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Sam Roberts

Publications and source records attributed to Sam Roberts.

18 recordsLinked to original sources
arXiv2026

Macromux: scalable postselection for high-threshold fault-tolerant quantum computation

We introduce a new resource-efficient scheme for fault-tolerant quantum computation known as `macroscale multiplexing' (or simply `Macromux'), that utilizes scalable postselection to significantly improve the threshold of a given fault-tolerant protocol against both Pauli and erasure errors. Macromux is a hierarchical method for postselecting on constant-size space-time windows of a fault tolerant protocol, requiring only constant additional overheads. The method can be straightforwardly implemented for any fault-tolerant protocol and in any architecture that has access to routing and memory, such as linear-optical fusion-based architectures. We construct fault-tolerant protocols that, to our knowledge, have the highest thresholds in the literature; we perform simulations of fusion-based schemes based on the surface code, showing a maximum possible increase in Pauli thresholds of up to a factor of $\sim6$ (from $1.0\%$ to $5.9\%$). Our schemes are highly-resource efficient, and can for example, double the loss thresholds of some photonic fusion-based protocols using as little as $3 \times$ overhead.

quant-ph↗
arXiv2025

Ising on the donut: Regimes of topological quantum error correction from statistical mechanics

Utility-scale quantum computers require quantum error correcting codes with large numbers of physical qubits to achieve sufficiently low logical error rates. The performance of quantum error correction (QEC) is generally predicted through large-scale numerical simulations, used to estimate thresholds, finite-size scaling, and exponential suppression of logical errors below threshold. The connection of QEC to models from statistical mechanics provides an alternative tool for analysing QEC performance. However, predicting the behaviour of these models also requires large-scale numerical simulations, as analytic solutions are not generally known. Here we exploit an exact mapping, from a toric code under bit-flip noise that is post-selected on being syndrome free to the exactly-solvable two-dimensional Ising model on a torus, to derive an analytic solution for the logical failure rate across its full domain of physical error rates. In particular, this mapping provides closed-form expressions for the logical failure rate in four distinct regimes: the path-counting, below-threshold (ordered), near-threshold (critical), and above-threshold (disordered) regimes. Our framework places a number of familiar and long-standing numerical observations on firm theoretical ground. It also motivates explicit ans\"atze for the conventional QEC setting of non-post-selected codes whose statistical mechanics mappings involve random-bond disorder. Specifically, we introduce an effective surface tension model for the below-threshold regime, and a new scaling ansatz for the near-threshold regime, derived from an analysis of the ground state energy cost distribution. By bridging statistical mechanics theory and quantum error correction practice, our results offer a new toolkit for designing, benchmarking, and understanding topological codes beyond current computational limits.

quant-ph↗
arXiv2023

Fault-tolerant complexes

Fault-tolerant complexes describe surface-code fault-tolerant protocols from a single geometric object. We first introduce fusion complexes that define a general family of fusion-based quantum computing (FBQC) fault-tolerant quantum protocols based on surface codes. We show that any 3-dimensional cell complex where each edge has four incident faces gives a valid fusion complex. This construction enables an automated search for fault tolerance schemes, allowing us to identify 627 examples within a moderate search time. We implement this using the open-source software tool Gavrog and present threshold results for a variety of schemes, finding fusion networks with higher erasure and Pauli thresholds than those existing in the literature. We then define more general structures we call fault-tolerant complexes that provide a homological description of fault tolerance from a large family of low-level error models, which include circuit-based computation, floquet-based computation, and FBQC with multi-qubit measurements. This extends the applicability of homological descriptions of fault tolerance, and enables the generation of many new schemes which have not been previously identified. We also define families of fault-tolerant complexes for color codes and 3d single-shot subsystem codes, which enables similar constructive methods, and we present several new examples of each.

quant-ph↗
arXiv2023

Unifying flavors of fault tolerance with the ZX calculus

There are several models of quantum computation which exhibit shared fundamental fault-tolerance properties. This article makes commonalities explicit by presenting these different models in a unifying framework based on the ZX calculus. We focus on models of topological fault tolerance - specifically surface codes - including circuit-based, measurement-based and fusion-based quantum computation, as well as the recently introduced model of Floquet codes. We find that all of these models can be viewed as different flavors of the same underlying stabilizer fault-tolerance structure, and sustain this through a set of local equivalence transformations which allow mapping between flavors. We anticipate that this unifying perspective will pave the way to transferring progress among the different views of stabilizer fault-tolerance and help researchers familiar with one model easily understand others.

