arXiv subjects

Mark Webster

Publications and source records attributed to Mark Webster.

18 recordsLinked to original sources

arXiv2026

Computing 256-bit elliptic curve discrete logarithms in 26 days on a fault-tolerant trapped-ion quantum computer with 20,000 qubits

One of the strengths of our recently proposed Walking Cat Architecture for a trapped-ion quantum computer is that it is straightforward to extend and optimize for a specific application. As a proof-of-concept, here we present such optimizations for solving the $256$-bit elliptic curve discrete logarithm problem (ECDLP) on $\mathtt{secp256k1}$, which is the elliptic curve used by blockchain technologies such as Bitcoin, using Shor's algorithm. We optimize the circuits from Schrottenloher's recent work and arrive at a logical quantum circuit for solving the ECDLP using about $1450$ qubits and $40\cdot 10^6$ Toffoli gates, with a rigorous lower bound on the logical-level success probability that holds with confidence at least $1-2^{-128}$. Using our compilation toolchain with manual optimization of the logical layout and integrated routing, we produce estimates for the logical measurement depth and the required number of physical qubits by compiling all components to measurement schedules that obey the architectural constraints. A key ingredient is a fast CCZ magic-state factory and a depth-one CCZ state injection, reducing the execution time of CCZ gates by a factor of $31$. We increase the logical-measurement parallelism using non-overlapping cat-based measurements in parallel, and we leverage the recently proposed logical CliNR protocol to speed up Clifford operations. To reduce the qubit overhead, we introduce a more efficient loss correction protocol, design a layout that allows us to recycle the CliNR ancilla qubits, and provision reusable cat-state resources according to the circuit's peak measurement parallelism. All results and optimizations combined, we conclude that a trapped-ion quantum computer based on our architecture can solve the ECDLP on $\mathtt{secp256k1}$ in approximately 25.7 days using 19,397 physical qubits with an estimated success probability of $63\%$.

quant-ph↗

arXiv2026

Fast logical operations in quantum LDPC codes using simple resource states

Quantum LPDC codes provide a substantial reduction in qubit overhead required for fault-tolerant quantum computation compared to surface code, thanks to their high encoding rate. However, operating simultaneously on multiple logical qubits encoded in the same block is more challenging and may slow down logical operations. Prior work addresses this problem by designing complex resource states to perform logical measurements in LDPC codes. Here, we propose an approach that only consumes cat states. Whereas previous work on cat-based measurements focuses on a single logical measurement, we design a protocol for the joint measurement of $\ell$ commuting logical operators. The key ingredient is the design of a scheduler code determining the measurement sequence and allowing for the decoding of all logical measurement outcomes. Numerical simulations with the LDPC codes Q70 and Q102 of the walking cat architecture show a speed-up of nearly $3\times$ over Viterbi measurements for the measurement of $\ell=20$ commuting logical operators. Combining our fast logical measurements with a new variant of the CliNR partial error correction scheme, we achieve a speed-up of up to $74\times$ for random Clifford circuits. Our approach also applies to non-Clifford gates, producing a speed-up of up to $5\times$ for Toffoli gates.

quant-ph↗

arXiv2026

Efficiently simulable quantum circuits with large entanglement, magic, and non-Gaussianity via code-compiled tensor networks

We introduce a family of quantum circuits that possess standard indicators of classical simulation hardness including high entanglement entropy, magic, and non-Gaussianity, yet admit efficient classical simulation via matrix product states (MPS). Our construction uses logical circuits of high-rate Calderbank-Shor-Steane (CSS) codes with enhanced symmetries. Using code automorphisms and transversal diagonal gates from higher levels of the Clifford hierarchy, we realize nonlocal logical Clifford and non-Clifford gates, showing how error-correcting codes can compile complex logical circuits into simple physical operations. Simulation efficiency rests on two properties: (i) diagonal transversal gates do not increase bond dimension, and (ii) permutations are tracked classically via on-the-fly relabeling, avoiding costly SWAP networks. Unlike Clifford or matchgate simulation, our method accepts a broad class of initial states, including dense entangled, magic, and non-Gaussian inputs, provided the encoded state retains an efficient MPS representation. We also release an exact phase-polynomial backend for monomial subfamilies, whose cost is set by higher-degree phase terms rather than entanglement growth. We demonstrate the method on an infinite polar CSS code family, showing bond dimension stays bounded by the encoding cost regardless of circuit depth. These results show that for some circuit families, standard resource measures are individually insufficient to indicate simulation hardness. As a near-term application, we use the compiled MPS as a classical reference for direct fidelity estimation of a quantum device running nontrivial logical circuits. Pauli sampling on the encoded reference, with a Clifford pushback through the known encoder, provides the ideal expectation values, so the logical output fidelity can be estimated from local Pauli readout alone, without costly state tomography.

