arXiv subjects

Mark L. Turner

Publications and source records attributed to Mark L. Turner.

4 recordsLinked to original sources

arXiv2026

Minimum Weight Decoding in the Colour Code is NP-hard

All utility-scale quantum computers will require some form of Quantum Error Correction in which logical qubits are encoded in a larger number of physical qubits. One promising encoding is known as the colour code which has broad applicability across all qubit types and can decisively reduce the overhead of certain logical operations when compared to other two-dimensional topological codes such as the surface code. However, whereas the surface code decoding problem can be solved exactly in polynomial time by finding minimum weight matchings in a graph, prior to this work, it was not known whether exact and efficient colour code decoding was possible. Optimism in this area, stemming from the colour code's significant structure and well understood similarities to the surface code, fanned this uncertainty. In this paper we resolve this, proving that exact decoding of the colour code is NP-hard -- that is, there does not exist a polynomial time algorithm unless P=NP. This highlights a notable contrast to some of the colour code's key competitors, such as the surface code, and motivates continued work in the narrower space of heuristic and approximate algorithms for fast, accurate and scalable colour code decoding.

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arXiv2026

Local Clustering Decoder as a fast and adaptive hardware decoder for the surface code

To avoid prohibitive overheads in performing fault-tolerant quantum computation, the decoding problem needs to be solved accurately and at speeds sufficient for fast feedback. Existing decoding systems fail to satisfy both of these requirements, meaning they either slow down the quantum computer or reduce the number of operations that can be performed before the quantum information is corrupted. We introduce the Local Clustering Decoder as a solution that simultaneously achieves the accuracy and speed requirements of a real-time decoding system. Our decoder is implemented on FPGAs and exploits hardware parallelism to keep pace with the fastest qubit types. Further, it comprises an adaptivity engine that allows the decoder to update itself in real-time in response to control signals, such as heralded leakage events. Under a realistic circuit-level noise model where leakage is a dominant error source, our decoder enables one million error-free quantum operations with 4x fewer physical qubits when compared to standard non-adaptive decoding. This is achieved whilst decoding in under 1 us per round with modest FPGA resources, demonstrating that high-accuracy real-time decoding is possible, and reducing the qubit counts required for large-scale fault-tolerant quantum computation.

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arXiv2025

Scalable decoding protocols for fast transversal logic in the surface code

Atomic, molecular and optical (AMO) approaches to quantum computing are promising due to their increased connectivity, long coherence times and apparent scalability. However, they have a significantly reduced cadence of syndrome extraction compared to superconducting devices, a potentially crippling slow-down given the substantial logical gate counts required for quantum advantage. Transversal logic, which exploits higher connectivity, has the potential to significantly speed up the logical clock rate by reducing the number of syndrome extraction rounds required, but current decoders for fast transversal logic are not scalable. This is not just because existing decoders are too slow to handle the large decoding volumes resulting from fast logic; transversal logic breaks the key structural properties that make real-time decoding of lattice surgery efficient. We introduce two new, windowed decoding protocols for transversal logic in the surface code that restore modularity and locality to the decoding problem. Using our protocols, we show that, with a very small space overhead, our scalable decoders unlock an order of magnitude speed-up for transversal logic compared to lattice surgery. Taken together, our results provide key evidence for the viability of large-scale algorithms on AMO qubits.

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arXiv2024

A real-time, scalable, fast and highly resource efficient decoder for a quantum computer

To unleash the potential of quantum computers, noise effects on qubits' performance must be carefully managed. The decoders responsible for diagnosing noise-induced computational errors must use resources efficiently to enable scaling to large qubit counts and cryogenic operation. Additionally, they must operate at speed, to avoid an exponential slowdown in the logical clock rate of the quantum computer. To overcome such challenges, we introduce the Collision Clustering decoder and implement it on FPGA and ASIC hardware. We simulate logical memory experiments using the leading quantum error correction scheme, the surface code, and demonstrate MHz decoding speed - matching the requirements of fast-operating modalities such as superconducting qubits - up to an 881 and 1057 qubits surface code with the FPGA and ASIC, respectively. The ASIC design occupies 0.06 mm$^2$ and consumes only 8 mW of power. Our decoder is both highly performant and resource efficient, unlocking a viable path to practically realising fault-tolerant quantum computers.

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