quant-ph↗
arXiv2023

Modular decoding: parallelizable real-time decoding for quantum computers

Universal fault-tolerant quantum computation will require real-time decoding algorithms capable of quickly extracting logical outcomes from the stream of data generated by noisy quantum hardware. We propose modular decoding, an approach capable of addressing this challenge with minimal additional communication and without sacrificing decoding accuracy. We introduce the edge-vertex decomposition, a concrete instance of modular decoding for lattice-surgery style fault-tolerant blocks which is remarkably effective. This decomposition of the global decoding problem into sub-tasks mirrors the logical-block-network structure of a fault-tolerant quantum circuit. We identify the buffering condition as a key requirement controlling decoder quality; it demands a sufficiently large separation (buffer) between a correction committed by a decoding sub-task and the data unavailable to it. We prove that the fault distance of the protocol is preserved if the buffering condition is satisfied. Finally, we implement edge-vertex modular decoding and apply it on a variety of quantum circuits, including the Clifford component of the 15-to-1 magic-state distillation protocol. Monte Carlo simulations on a range of buffer sizes provide quantitative evidence that buffers are both necessary and sufficient to guarantee decoder accuracy. Our results show that modular decoding meets all the practical requirements necessary to support real-world fault-tolerant quantum computers.

quant-ph↗
arXiv2022

Fault-tolerant Post-Selection for Low Overhead Magic State Preparation

We introduce a framework for fault-tolerant post-selection (FTPS) of fault-tolerant codes and channels -- such as those based on surface-codes -- using soft-information metrics based on visible syndrome and erasure information. We introduce several metrics for ranking configurations of syndromes and erasures. In particular, we introduce the \emph{logical gap} (and variants thereof) as a powerful soft-information metric for predicting logical error rates of fault-tolerant channels based on topological error-correcting codes. The logical gap is roughly the unsigned weight difference between inequivalent logical corrections and is adaptable to any tailored noise model or decoder. We deploy this framework to prepare high-quality surface code magic states with low overhead under a model of independent and identically distributed (\emph{i.i.d.}) Pauli and erasure errors. Post-selection strategies based on the logical gap can suppress the encoding error rate of a magic state preparation channel to the level of the physical error rate with low overhead. For example, when operating at $60\%$ the bulk threshold of the corresponding surface code, an overall reduction of the encoding error rate by a factor of $15$ is achievable with a relative overhead factor of ${< 2}$ (approximately $23$ times less than that of simple syndrome-counting rules). We analyze a schematic buffer architecture for implementing post-selection rules on magic state factories in the context of magic state distillation. The FTPS framework can be utilized for mitigating errors in more general fault-tolerant logical channels.

quant-ph↗
arXiv2022

The Stability of Transient Relationships

In contrast to long-term relationships, far less is known about the temporal evolution of transient relationships, although these constitute a substantial fraction of people's communication networks. Previous literature suggests that ratings of relationship emotional intensity decay gradually until the relationship ends. Using mobile phone data from three countries (US, UK, and Italy), we demonstrate that the volume of communication between ego and its transient alters does not display such a systematic decay, instead showing a lack of any dominant trends. This means that the communication volume of egos to groups of similar transient alters is stable. We show that alters with longer lifetimes in ego's network receive more calls, with the lifetime of the relationship being predictable from call volume within the first few weeks of first contact. This is observed across all three countries, which include samples of egos at different life stages. The relation between early call volume and lifetime is consistent with the suggestion that individuals initially engage with a new alter so as to evaluate their potential as a tie in terms of homophily.