quant-ph↗

arXiv2026

Fault-Tolerant Quantum Computing with Trapped Ions: The Walking Cat Architecture

We propose a fault-tolerant quantum computer architecture for trapped-ion devices, which we call the walking cat architecture. Our blueprint includes a compiler, a detailed description of all the quantum error-correction protocols, a micro-architecture, a sufficiently fast decoder, and thorough simulations. The backbone of the architecture is a cat factory, producing cat states distributed throughout the machine, which are consumed to perform logical operations. The walking cat architecture is based entirely on a modern quantum error-correction approach called low-density parity-check (LDPC) codes. We identify promising instances of the walking cat architecture, such as (1) a simple architecture based on a single LDPC code, (2) a fast architecture based on fast logical gates relying on a [[70, 6, 9]] code, equipped with Clifford-frame tracking for any 6-qubit Clifford gate, and (3) a dense architecture based on a [[102, 22, 9]]] code encoding 22 logical qubits per memory block. Our dense architecture provides a design with 110 logical qubits executing about one million T gates per day using only 2,514 physical qubits. We estimate that the quantum Hamiltonian simulation of a Heisenberg model on 100 sites can be executed within one month with 10,000 physical qubits, including all shots required to achieve chemical accuracy, suggesting that such a device could enter the regime of classically intractable physics simulations. Our design relies on hardware components that have been experimentally demonstrated on small devices. We emphasize simplicity over hypothetical performance to facilitate the practical realization of this machine. Based on this approach, we believe that a fault-tolerant quantum computer with hundreds of logical qubits capable of running millions of logical gates can be built in the near term, providing a platform to explore a broad range of applications.

quant-ph↗

arXiv2026

Distance-Finding Algorithms for Quantum Codes and Circuits

The distance of a classical or quantum code is a key figure of merit which reflects its capacity to detect errors. Quantum LDPC code families have considerable promise in reducing the overhead required for fault-tolerant quantum computation, but calculating their distance is challenging with existing methods. We generally assess the performance of a quantum code under circuit level error models, and for such scenarios the circuit distance is an important consideration. Calculating circuit distance is in general more difficult than finding the distance of the corresponding code as the detector error matrix of the circuit is usually much larger than the code's check matrix. In this work, we benchmark a wide range of distance-finding methods for various classical and quantum code families, as well as syndrome-extraction circuits. We consider both exact methods (such as Brouwer-Zimmermann, connected cluster, SAT and mixed integer programming) and heuristic methods which have lower run-time but can only give a bound on distance (examples include random information set, syndrome decoder algorithms, and Stim undetectable error methods). We further develop the QDistEvol algorithm and show that it performs well for the quantum LDPC codes in our benchmark. The algorithms and test data have been made available to the community in the codeDistance Python package.

quant-ph↗

arXiv2025

Mechanistic Insights Into How Rewiring and Bifurcation Angle Affect DK-Crush Stent Deployment

