arXiv subjects

Thomas R. Scruby

Publications and source records attributed to Thomas R. Scruby.

10 recordsLinked to original sources

arXiv2026

Efficiently tracking errors and outcomes in universal quantum circuits

We present a method for efficient simulation of error propagation and decoding in universal fault-tolerant quantum circuits under stochastic Pauli noise, requiring only that the circuit has a high fault distance and that all logical non-Clifford operations are implemented by physical T, CS and CCZ gates. This is achieved using modified Pauli frame-based error tracking in which the frame contains no logical information. Decoding success is identified by verifying that the Pauli frame is still logically trivial after decoding. Using the results of Ref. [1] and the observation that the distribution of non-logical measurement outcomes in the circuit is independent of the logical state, we show that we can accurately sample all detector outcomes. Our approach can also simulate circuits containing adaptive operations conditioned on logical measurements, provided these measurements have a known outcome distribution. This applies to the majority of adaptive operations such as state teleportation and preparation by measurement. Our method only detects decoding failures and so is consistent with complexity-theoretic expectations as it cannot be used to sample from the noiseless outcome distribution of the logical circuit.

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arXiv2026

Efficiently estimating failure rates of fault-tolerant logical non-Clifford blocks

Useful quantum computation requires the fault-tolerant implementations of a universal gate set which are generically not efficiently simulable. We devise an algebraic framework that allows for efficient sampling from the measurement distribution of fault-tolerant circuits that implement diagonal logic gates in the third level of the Clifford hierarchy. Upon successful sampling we also provide sufficient conditions for decoding success. The resulting estimate for the logical failure rate is an overestimate, which becomes more accurate for blocks that are fault tolerant against arbitrary local errors. The non-Clifford simulation overhead is independent of the number of logical qubits, making the method particularly attractive for large-scale simulations. The framework is based on viewing the non-Clifford gates in the circuit as a cohomology invariant of an underlying spacetime fault complex. The method can also be interfaced with Clifford simulators to simulate larger fault-tolerant circuits and algorithmic subroutines.

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arXiv2026

Bacon-Shor Board Games

We identify a period-4 measurement schedule for the checks of the Bacon-Shor code that fully covers spacetime with constant-weight detectors, and is numerically observed to provide the code with a threshold. Unlike previous approaches, our method does not rely on code concatenation and instead arises as the solution to a coloring game on a square grid. Under a uniform circuit-level noise model, we observe a threshold of approximately $0.3\%$ when decoding with minimum weight perfect matching, and we conjecture that this could be improved using a more tailored decoder.

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arXiv2026

Scalable quantum error correction tailored for a heavy-hex qubit array

To produce an operable quantum computer that is made with imperfect hardware, we must design and test scalable quantum error correcting codes that are suited for the devices we can build and, in unison, develop decoding strategies that accommodate device-specific noise characteristics. Here, we introduce the \emph{dynamic compass code}, a subsystem code with a novel syndrome extraction cycle, that has a competitive threshold while making efficient use of qubits arranged on a heavy-hex lattice. We use a superconducting qubit array to implement a distance-5 instance of this code, and demonstrate how detailed noise characterisation can boost decoder performance to yield significant improvements in logical error rates. We perform averaged circuit eigenvalue sampling (ACES) to acquire detailed context-dependent error information on all elements of the syndrome extraction process. Furthermore, we leverage soft information produced from measurement devices to augment the decoder with measurement error information and detect leakage errors for exclusion through post-selection. Our noise-informed approach yields up to 38.3\% improvement in the logical error rate of a distance-5 implementation of the dynamic compass code in experiment.

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arXiv2026

High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory

We present a new family of quantum low-density parity-check codes, which we call radial codes, obtained from the lifted product of a specific subset of classical quasi-cyclic codes. The codes are defined using a pair of integers $(r,s)$ and have parameters $[\![2r^2s,2(r-1)^2,\leq2s]\!]$, with numerical studies suggesting average-case distance linear in $s$. In simulations of circuit-level noise, we observe comparable error suppression to surface codes of similar distance while using approximately five times fewer physical qubits. This is true even when radial codes are decoded using a single-shot approach, which can allow for faster logical clock speeds and reduced decoding complexity. We describe an intuitive visual representation, canonical basis of logical operators and optimal-length stabiliser measurement circuits for these codes, and argue that their error correction capabilities, tunable parameters and small size make them promising candidates for implementation on near-term quantum devices.

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arXiv2026

Low-valency scalable quantum error correction with a dynamic compass code

The ongoing development of hardware that is capable of reliably executing general quantum algorithms requires quantum error-correcting codes that are both practical for realisation and rapidly reduce logical error rates as they are scaled up. Here we introduce the dynamic compass code, a code that can be implemented with a modest footprint on the heavy-hex lattice while also demonstrating a threshold. The dynamic code is obtained by choosing a novel measurement schedule for the syndrome extraction circuit of the heavy-hex subsystem code. We numerically evaluate its performance and observe that different choices of schedule can provide a trade-off in protection against logical errors in the $X$ vs $Z$ basis. We also demonstrate that this new measurement schedule provides the code with a threshold for stability experiments. We finally show how the dynamic compass code could be used for fault-tolerant logic by illustrating lattice surgery between code patches.

