arXiv subjects

Viv Kendon

Publications and source records attributed to Viv Kendon.

At least 19 recordsLinked to original sources

arXiv2026

Numerical methods for the simulation of quantum walks and quantum annealing

It is known that Chebyshev based polynomial approximation gives a near-optimal rate of convergence for calculating a function of a Hermitian matrix. However, previous work has not discussed the option of true minimax approximation, nor the specifics of writing a high performance implementation with a rigorous analysis of errors. This work provides such an analysis and an open-source implementation of three approximation methods in C++.

math.NA↗

arXiv2026

When does a control system compute? Digital, mechanical and open-loop systems

Control systems are ubiquitous in modern technology, comprising an engineered plant to be kept within specific, often fine-tuned, limits, and a separate controller that ensures this is the case. While modern controllers often employ digital computers, other examples are purely mechanical, or even biological. It is an open question whether computation is happening within all controllers by virtue of them being part of a control system. Abstraction/ Representation theory (ART) has been developed to tackle just this question of whether a physical system is computing. Here, we demonstrate how to use ART to model control systems, and analyse them for computational properties. We determine that the plant of a control system is (a proxy for) the representational entity necessary in ART for the existence of any computation: the plant is the user of the controller. We consider specific systems: a digital thermostat, an electro-mechanical thermostat, the purely mechanical centrifugal governor, and an open-loop human-controlled heating system. We show that all these systems, and control systems in general, are performing some degree of computation. As an initial use of these results, we apply them to computationalism within cognitive theory: we show the governor is computing, so it cannot play its role of counter-example in the question of whether the brain is too.

cs.ET↗

arXiv2026

Novel models of computation from novel physical substrates: a bosonic example

Unconventional physical computing is producing many novel and exotic devices that can potentially be used in a computational mode. Currently, these tend to be used to implement traditional models of computation, such as boolean logic circuits, or neuromorphic approaches. This runs the risk of failing to exploit the devices to their full potential. Here we describe a methodology for deriving a model of computation and domain specific language more closely matched to a given physical device's capabilities, and illustrate it with a case study of bosonic computing as implemented by a physical multi-component interferometer.

cs.ET↗

arXiv2026

Quantum annealing and condensed matter physics

Quantum annealing leverages the properties of interacting quantum spin systems to solve computational problems, typically optimisation problems. Current hardware now has capabilities that can be used to solve condensed matter physics problems, too. In this topical review, we provide an overview of quantum annealing aimed at condensed matter physicists, to show the mutual benefits of working together to understand and improve how quantum annealers work, and to use them to advance condensed matter physics.

quant-ph↗

arXiv2025

Continuum Limits of Lazy Open Quantum Walks

We derive the continuous spacetime limit of the one dimensional lazy discrete time quantum walk, obtaining explicit macroscopic evolution equations for a three state model in the presence of decoherence. While continuum limits of two state quantum walks are well established, an explicit continuous spacetime formulation for the lazy three state walk, particularly including noise, has not previously been constructed. Using an SU(3) representation of a Grover type coin together with a Lindblad formulation of decoherence acting either on the coin or the spatial subspace, we systematically expand the discrete dynamics in both space and time to obtain continuum master equations governing the coarse grained evolution. The resulting generators yield a genuine partial differential equation description of the walk, going beyond purely probabilistic or spectral correspondences. We show that the unitary limit is governed by a Dirac-type SU(3) Hamiltonian describing ballistic advection of left and right moving modes coupled by local symmetric mixing, with the rest state acting as an additional internal degree of freedom. Coin dephasing selectively damps internal coherences while preserving coherent spatial transport, whereas spatial dephasing suppresses long range spatial interference and rapidly drives the dynamics toward classical behaviour. This continuum framework clarifies how internal symmetry, rest state coupling, and distinct decoherence channels shape large scale transport in lazy open quantum walks, and provides a foundation for future extensions toward multichannel quantum transport models and quantum-inspired algorithms.