Background Double Kissing Crush (DKC) is a preferred two-stent technique for complex coronary bifurcation lesions. Proximal cell rewiring is routinely recommended to reduce technical failure, and DKC is considered effective across various bifurcation angles. However, it remains unclear whether this standard approach is optimal for all patients. This study investigates the interaction between bifurcation angle and rewiring configuration to identify anatomy-specific strategies. Methods Computational modeling of the DKC procedure was used to simulate 12 DKC procedures across three left main bifurcation angles (45{\deg}, 70{\deg}, and 100{\deg}) and four rewiring configurations: proximal-proximal (P-P), proximal-distal (P-D), distal-proximal (D-P), and distal-distal (D-D). Evaluation metrics included stent malapposition, side branch ostium clearance, arterial wall stress, low time-averaged endothelial shear stress, and high shear rates. Results DKC performed in wide bifurcations (100{\deg}) resulted in worse outcomes, with malapposition reaching 18%, side branch clearance down to 23%, and up to twice the exposure to adverse high shear rates compared to narrower angles. In contrast, intermediate (70{\deg}) and narrow (45{\deg}) angles generally resulted in more favorable outcomes, though optimal rewiring varied by angle. Proximal strategies, i.e. P-P and P-D, were most effective at 70{\deg}, while D-D performed best at 45{\deg}. No single strategy was consistently superior across all bifurcation angles. Conclusions DKC outcomes depend on bifurcation angle and can be optimized by tailoring rewiring strategies, challenging the current clinical understanding. These findings support anatomy-specific procedural planning and intravascular imaging to guide rewiring. This study provides a mechanistic rationale to improve clinical decision-making and tailor bifurcation interventions.

physics.med-ph↗

arXiv2025

Colour Codes Reach Surface Code Performance using Vibe Decoding

Two-dimensional quantum colour codes hold significant promise for quantum error correction, offering advantages such as planar connectivity and low overhead logical gates. Despite their theoretical appeal, the practical deployment of these codes faces challenges due to complex decoding requirements compared to surface codes. This paper introduces vibe decoding which, for the first time, brings colour code performance on par with the surface code under practical decoding. Our approach leverages an ensemble of belief propagation decoders - each executing a distinct serial message passing schedule - combined with localised statistics post-processing. We refer to this combined protocol as VibeLSD. The VibeLSD decoder is highly versatile: our numerical results show it outperforms all practical existing colour code decoders across various syndrome extraction schemes, noise models, and error rates. By estimating qubit footprints through quantum memory simulations, we show that colour codes can operate with overhead that is comparable to, and in some cases lower than, that of the surface code. This, combined with the fact that localised statistics decoding is a parallel algorithm, makes VibeLSD suitable for implementation on specialised hardware for real-time decoding. Our results establish the colour code as a practical architecture for near-term quantum hardware, providing improved compilation efficiency for both Clifford and non-Clifford gates without incurring additional qubit overhead relative to the surface code.

quant-ph↗

arXiv2025

Are Ultrathin Stents Optimal for Bifurcation Lesions? Insights from Computational Modelling of Provisional and DK-Crush Techniques

Complex coronary bifurcation lesions remain challenging in percutaneous coronary intervention, with stent design and deployment strategy influencing clinical outcomes. This study compares the mechanical and hemodynamic performance of the ultrathin-strut Orsiro and thin-strut Xience Sierra stent in Provisional Side Branch (PSB) and Double Kissing Crush (DKC) techniques. We used finite element analyses of bifurcation stent deployment to assess malapposition, ostium clearance, and arterial wall stress for both techniques. Computational fluid dynamics simulations quantified the luminal exposure to low Time-Averaged Endothelial Shear Stress (TAESS below 0.4 Pa) and high shear rates (above 1000 1/s). In PSB, Orsiro showed higher malapposition (13.0% vs 9.6%) but improved SB ostium clearance (77% vs 64%) and lower low-TAESS exposure (30.3% vs 33.6%) compared to Xience. Orsiro also produced higher arterial wall stresses, particularly during kissing balloon inflation. In DKC, differences in malapposition and ostium clearance diminished between stents, though Orsiro retained a hemodynamic advantage with lower low-TAESS (28.2% vs 36.3%).Stent design influenced outcomes more strongly in PSB, where anatomical interaction and platform-specific behavior impacted both structural and hemodynamic results. In DKC, procedural complexity minimized those differences, making the stenting technique the primary performance driver. Nonetheless, Orsiro consistently preserved more favorable flow conditions. These findings highlight the need to match device selection with lesion characteristics in PSB, while in DKC, optimizing procedural steps may have a greater impact than the choice of stent platform.

