arXiv subjects

Nicholas Chancellor

Publications and source records attributed to Nicholas Chancellor.

At least 37 records · Page 2Linked to original sources

arXiv2024

Load Balancing For High Performance Computing Using Quantum Annealing

With the advent of exascale computing, effective load balancing in massively parallel software applications is critically important for leveraging the full potential of high performance computing systems. Load balancing is the distribution of computational work between available processors. Here, we investigate the application of quantum annealing to load balance two paradigmatic algorithms in high performance computing. Namely, adaptive mesh refinement and smoothed particle hydrodynamics are chosen as representative grid and off-grid target applications. While the methodology for obtaining real simulation data to partition is application specific, the proposed balancing protocol itself remains completely general. In a grid based context, quantum annealing is found to outperform classical methods such as the round robin protocol but lacks a decisive advantage over more advanced methods such as steepest descent or simulated annealing despite remaining competitive. The primary obstacle to scalability is found to be limited coupling on current quantum annealing hardware. However, for the more complex particle formulation, approached as a multi-objective optimization, quantum annealing solutions are demonstrably Pareto dominant to state of the art classical methods across both objectives. This signals a noteworthy advancement in solution quality which can have a large impact on effective CPU usage.

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↗

arXiv2023

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↗

arXiv2023

Graphical Structures for Design and Verification of Quantum Error Correction

We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the zx-calculus of quantum observables. The resulting framework leads to a construction for stabilizer codes that allows us to design and verify a broad range of quantum codes based on classical ones, and that gives a means of discovering large classes of codes using both analytical and numerical methods. We focus in particular on the smaller codes that will be the first used by near-term devices. We show how CSS codes form a subset of CPC codes and, more generally, how to compute stabilizers for a CPC code. As an explicit example of this framework, we give a method for turning almost any pair of classical [n,k,3] codes into a [[2n - k + 2, k, 3]] CPC code. Further, we give a simple technique for machine search which yields thousands of potential codes, and demonstrate its operation for distance 3 and 5 codes. Finally, we use the graphical tools to demonstrate how Clifford computation can be performed within CPC codes. As our framework gives a new tool for constructing small- to medium-sized codes with relatively high code rates, it provides a new source for codes that could be suitable for emerging devices, while its zx-calculus foundations enable natural integration of error correction with graphical compiler toolchains. It also provides a powerful framework for reasoning about all stabilizer quantum error correction codes of any size.

quant-ph↗

arXiv2022

NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems

In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor's algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world problems. It is likely that quantum methods can efficiently solve certain (NP-)hard optimization problems where classical approaches fail. In our perspective, we examine the field of quantum optimization where we solve optimisation problems using quantum computers. We demonstrate this through a proper use case and discuss the current quality of quantum computers, their solver capabilities, and benchmarking difficulties. Although we show a proof-of-concept rather than a full benchmark, we use the results to emphasize the importance of using appropriate metrics when comparing quantum and classical methods. We conclude with discussion on some recent quantum optimization breakthroughs and the current status and future directions.

quant-ph↗

arXiv2022

Suppressing unwanted fluctuations in QAOA and approximate quantum annealing

The quantum approximate optimisation algorithm (QAOA) was partially inspired by digitising quantum annealing. Based on this inspiration, we develop techniques to use the additional flexibility of a universal gate-model quantum computer to mitigate fluctuation effects which are known to distort the search space within quantum annealing and lead to false minima. We find that even just the added ability to take Pauli X measurements allows us to modify the mixer angles to counteract these effects by scaling mixer terms in a way proportional to the diagonal elements of the Fubini-Study metric. We find that mitigating these effects can lead to higher success probabilities in cases where the energy landscape is distorted and that we can use the same Pauli X measurements to target which variables are likely to be susceptible to strong fluctuations. The effects of the methods we introduce are relevant even at relatively low depth of $p=10-20$, suggesting that the techniques we are developing are likely to be relevant in the near term. Furthermore, since these methods rely on controlling a degree of freedom which is not typically modified in QAOA, our methods will be compatible with a wide range of other QAOA innovations. We further verify that these fluctuation effects can be observed on an IonQ Harmony QPU.