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arXiv2025

Quantum Rainbow Codes: Achieving Linear Rate, Growing Distance and Transversal Non-Clifford Gates with Generalised Colour Codes

We introduce rainbow codes, a novel class of quantum error correcting codes generalising colour codes and pin codes. Rainbow codes can be defined on any $D$-dimensional simplicial complex that admits a valid $(D + 1)$-colouring of its $0$-simplices. We study in detail the case where these simplicial complexes are derived from chain complexes obtained via the hypergraph product and, by reinterpreting these codes as collections of colour codes joined at domain walls, show that we can obtain code families with growing distance and number of encoded qubits as well as logical non-Clifford gates implemented by transversal application of $T$ and $T^†$. By combining these techniques with the quasi-hyperbolic colour codes of Zhu et al. (arXiv:2310.16982) we obtain a family of codes with transversal non-Clifford gates and parameters $[\![n, Θ(n), Θ(log(n))]\!]$. This is the first example of a family of LDPC codes with linear rate, growing distance and transversal non-Clifford gates, which are necessary conditions for the magic-state distillation parameter $γ=\textrm{log}_d (n/k)$ to be made arbitrarily small. In contrast to several other constructions that satisfy these requirements, our codes are natively defined on qubits, are LDPC, and have non-Clifford gates implementable by single-qubit (rather than entangling) physical operations, but are not asymptotically good.

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arXiv2025

Fault-tolerant Quantum Computation without Distillation on a 2D Device

We show how looped pipeline architectures - which use short-range shuttling of physical qubits to achieve a finite amount of non-local connectivity - can be used to efficiently implement the fault-tolerant non-Clifford gate between 2D surface codes described in (Sci. Adv. 6, eaay4929 (2020)). The shuttling schedule needed to implement this gate is only marginally more complex than is required for implementing the standard 2D surface code in this architecture. We compare the resource cost of this operation with the cost of magic state distillation and find that, at present, this comparison is heavily in favour of distillation. The high cost of the non-Clifford gate is almost entirely due to the relatively low performance of the just-in-time decoder used as part of this process, which necessitates very large code distances in order to achieve suitably low logical error rates. We argue that, as very little attention has previously been given to the study and optimisation of these decoders, there are potentially significant improvements to be made in this area.

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arXiv2022

Non-Pauli Errors in the Three-Dimensional Surface Code

A powerful feature of stabiliser error correcting codes is the fact that stabiliser measurement projects arbitrary errors to Pauli errors, greatly simplifying the physical error correction process as well as classical simulations of code performance. However, logical non-Clifford operations can map Pauli errors to non-Pauli (Clifford) errors, and while subsequent stabiliser measurements will project the Clifford errors back to Pauli errors the resulting distributions will possess additional correlations that depend on both the nature of the logical operation and the structure of the code. Previous work has studied these effects when applying a transversal $T$ gate to the three-dimensional colour code and shown the existence of a non-local "linking charge" phenomenon between membranes of intersecting errors. In this work we generalise these results to the case of a $CCZ$ gate in the three-dimensional surface code and find that many aspects of the problem are much more easily understood in this setting. In particular, the emergence of linking charge is a local effect rather than a non-local one. We use the relative simplicity of Clifford errors in this setting to simulate their effect on the performance of a single-shot magic state preparation process (the first such simulation to account for the full effect of these errors) and find that their effect on the threshold is largely determined by probability of $X$ errors occurring immediately prior to the application of the gate, after the most recent stabiliser measurement.

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arXiv2021

Universal Fault-Tolerant Quantum Computing with Stabiliser Codes

The quantum logic gates used in the design of a quantum computer should be both universal, meaning arbitrary quantum computations can be performed, and fault-tolerant, meaning the gates keep errors from cascading out of control. A number of no-go theorems constrain the ways in which a set of fault-tolerant logic gates can be universal. These theorems are very restrictive, and conventional wisdom holds that a universal fault-tolerant logic gate set cannot be implemented natively, requiring us to use costly distillation procedures for quantum computation. Here, we present a general framework for universal fault-tolerant logic with stabiliser codes, together with a no-go theorem that reveals the very broad conditions constraining such gate sets. Our theorem applies to a wide range of stabiliser code families, including concatenated codes and conventional topological stabiliser codes such as the surface code. The broad applicability of our no-go theorem provides a new perspective on how the constraints on universal fault-tolerant gate sets can be overcome. In particular, we show how non-unitary implementations of logic gates provide a general approach to circumvent the no-go theorem, and we present a rich landscape of constructions for logic gate sets that are both universal and fault-tolerant. That is, rather than restricting what is possible, our no-go theorem provides a signpost to guide us to new, efficient architectures for fault-tolerant quantum computing.

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