physics.soc-ph↗
arXiv2022

Hierarchies of resources for measurement-based quantum computation

For certain restricted computational tasks, quantum mechanics provides a provable advantage over any possible classical implementation. Several of these results have been proven using the framework of measurement-based quantum computation (MBQC), where non-locality and more generally contextuality have been identified as necessary resources for certain quantum computations. Here, we consider the computational power of MBQC in more detail by refining its resource requirements, both on the allowed operations and the number of accessible qubits. More precisely, we identify which Boolean functions can be computed in non-adaptive MBQC, with local operations contained within a finite level in the Clifford hierarchy. Moreover, for non-adaptive MBQC restricted to certain subtheories such as stabiliser MBQC, we compute the minimal number of qubits required to compute a given Boolean function. Our results point towards hierarchies of resources that more sharply characterise the power of MBQC beyond the binary of contextuality vs non-contextuality.

quant-ph↗
arXiv2021

Logical blocks for fault-tolerant topological quantum computation

Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and resource overheads of universal logical gate sets have so far been limited. In this paper, we present a comprehensive framework for universal fault-tolerant logic motivated by the combined need for platform-independent logical gate definitions, flexible and scalable tools for numerical analysis, and exploration of novel schemes for universal logic that improve resource overheads. Central to our framework is the description of logical gates holistically in a way which treats space and time on a similar footing. Focusing on schemes based on surface codes, we introduce explicit, but platform-independent representations of topological logic gates -- called logical blocks -- and generate new, overhead-efficient methods for universal quantum computation. As a specific example, we propose fault-tolerant schemes based on surface codes concatenated with more general low-density parity check (LDPC) codes. The logical blocks framework enables a convenient mapping from an abstract description of the logical gate to a precise set of physical instructions for both circuit-based and fusion-based quantum computation (FBQC). Using this, we numerically simulate a surface-code-based universal gate set implemented with FBQC, and verify that their thresholds are consistent with the bulk memory threshold. We find that boundaries, defects, and twists can significantly impact the logical error rate scaling, with periodic boundary conditions potentially halving the resource requirements. Motivated by the favorable logical error rates for boundaryless computation, we introduce a novel computational scheme based on the teleportation of twists that may offer further resource reductions.

quant-ph↗
arXiv2021

Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules

We estimate the resources required in the fusion-based quantum computing scheme to simulate electrolyte molecules in Li-ion batteries on a fault-tolerant, photonic quantum computer. We focus on the molecules that can provide practical solutions to industrially relevant problems. Certain fault-tolerant operations require the use of single-qubit "magic states" prepared by dedicated "magic state factories" (MSFs). Producing and consuming magic states in parallel is typically a prohibitively expensive task, resulting in the serial application of fault-tolerant gates. However, for the systems considered, the MSF constitutes a negligible fraction of the total footprint of the quantum computer, allowing for the use of multiple MSFs to produce magic states in parallel. We suggest architectural and algorithmic techniques that can accommodate such a capability. We propose a method to consume multiple magic states simultaneously, which can potentially lead to an order of magnitude reduction in the computational runtime without additional expense in the footprint.

quant-ph↗
arXiv2021

Interleaving: Modular architectures for fault-tolerant photonic quantum computing

Useful fault-tolerant quantum computers require very large numbers of physical qubits. Quantum computers are often designed as arrays of static qubits executing gates and measurements. Photonic qubits require a different approach. In photonic fusion-based quantum computing (FBQC), the main hardware components are resource-state generators (RSGs) and fusion devices connected via waveguides and switches. RSGs produce small entangled states of a few photonic qubits, whereas fusion devices perform entangling measurements between different resource states, thereby executing computations. In addition, low-loss photonic delays such as optical fiber can be used as fixed-time quantum memories simultaneously storing thousands of photonic qubits. Here, we present a modular architecture for FBQC in which these components are combined to form "interleaving modules" consisting of one RSG with its associated fusion devices and a few fiber delays. Exploiting the multiplicative power of delays, each module can add thousands of physical qubits to the computational Hilbert space. Networks of modules are universal fault-tolerant quantum computers, which we demonstrate using surface codes and lattice surgery as a guiding example. Our numerical analysis shows that in a network of modules containing 1-km-long fiber delays, each RSG can generate four logical distance-35 surface-code qubits while tolerating photon loss rates above 2% in addition to the fiber-delay loss. We illustrate how the combination of interleaving with further uses of non-local fiber connections can reduce the cost of logical operations and facilitate the implementation of unconventional geometries such as periodic boundaries or stellated surface codes. Interleaving applies beyond purely optical architectures, and can also turn many small disconnected matter-qubit devices with transduction to photons into a large-scale quantum computer.