quant-ph↗

arXiv2022

Understanding domain-wall encoding theoretically and experimentally

We analyze the method of encoding pairwise interactions of higher-than-binary discrete variables (these models are sometimes referred to as discrete quadratic models) into binary variables based on domain walls on one dimensional Ising chains. We discuss how this is relevant to quantum annealing, but also many gate model algorithms such as VQE and QAOA. We theoretically show that for problems of practical interest for quantum computing and assuming only quadratic interactions are available between the binary variables, it is not possible to have a more efficient general encoding in terms of number of binary variables per discrete variable. We furthermore use a D-Wave Advantage 1.1 flux qubit quantum annealing computer to show that the dynamics effectively freeze later for a domain-wall encoding compared to a traditional one-hot encoding. This second result could help explain the dramatic performance improvement of domain wall over one hot which has been seen in a recent experiment on D-Wave hardware. This is an important result because usually problem encoding and the underlying physics are considered separately, our work suggests that considering them together may be a more useful paradigm. We argue that this experimental result is also likely to carry over to a number of other settings, we discuss how this has implications for gate-model and quantum-inspired algorithms.

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↗

arXiv2022

Hybrid quantum-classical algorithms in the noisy intermediate-scale quantum era and beyond

Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already been performed. In this perspective, we discuss in a very broad sense what it means for an algorithm to be hybrid quantum-classical. We first explore this concept very directly, by building a definition based on previous work in abstraction/representation theory, arguing that what makes an algorithm hybrid is not directly how it is run (or how many classical resources it consumes), but whether classical components are crucial to an underlying model of the computation. We then take a broader view of this question, reviewing a number of hybrid algorithms and discussing what makes them hybrid, as well as the history of how they emerged, and considerations related to hardware. This leads into a natural discussion of what the future holds for these algorithms. To answer this question, we turn to the use of specialized processors in classical computing.The classical trend is not for new technology to completely replace the old, but to augment it. We argue that the evolution of quantum computing is unlikely to be different: hybrid algorithms are likely here to stay well past the NISQ era and even into full fault-tolerance, with the quantum processors augmenting the already powerful classical processors which exist by performing specialized tasks.

quant-ph↗

arXiv2022

Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries

A finite length ferromagnetic chain with opposite spin polarisation imposed at its two ends is one of the simplest frustrated spin models. In the clean classical limit the domain wall inserted on account of the boundary conditions resides with equal probability on any one of the bonds, and the degeneracy is precisely equal to the number of bonds. If quantum mechanics is introduced via a transverse field, the domain wall will behave as a particle in a box, and prefer to be nearer the middle of the chain rather than the ends. A simple characteristic of a real quantum annealer is therefore which of these limits obtains in practice. Here we have used the ferromagnetic chain with antiparallel boundary spins to test a real flux qubit quantum annealer and discover that contrary to both expectations, the domain walls found are non-uniformly distributed on account of effective random longitudinal fields present notwithstanding tuning carried out to zero out such fields when the couplings between qubits are nominally zero. We present a simple derivation of the form of the distribution function for the domain walls, and show also how the effect we have discovered can be used to determine the strength of the effective random fields (noise) characterising the annealer. The noise measured in this fashion is smaller than what is seen during the single qubit tuning process, but nonetheless qualitatively affects the outcome of the simulation performed by the annealer.

quant-ph↗

arXiv2021

AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states

From Feynman diagrams to tensor networks, diagrammatic representations of computations in quantum mechanics have catalysed progress in physics. These diagrams represent the underlying mathematical operations and aid physical interpretation, but cannot generally be computed with directly. In this paper we introduce the ZXH-calculus, a graphical language based on the ZX-calculus, that we use to represent and reason about many-body states entirely graphically. As a demonstration, we express the 1D AKLT state, a symmetry protected topological state, in the ZXH-calculus by developing a representation of spins higher than 1/2 within the calculus. By exploiting the simplifying power of the ZXH-calculus rules we show how this representation straightforwardly recovers the AKLT matrix-product state representation, the existence of topologically protected edge states, and the non-vanishing of a string order parameter. Extending beyond these known properties, our diagrammatic approach also allows us to analytically derive that the Berry phase of any finite-length 1D AKLT chain is $π$. In addition, we provide an alternative proof that the 2D AKLT state on a hexagonal lattice can be reduced to a graph state, demonstrating that it is a universal quantum computing resource. Lastly, we build 2D higher-order topological phases diagrammatically, which we use to illustrate a symmetry-breaking phase transition. Our results show that the ZXH-calculus is a powerful language for representing and computing with physical states entirely graphically, paving the way to develop more efficient many-body algorithms and giving a novel diagrammatic perspective on quantum phase transitions.

cond-mat.other↗

arXiv2021

Controller-based Energy-Aware Wireless Sensor Network Routing using Quantum Algorithms