quant-ph↗

arXiv2025

Lazy Quantum Walks with Native Multiqubit Gates

Quantum walks, the quantum analogue of the classical random walk, have been shown to underpin quantum algorithms for fluid dynamics. We propose the quantum half-adder gate method for quantum walks as a good benchmark algorithm, specifically to compare native two-qubit gate and native multiqubit gate implementations. Neutral atom hardware is a promising choice of platform for implementing quantum walks due to its ability to implement native multiqubit (>2-qubit) gates and to dynamically re-arrange qubits. Using detailed realistic error modelling for multiqubit Rydberg gates via two-photon adiabatic rapid passage, we present the gate sequences and predicted final state fidelities for some small one dimensional quantum walks, including lazy quantum walks; lazy quantum walks include a rest state, which is needed for quantum walks for fluid simulation. Our simulations pinpoint the sweet spot where native multiqubit gates provide an advantage compared with decomposing the gate into multiple smaller higher fidelity gates.

quant-ph↗

arXiv2025

Heuristics for multi-stage quantum walks to find Ising ground states

One way to approximate a quantum annealing schedule is to use multiple quantum walks chained together, without intermediate measurements, to produce a multi-stage quantum walk (MSQW). Previous work has shown that a MSQW is better than QAOA (quantum alternating operator ansatz) for solving optimization tasks using multiple stages [Gerblich et al, arXiv:2407.06663]. In this work, we develop an efficient heuristic for choosing the free parameters in MSQW, and use it to obtain improved scaling compared to single stage quantum walks. We show numerically that the heuristic works well for problems with a large minimum energy gap, giving a polynomial scaling in the number of stages, and leading to an overall algorithm that scales polynomially in time. For problems with a small minimum gap, the scaling breaks down such that adding more stages decreases the success probability, leading to an overall scaling that is exponential in time as expected. Our methods are general and can be applied to any optimization problem to obtain good annealing schedules.

quant-ph↗

arXiv2025

Improving success probability in the LHZ parity embedding by computing with quantum walks

The LHZ parity embedding is one of the front-running methods for implementing difficult-to-engineer long-range interactions in quantum optimisation problems. Continuous-time quantum walks are a leading approach for solving quantum optimisation problems. Due to them populating excited states, quantum walks can avoid the exponential gap closing problems seen in other continuous-time techniques such as quantum annealing and adiabatic quantum computation (AQC). An important question therefore, is how continuous-time quantum walks perform in combination with the LHZ parity embedding. By numerically simulating continuous-time quantum walks on 4, 5 and 6 logical qubit Sherrington-Kirkpatrick (SK) Ising spin glass instances embedded onto the LHZ parity architecture, we are able to verify the continued efficacy of heuristics used to estimate the optimal hopping rate and the numerical agreement with the theory behind the location of the lower bound of the LHZ parity constraint strength. In addition, by comparing several different LHZ-based decoding methods, we were able to identify post-readout error correction techniques which were able to improve the success probability of the quantum walk.

quant-ph↗

arXiv2025

A Review and Collection of Metrics and Benchmarks for Quantum Computers: definitions, methodologies and software

Quantum computers have the potential to provide an advantage over classical computers in a number of areas. Numerous metrics to benchmark the performance of quantum computers, ranging from their individual hardware components to entire applications, have been proposed over the years. Navigating the resulting extensive literature can be overwhelming. Objective comparisons are further hampered in practice as different variations of the same metric are used, and the data disclosed together with a reported metric value is often not sufficient to reproduce the measurements. This article addresses these challenges by providing a review of metrics and benchmarks for quantum computers and 1) a comprehensive collection of benchmarks allowing holistic comparisons of quantum computers, 2) a consistent format of the definitions across all metrics including a transparent description of the methodology and of the main assumptions and limitations, and 3) a reproducible approach by linking the metrics to open-source software used to evaluate them. We identify five areas where international standardization working groups could be established, namely: i) the identification and agreement on the categories of metrics that comprehensively benchmark device performance; ii) the identification and agreement on a set of well-established metrics that together comprehensively benchmark performance; iii) the identification of metrics specific to hardware platforms, including non-gate-based quantum computers; iv) inter-laboratory comparison studies to develop best practice guides for measurement methodology; and v) agreement on what data and software should be reported together with a metric value to ensure trust, transparency and reproducibility. We provide potential routes to advancing these areas. We expect this compendium to accelerate the progress of quantum computing hardware towards quantum advantage.