physics.med-ph↗

arXiv2025

Universal fault tolerant quantum computation in 2D without getting tied in knots

We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a path integral framework which provides both a macroscopic picture for different logical gates as well as a way to derive the associated microscopic circuits. We also show an equivalence between our approach and prior proposals where a 2D array of qubits reproduces the action of a transversal gate in a 3D stabilizer code over time, thus, establishing a new connection between 3D codes and 2D non-Abelian topological phases. We prove a threshold theorem for our protocols under local stochastic circuit noise using a just-in-time decoder to correct the non-Abelian code.

quant-ph↗

arXiv2025

Heuristic and Optimal Synthesis of CNOT and Clifford Circuits

Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In this work we present methods for CNOT and general Clifford circuit synthesis which can be used to minimise either the entangling two-qubit gate count or the circuit depth. We present three families of algorithms - optimal synthesis which works on small circuits, A* synthesis for intermediate-size circuits and greedy synthesis for large circuits. We benchmark against existing methods in the literature and show that our approach results in circuits with lower two-qubit gate count than previous methods. The algorithms have been implemented in a GitHub repository for use by the classical and quantum computing community.

quant-ph↗

arXiv2025

Automorphism Ensemble Decoding of Quantum LDPC Codes

We introduce AutDEC, a fast and accurate decoder for quantum error-correcting codes with large automorphism groups. Our decoder employs a set of automorphisms of the quantum code and an ensemble of belief propagation (BP) decoders. Each BP decoder is given a syndrome which is transformed by one of the automorphisms, and is run in parallel. For quantum codes, the accuracy of BP decoders is limited because short cycles occur in the Tanner graph and our approach mitigates this effect. We demonstrate decoding accuracy comparable to BP-OSD-0 with a lower time overhead for Quantum Reed-Muller (QRM) codes in the code capacity setting, and Bivariate Bicycle (BB) codes under circuit level noise. We provide a Python repository for use by the community and the results of our simulations.

quant-ph↗

arXiv2025

Low-overhead Magic State Circuits with Transversal CNOTs

With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an algorithm that can recompile and simplify a circuit of consecutive multi-qubit phase rotations, we manage to construct fault-tolerant circuits for CCZ, CS and T states with much lower CNOT depths and qubit counts than before and minimal T-depth for the given workspace. These circuits can play crucial roles in fault-tolerant computation with transversal CNOTs, and we hope that the algorithms and methods developed in this paper can be used to further simplify other protocols in similar contexts.

quant-ph↗

arXiv2024

Fault-Tolerant Logical Clifford Gates from Code Automorphisms

We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group, and impose constraints based on the Clifford operators permitted. We provide a rigorous formulation of the method for finding automorphisms of stabilizer codes and generalize ZX-dualities to non-CSS codes. We provide a Python package implementing our algorithms which uses the computational algebra system MAGMA. Our algorithms map automorphism group generators to physical circuits, calculate Pauli corrections based on the destabilizers of the code, and determine their logical action. We discuss the fault tolerance of the circuits and include examples of gates through automorphisms for the [[4,2,2]] and perfect [[5,1,3]] codes, bivariate bicycle codes, and the best known distance codes.

quant-ph↗

arXiv2024

Engineering Quantum Error Correction Codes Using Evolutionary Algorithms

Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored for a particular error model may have much better performance. In this work, we present a novel evolutionary algorithm which searches for an optimal stabiliser code for a given error model, number of physical qubits and number of encoded qubits. We demonstrate an efficient representation of stabiliser codes as binary strings -- this allows for random generation of valid stabiliser codes, as well as mutation and crossing of codes. Our algorithm finds stabiliser codes whose distance closely matches the best-known-distance codes of codetables.de for n <= 20 physical qubits. We perform a search for optimal distance CSS codes, and compare their distance to the best-known-codes. Finally, we show that the algorithm can be used to optimise stabiliser codes for biased error models, demonstrating a significant improvement in the undetectable error rate for [[12, 1]] codes versus the best-known-distance code with the same parameters. As part of this work, we also introduce an evolutionary algorithm QDistEvol for finding the distance of quantum error correction codes.

quant-ph↗

arXiv2024

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 $T^\dag$. 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 $[\![n, \Theta(n), \Theta(log(n))]\!]$. 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 $\gamma =\textrm{log}_d (n/k)$ 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.