quant-ph↗
arXiv2020

3-Fermion topological quantum computation

We present a scheme for universal topological quantum computation based on Clifford complete braiding and fusion of symmetry defects in the 3-Fermion anyon theory, supplemented with magic state injection. We formulate a fault-tolerant measurement-based realisation of this computational scheme on the lattice using ground states of the Walker--Wang model for the 3-Fermion anyon theory with symmetry defects. The Walker--Wang measurement-based topological quantum computation paradigm that we introduce provides a general construction of computational resource states with thermally stable symmetry-protected topological order. We also demonstrate how symmetry defects of the 3-Fermion anyon theory can be realized in a 2D subsystem code due to Bomb\'{i}n -- making contact with an alternative implementation of the 3-Fermion defect computation scheme via code deformations.

quant-ph↗
arXiv2018

Universal fault-tolerant measurement-based quantum computation

Certain physical systems that one might consider for fault-tolerant quantum computing where qubits do not readily interact, for instance photons, are better suited for measurement-based quantum-computational protocols. Here we propose a measurement-based model for universal quantum computation that simulates the braiding and fusion of Majorana modes. To derive our model we develop a general framework that maps any scheme of fault-tolerant quantum computation with stabilizer codes into the measurement-based picture. As such, our framework gives an explicit way of producing fault-tolerant models of universal quantum computation with linear optics using protocols developed using the stabilizer formalism. Given the remarkable fault-tolerant properties that Majorana modes promise, the main example we present offers a robust and resource efficient proposal for photonic quantum computation.

quant-ph↗
arXiv2018

Symmetry-protected self-correcting quantum memories

A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin-lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional on-site symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D "cluster-state" model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET-ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models where the symmetry appears naturally, without needing to be enforced externally.

quant-ph↗
arXiv2018

Contextuality as a resource for measurement-based quantum computation beyond qubits

Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate non-linear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality - the possible local measurement outcomes cannot all be pre-assigned. However, this connection is restricted to the special case when the local measured systems are qubits, which have unusual properties from the perspective of contextuality. A single qubit cannot allow for a proof of contextuality, unlike higher-dimensional systems, and multiple qubits can allow for state-independent contextuality with only Pauli observables, again unlike higher-dimensional generalisations. Here we identify precisely that strong non-locality is necessary in a qudit measurement-based computation that evaluates high-degree polynomial functions with only linear control. We introduce the concept of local universality, which places a bound on the space of output functions accessible under the constraint of single-qudit measurements. Thus, the partition of a physical system into subsystems plays a crucial role for the increase in computational power. A prominent feature of our setting is that the enabling resources for qubit and qudit measurement-based computations are of the same underlying nature, avoiding the pathologies associated with qubit contextuality.

quant-ph↗
arXiv2017

Topological proofs of contextuality in quantum mechanics

We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies to the parity proofs first discussed by Mermin, as well as a different type of contextuality proofs based on symmetry transformations. The topological arguments presented can be used in the state-dependent and the state-independent case.

quant-ph↗
arXiv2016

Symmetry protected topological order at nonzero temperature

We address the question of whether symmetry-protected topological (SPT) order can persist at nonzero temperature, with a focus on understanding the thermal stability of several models studied in the theory of quantum computation. We present three results in this direction. First, we prove that nontrivial SPT order protected by a global on-site symmetry cannot persist at nonzero temperature, demonstrating that several quantum computational structures protected by such on-site symmetries are not thermally stable. Second, we prove that the 3D cluster state model used in the formulation of topological measurement-based quantum computation possesses a nontrivial SPT-ordered thermal phase when protected by a global generalized (1-form) symmetry. The SPT order in this model is detected by long-range localizable entanglement in the thermal state, which compares with related results characterizing SPT order at zero temperature in spin chains using localizable entanglement as an order parameter. Our third result is to demonstrate that the high error tolerance of this 3D cluster state model for quantum computation, even without a protecting symmetry, can be understood as an application of quantum error correction to effectively enforce a 1-form symmetry.

quant-ph↗