Energy efficient routing in wireless sensor networks has attracted attention from researchers in both academia and industry, most recently motivated by the opportunity to use SDN (software defined network)-inspired approaches. These problems are NP-hard, with algorithms needing computation time which scales faster than polynomial in the problem size. Consequently, heuristic algorithms are used in practice, which are unable to guarantee optimally. In this short paper, we show proof-of-principle for the use of a quantum annealing processor instead of a classical processor, to find optimal or near-optimal solutions very quickly. Our preliminary results for small networks show that this approach using quantum computing has great promise and may open the door for other significant improvements in the efficacy of network algorithms.

cs.ET↗

arXiv2021

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↗

arXiv2021

Inclusive learning for quantum computing: supporting the aims of quantum literacy using the puzzle game Quantum Odyssey

With a vast domain of applications and now having quantum computing hardware available for commercial use, an education challenge arises in getting people of various background to become quantum literate. Quantum Odyssey is a new piece of computer software that promises to be a medium where people can learn quantum computing without any previous requirements. It aims to achieve this through visual cues and puzzle play, without requiring the user to possess a background in computer coding or even linear algebra, which are traditionally a must to work on quantum algorithms. In this paper we report our findings on an UKRI Citizen Science grant that involves using Quantum Odyssey to teach how to construct quantum computing algorithms. Sessions involved 30 minutes of play, with 10 groups of 5 students, ranging between 11 to 18 years old, in two schools in the UK. Results show the Quantum Odyssey visual methods are efficient in portraying counterintuitive quantum computational logic in a visual and interactive form. This enabled untrained participants to quickly grasp difficult concepts in an intuitive way and solve problems that are traditionally given today in Masters level courses in a mathematical form. The results also show an increased interest in quantum physics after play, a higher openness and curiosity to learn the mathematics behind computing on quantum systems. Participants developed a visual, rather than mathematical intuition, that enabled them to understand and correctly answer entry level technical quantum information science.

physics.ed-ph↗

arXiv2021

Performance of Domain-Wall Encoding for Quantum Annealing

In this paper we experimentally test the performance of the recently proposed domain-wall encoding of discrete variables from [Chancellor Quantum Sci. Technol. 4 045004] on Ising model flux qubit quantum annealers. We compare this encoding with the traditional one-hot methods and find that they outperform the one-hot encoding for three different problems at different sizes both of the problem and of the variables. From these results we conclude that the domain-wall encoding yields superior performance against a variety of metrics furthermore, we do not find a single metric by which one hot performs better. We even find that a 2000Q quantum annealer with a drastically less connected hardware graph but using the domain-wall encoding can outperform the next generation Advantage processor if that processor uses one-hot encoding.

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

Fluctuation guided search in quantum annealing

Quantum annealing has great promise in leveraging quantum mechanics to solve combinatorial optimisation problems. However, to realize this promise to it's fullest extent we must appropriately leverage the underlying physics. In this spirit, I examine how the well known tendency of quantum annealers to seek solutions where more quantum fluctuations are allowed can be used to trade off optimality of the solution to a synthetic problem for the ability to have a more flexible solution, where some variables can be changed at little or no cost. I demonstrate this tradeoff experimentally using the reverse annealing feature a D-Wave Systems QPU for both problems composed of all binary variables, and those containing some higher-than-binary discrete variables. I further demonstrate how local controls on the qubits can be used to control the levels of fluctuations and guide the search. I discuss places where leveraging this tradeoff could be practically important, namely in hybrid algorithms where some penalties cannot be directly implemented on the annealer and provide some proof-of-concept evidence of how these algorithms could work.

quant-ph↗

arXiv2020

Toward a standardized methodology for constructing quantum computing use cases

We propose a standardized methodology for developing and evaluating use cases for quantum computers and quantum inspired methods. This methodology consists of a standardized set of questions which should be asked to determine how and indeed if, near term quantum computing can play a role in a given application. Developing such a set of questions is important because it allows different use cases to be evaluated in a fair and objective way, rather than considering each case on an ad hoc basis which could lead to an evaluation which focuses on positives of a use case, while ignoring weaknesses. To demonstrate our methodology we apply it to a concrete use case, ambulance dispatch, and find that there are some ways in which near term quantum computing could be deployed sensibly, but also demonstrate some cases ways in which its use would not be advised. The purpose of this paper is to initiate a dialogue within the community of quantum computing scientists and potential end users on what questions should be asked when developing real world use cases.

cs.AI↗