quant-ph↗

arXiv2024

Advantages of multistage quantum walks over QAOA

Methods to find the solution state for optimization problems encoded into Ising Hamiltonians are a very active area of current research. In this work we compare the quantum approximate optimization algorithm (QAOA) with multi-stage quantum walks (MSQW). Both can be used as variational quantum algorithms, where the control parameters are optimized classically. A fair comparison requires both quantum and classical resources to be assessed. Alternatively, parameters can be chosen heuristically, as we do in this work, providing a simpler setting for comparisons. Using both numerical and analytical methods, we obtain evidence that MSQW outperforms QAOA, using equivalent resources. We also show numerically for random spin glass ground state problems that MSQW performs well even for few stages and heuristic parameters, with no classical optimization.

quant-ph↗

arXiv2023

Cycle discrete-time quantum walks on a noisy quantum computer

The rapid development of quantum computing has led to increasing interest in quantum algorithms for a variety of different applications. Quantum walks have also experienced a surge in interest due to their potential use in quantum algorithms. Using the qiskit software package, we test how accurately the current generation of quantum computers provided by IBM can simulate a cycle discrete-time quantum walk. Implementing an 8-node, 8-step walk and a simpler 4-node, 4-step discrete-time quantum walk on an IBM quantum device known as ibmq_quito, the results for each step of the respective walks are presented. A custom noise model is developed in order to estimate that noise levels in the ibmq_santiago quantum device would need to be reduced by at least 94% in order to execute a 16-node, 16-step cycle discrete-time quantum walk to a reasonable level of fidelity.

quant-ph↗

arXiv2022

Comparing the hardness of MAX 2-SAT problem instances for quantum and classical algorithms

An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various continuous-time quantum algorithms and a comparable classical algorithm. This has two motivations: to investigate whether small-sized problem instances, which are commonly used in numerical simulations of quantum algorithms for benchmarking purposes, are a good representation of larger instances in terms of their hardness to solve, and to determine the applicability of continuous-time quantum algorithms in a portfolio approach, where we take advantage of the variation in the hardness of instances between different algorithms by running them in parallel. We find that, while there are correlations in instance hardness between all of the algorithms considered, they appear weak enough that a portfolio approach would likely be desirable in practice. Our results also show a widening range of hardness of randomly generated instances as the problem size is increased, which demonstrates both the difference in the distribution of hardness at small sizes and the value of a portfolio approach that can reduce the number of extremely hard instances. We identify specific weaknesses of these quantum algorithms that can be overcome with a portfolio approach, such their inability to efficiently solve satisfiable instances (which is easy classically).

quant-ph↗

arXiv2022

Using copies to improve precision in continuous-time quantum computing

In the quantum optimisation setting, we build on a scheme introduced by Young et al [PRA 88, 062314, 2013], where physical qubits in multiple copies of a problem encoded into an Ising spin Hamiltonian are linked together to increase the logical system's robustness to error. We introduce several innovations that improve this scheme significantly. First, we note that only one copy needs to be correct by the end of the computation, since solution quality can be checked efficiently. Second, we find that ferromagnetic links do not generally help in this "one correct copy" setting, but anti-ferromagnetic links do help on average, by suppressing the chance of the same error being present on all of the copies. Third, we find that minimum-strength anti-ferromagnetic links perform best, by counteracting the spin-flips induced by the errors. We have numerically tested our innovations on small instances of spin glasses from Callison et al [NJP 21, 123022, 2019], and we find improved error tolerance for three or more copies in configurations that include frustration. Interpreted as an effective precision increase, we obtain several extra bits of precision for three copies connected in a triangle. This provides proof-of-concept of a method for scaling quantum annealing beyond the precision limits of hardware, a step towards fault tolerance in this setting.

quant-ph↗

arXiv2021

Generalising multipartite concentratable entanglement for practical applications: mixed, qudit, and optical states

