vital role in architectures like neutral atoms and ion traps. This is because transversal gates reduce the number of QEC cycles required compared to lattice surgery (the method that allows superconducting qubits to perform error-corrected logical gates given fixed connectivity).
By comparison, a CNOT by lattice surgery typically requires measuring the code’s stabilisers for time linear in the code distance – a big difference to the small, constant number of rounds needed between transversal CNOTs. Transversal logic matters to AMO qubits because they have physical gate times that are more than 100 times slower than those in superconducting qubits. Therefore, AMO platforms will seek to leverage their greater connectivity to perform logic transversally, escaping more expensive lattice surgery routines.
However, the complexity introduced by transversal gates results in a more intricate decoding challenge known as a correlated (or hypergraph) decoding problem. A common assumption has been that the inapplicability of existing windowing schemes to fast transversal logic and the growth of the decoding volume in this particular setting makes a transversal speedup difficult to attain in practice.
Windowing schemes are crucial for real-time decoding, as they allow the decoding problem to be divided into small, manageable chunks and the QEC system to respond to a continuous stream of measurement data from the quantum computer. Typically, windowing assumes highly structured models of error propagation with locality in the error information – something that breaks down when logical qubits move around between every round of syndrome extraction. As a result, progress with efficient, real-time decoding remains essential to overcoming this challenge.
To address this, we've reformulated the spatial windowing problem as a ‘sparse message passing algorithm’: each logical qubit is decoded independently in an iterative fashion, each time exchanging messages with other decoders looking after other logical qubits.
In such a way, we arrive at small, modular decoding windows. Armed with this scalable decoder, we studied this technique’s performance in the context of both deep Clifford and non-Clifford logic, focusing on the structural properties of the T gate realised via teleportation.
A key finding is a surprising resilience property that sheds light on why fast transversal gates can be sustained. We characterised how this resilience interacts with the necessity of spatial windowing under our “ghost” decoding protocol and extended it with a further decoding protocol called "patience" to improve accuracy in the non-Clifford setting.
By introducing the ghost protocol and addressing the need for spatial windowing, we believe our work provides a stepping stone towards realising the promise of transversal logic and achieving scalable error correction in AMO quantum computers.
We're excited by the prospect that our work may influence future research in the qLDPC space, where similar decoding techniques could secure a compelling spacetime advantage. Read the full paper here.