quant-ph↗

arXiv2023

Sex-Specific Variances in Anatomy and Blood Flow of the Left Main Coronary Bifurcation: Implications for Coronary Artery Disease Risk

Studies have shown marked sex disparities in Coronary Artery Diseases (CAD) epidemiology, yet the underlying mechanisms remain unclear. We explored sex disparities in the coronary anatomy and the resulting haemodynamics in patients with suspected, but no significant CAD. Left Main (LM) bifurcations were reconstructed from CTCA images of 127 cases (42 males and 85 females, aged 38 to 81). Detailed shape parameters were measured for comparison, including bifurcation angles, curvature, and diameters, before solving the haemodynamic metrics using CFD. The severity and location of the normalised vascular area exposed to physiologically adverse haemodynamics were statistically compared between sexes for all branches. We found significant differences between sexes in potentially adverse haemodynamics. Females were more likely than males to exhibit adversely low Time Averaged Endothelial Shear Stress along the inner wall of a bifurcation (16.8% vs. 10.7%). Males had a higher percentage of areas exposed to both adversely high Relative Residence Time (6.1% vs 4.2%, p=0.001) and high Oscillatory Shear Index (4.6% vs 2.3%, p<0.001). However, the OSI values were generally small and should be interpreted cautiously. Males had larger arteries (M vs F, LM: 4.0mm vs 3.3mm, LAD: 3.6mm 3.0mm, LCX:3.5mm vs 2.9mm), and females exhibited higher curvatures in all three branches (M vs F, LM: 0.40 vs 0.46, LAD: 0.45 vs 0.51, LCx: 0.47 vs 0.55, p<0.001) and larger inflow angle of the LM trunk (M: 12.9{\deg} vs F: 18.5{\deg}, p=0.025). Haemodynamic differences were found between male and female patients, which may contribute, at least in part, to differences in CAD risk. This work may facilitate a better understanding of sex differences in the clinical presentation of CAD, contributing to improved sex-specific screening, especially relevant for women with CAD who currently have worse predictive outcomes.

physics.med-ph↗

arXiv2022

Computed tomography coronary angiogram images, annotations and associated data of normal and diseased arteries

Computed Tomography Coronary Angiography (CTCA) is a non-invasive method to evaluate coronary artery anatomy and disease. CTCA is ideal for geometry reconstruction to create virtual models of coronary arteries. To our knowledge there is no public dataset that includes centrelines and segmentation of the full coronary tree. We provide anonymized CTCA images, voxel-wise annotations and associated data in the form of centrelines, calcification scores and meshes of the coronary lumen in 20 normal and 20 diseased cases. Images were obtained along with patient information with informed, written consent as part of Coronary Atlas (https://www.coronaryatlas.org/). Cases were classified as normal (zero calcium score with no signs of stenosis) or diseased (confirmed coronary artery disease). Manual voxel-wise segmentations by three experts were combined using majority voting to generate the final annotations. Provided data can be used for a variety of research purposes, such as 3D printing patient-specific models, development and validation of segmentation algorithms, education and training of medical personnel and in-silico analyses such as testing of medical devices.

cs.CV↗

arXiv2013

The Rate of Convergence for Approximate Bayesian Computation

Approximate Bayesian Computation (ABC) is a popular computational method for likelihood-free Bayesian inference. The term "likelihood-free" refers to problems where the likelihood is intractable to compute or estimate directly, but where it is possible to generate simulated data $X$ relatively easily given a candidate set of parameters $\theta$ simulated from a prior distribution. Parameters which generate simulated data within some tolerance $\delta$ of the observed data $x^*$ are regarded as plausible, and a collection of such $\theta$ is used to estimate the posterior distribution $\theta\,|\,X\!=\!x^*$. Suitable choice of $\delta$ is vital for ABC methods to return good approximations to $\theta$ in reasonable computational time. While ABC methods are widely used in practice, particularly in population genetics, study of the mathematical properties of ABC estimators is still in its infancy. We prove that ABC estimates converge to the exact solution under very weak assumptions and, under slightly stronger assumptions, quantify the rate of this convergence. Our results can be used to guide the choice of the tolerance parameter $\delta$.

math.ST↗