The controlled SWAP test for detecting and quantifying entanglement applied to pure qubit states is robust to small errors in the states and efficient for large multi-qubit states (Foulds et al. 2021 Quantum Sci. Technol. 6, 035002 (doi:10.1088/2058-9565/abe458)). We extend this, and the related measure concentratable entanglement (CE), to enable important practical applications in quantum information processing. We investigate the lower bound of concentratable entanglement given in (Beckey et al. 2023 Phys. Rev. A 107, 062425 (doi:10.1103/physreva.107.062425)) and conjecture an upper bound of the mixed-state concentratable entanglement that is robust to c-SWAP test errors. Since experimental states are always slightly mixed, our work makes the c-SWAP test and CE measure suitable for application in experiments to characterize entanglement. We further present the CE of some key higher-dimensional states such as qudit states and entangled optical states to validate the CE as a higher-dimensional measure of entanglement. This article is part of the theme issue 'The quantum theory of light'.

quant-ph↗

arXiv2021

An energetic perspective on rapid quenches in quantum annealing

There are well developed theoretical tools to analyse how quantum dynamics can solve computational problems by varying Hamiltonian parameters slowly, near the adiabatic limit. On the other hand, there are relatively few tools to understand the opposite limit of rapid quenches, as used in quantum annealing and (in the limit of infinitely rapid quenches) in quantum walks. In this paper, we develop several tools which are applicable in the rapid quench regime. Firstly, we analyse the energy expectation value of different elements of the Hamiltonian. From this, we show that monotonic quenches, where the strength of the problem Hamiltonian is consistently increased relative to fluctuation (driver) terms, will yield a better result on average than random guessing. Secondly, we develop methods to determine whether dynamics will occur locally under rapid quench Hamiltonians, and identify cases where a rapid quench will lead to a substantially improved solution. In particular, we find that a technique we refer to as "pre-annealing" can significantly improve the performance of quantum walks. We also show how these tools can provide efficient heuristic estimates for Hamiltonian parameters, a key requirement for practical application of quantum annealing.

quant-ph↗

arXiv2020

The controlled SWAP test for determining quantum entanglement

Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a pure state. Here we show that the test can evidence the presence of entanglement (and further, genuine n-qubit entanglement), can distinguish entanglement classes, and that the concurrence of a two-qubit state is related to the test's output probabilities. We also propose a multipartite measure of entanglement that acts similarly for n-qubit states. The number of copies required to detect entanglement decreases for larger systems, to four on average for many (n>8) qubits for maximally entangled states. For non-maximally entangled states, the average number of copies of the test state required to detect entanglement increases with decreasing entanglement. Furthermore, the results are robust to second order when typical small errors are introduced to the state under investigation.

quant-ph↗

arXiv2020

Search range in experimental quantum annealing

We construct an Ising Hamiltonian with an engineered energy landscape such that it has a local energy minimum which is near to the true global minimum solution, and further away from a false minimum. Using a technique established in previous experiments, we design our experiment such that (at least on timescales relevant to our study) the false minimum is reached preferentially in forward annealing due to high levels of quantum fluctuations. This allows us to demonstrate the key principle of reverse annealing, that the solution space can be searched locally, preferentially finding nearby solutions, even in the presence of a false minimum. The techniques used here are, to the best of our knowledge, distinct from previously used experimental techniques, and allow us to probe the fundamental search range of the device in a way which has not been previously explored. We perform these experiments on two flux qubit quantum annealers, one with higher noise levels than the other. We find evidence that the lower noise device is more likely to find the more distant energy minimum (the false minimum in this case), suggesting that reducing noise fundamentally increases the range over which flux qubit quantum annealers are able to search. Our work explains why reducing the noise leads to improved performance on these quantum annealers. This supports the idea that these devices may be able to search over broad regions of the solution space quickly, one of the core reasons why quantum annealers are viewed as a potential avenue for a quantum computational advantage.

quant-ph↗

arXiv2020

How to Compute Using Quantum Walks

Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since it applies to computations run on qubit-based quantum computers in the single walker case, and physical quantum walks in the multi-walker case (quantum cellular automata). Nonetheless, quantum walks are powerful tools for quantum computing when correctly applied. In this paper, I explain the relationship between quantum walks as models and quantum walks as computational tools, and give some examples of their application in both contexts.

cs.ET↗